Decomposing capacity utilization in data envelopment analysis: An application to banks in India

This paper briefly reviews the existing methods of capacity utilization in nonparametric framework from economic perspectives, and then suggests an alternative in the light of limitations therein. In the spirit of work by Coelli et al. [Coelli, T.J., Grifell-Tatje, E., Perelman, S., 2002. Capacity utilisation and profitability: A decomposition of short run profit efficiency. International Journal of Production Economics 79, 261–278], we propose two methods, radial and non-radial, to decompose the input-based physical (technological) capacity utilization into various meaningful components viz., technical inefficiency, ray economic capacity utilization and optimal capacity idleness. A case study of Indian banking industry is taken as an example to illustrate the potential application of these two methods of decomposition. Our two broad empirical findings are that first, competition created after financial sector reforms generates high efficiency growth, and reduces excess capacity; second, the cost gap of the short-run cost from the actual cost is higher for the nationalized banks over the private banks indicating that the former banks, though old, do not reflect their learning experience in their cost minimizing behavior.     

Comparative analysis of banking production frameworks in eastern european financial markets

This paper performs comparative analysis of the non-radial Russell output technical efficiency measures of 13 Eastern European banking systems assuming a banking production with risk as an undesirable output and where output components can be negative. This is analysed utilizing three modelling specifications; the intermediation, production and profit methodologies. Along with distribution and inter-distribution mobility analysis of the efficiency scores across alternative methodologies, we also estimate and statistically compare the distributions of estimated efficiency scores using the bootstrap-based Simar–Zelenyuk-adapted-Li test. The results suggest that although the efficiency levels differ across the approaches, change in positions of the banks relative to the mean is not substantial across the three methodologies.     

Bridging radial and non-radial measures of efficiency in DEA

Data envelopment analysis (DEA) has been utilized worldwide for measuring efficiencies of banks, telecommunications, electric utilities and so forth. Yet, the existing models have some well-known shortcomings that limit their usefulness. In DEA we have two fundamental approaches to measuring efficiency with very different characteristics; radial and non-radial. We demonstrate a method for linking these two approaches in a unified framework called Connected-SBM (slacks-based measure). It includes two scalar parameters, and by changing the parameter values we can relocate the analysis anywhere between the radial and the non-radial models. An appropriate choice of these parameters can overcome the key shortcomings inherent in the two approaches, namely, proportionality and mixed patterns of slacks.     

Product mixes as objects of choice in non-parametric efficiency measurement

Non-radial measures of technical efficiency essentially differ from their radial counterparts in that the product mix of the efficient reference is allowed to be different from the product mix of the evaluated observation. Whereas existing non-radial measures are still based on the product mix of the evaluated, i.e., possibly inefficient observation, we change the perspective and propose a measure based on the mix properties of the efficient reference. The resulting `inverse' measure can be considered as complementary to the Färe–Lovell (or “Russell”) efficiency measure.     

A circular global profit Malmquist productivity index in data envelopment analysis

To remove the difficulty caused by different profit frontiers in different periods of time for calculating profit efficiency changes and its components, this paper proposes a circular global profit Malmquist productivity index. This index is applicable when the input costs and output prices are known and when producers seek to maximize the total profit of their decision making units (DMUs). To this end, first, two methods are introduced to obtain the common costs and prices with or without the decision maker’s preferences, and then, a common profit efficient frontier is obtained. The proposed index can be decomposed into several circular components, viz., profit efficiency change, profit technical change, technical efficiency change, allocative efficiency change, technical change, and cost/price change. The proposed index is then generalised to compare the productivity of two different units at two different points in time. The global profit Malmquist productivity index developed here is unique and is computed using nonparametric linear programming model known as data envelopment analysis (DEA), and there is no need to resort to the geometric mean in the calculation. To illustrate the proposed index and its components, numerical examples at three successive periods of time are given.     

A non-radial DEA approach to measuring environmental performance

Data envelopment analysis (DEA) has gained great popularity in environmental performance measurement because it can provide a synthetic standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. Past studies about the application of DEA to environmental performance measurement often follow the concept of radial efficiency measures. In this paper, we present a non-radial DEA approach to measuring environmental performance, which consists of a non-radial DEA-based model for multilateral environmental performance comparisons and a non-radial Malmquist environmental performance index for modeling the change of environmental performance over time. A case study of OECD countries using the proposed non-radial DEA approach is also presented. It is found that the environmental performance of OECD countries as a whole has been improved from 1995 to 1997.     

Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

非期望产出的DEA效率评价

将非期望产出作为投入应用到传统DEA模型上,解决了非期望产出生产活动的效率评价问题.结合生产可能集,将非期望产出直接反映到生产可能集中,建立了基于投入导向的径向和非径向两种DEA模型.并对两种DEA模型效率值的大小关系、相对有效性的等价性问题进行了证明,指出非径向DEA模型更能准确的实现效率定量评价.     

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.     

Distribution of cost and profit efficiency: Evidence from Indian banking

This paper uses the nonparametric DEA methodology to estimate cost and profit efficiency of Indian banks during the post-reform period. The results show considerable variation in average levels of profit efficiency across various ownership categories of banks. In general, state owned banks are found to be more efficient than their private counter parts. Further, efficiency tends to be low among the small banks (assets up to Rs. 50 billion), indicating that at the existing scale of operations, these banks are operating far below the efficient frontier. We also examine the distribution of efficiency using nonparametric kernel density estimates. The analysis reveals a rightward-shift of the efficiency distribution over the years. A major part of this shift comes from the state owned banks. Based on the conditional distribution, the study finds strong evidence of ownership explaining the efficiency differential of banks. Additionally, bank size and product-mix are also found to be important, although to a lesser extent.     

考虑服务水平的商业银行综合效率评价研究

商业银行是我国银行体系的主体,提高银行的经营效率和服务水平是当前金融改革的重点。已有的研究较多关注于银行的收益,对银行的非期望产出如呆坏账及服务水平等关注较少。本文运用多个处理非期望产出的DEA模型,对2008年中国商业银行的效率进行了评价分析。文章在改进熵DEA方法的基础上,利用指标体系对商业银行的综合效率进行了测度并对比了处于多模型条件下模型的区分度问题。研究结果显示,呆坏账、服务水平(等待时间)等非期望产出对商业银行的效率意义重大;股份制商业银行的效率普遍高于国有商业银行,因此国有商业银行的股份制改造是一个积极的方向。最后,根据实证分析的结果提出的效率改进建议对商业银行的自身发展和管理当局的改革规划都具有重要的指导意义。     

Determinants of bank efficiency: The case of Brazil

This paper analyzes the efficiency of the Brazilian banking sector over the post-privatization period of 2000–2007. We employ a Bayesian stochastic frontier approach, which provides exact efficiency estimates and confidence intervals and thus, allows an accurate comparison across institutions and bank groups. The results suggest that large banks are the most cost and profit efficient, supporting the concentration process observed in recent years. Foreign banks have achieved a good performance through either the establishment of new affiliates and the acquisition of local banks. The remaining public banks have had improvements in cost efficiency, but are relatively profit inefficient. Finally, we observe a positive impact of capitalization on efficiency.     

Cost,revenue and profit efficiency measurement in DEA: A directional distance function approach

Estimation of efficiency of firms in a non-competitive market characterized by heterogeneous inputs and outputs along with their varying prices is questionable when factor-based technology sets are used in data envelopment analysis (DEA). In this scenario, a value-based technology becomes an appropriate reference technology against which efficiency can be assessed. In this contribution, the value-based models of Tone (2002) are extended in a directional DEA set up to develop new directional cost- and revenue-based measures of efficiency, which are then decomposed into their respective directional value-based technical and allocative efficiencies. These new directional value-based measures are more general, and include the existing value-based measures as special cases. These measures satisfy several desirable properties of an ideal efficiency measure. These new measures are advantageous over the existing ones in terms of (1) their ability to satisfy the most important property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3) flexibility in providing the decision makers with the option of specifying preferable direction vectors to incorporate their preferences. Finally, under the condition of no prior unit price information, a directional value-based measure of profit inefficiency is developed for firms whose underlying objectives are profit maximization. For an illustrative empirical application, our new measures are applied to a real-life data set of 50 US banks to draw inferences about the production correspondence of banking industry.     

Foreign versus domestic banks’ performance in the UK: a multicriteria approach

Although the banking sector in the UK is one of the most open and it is characterized by an increasing foreign bank presence, it remains relatively under-researched compared to studies for other countries. The objective of this paper is to investigate the performance of the UK banking sector focusing on the performance of the domestic banks as opposed to the performance of the foreign banks in order to test the hypothesis of higher performance of the domestic banks in a developed market. For this purpose, the UTADIS multicriteria methodology is employed to compare domestic and foreign banks performance over multiple criteria, such as profitability, liquidity, risk and efficiency, using a data sample covering 26 domestic and 32 foreign banks operating in the UK over the period 1998 to 2001. The results of the study, support the home advantage hypothesis, suggesting that the higher performance of domestic banks compared to foreign banks is also the case in the UK. The most important distinguishing performance factors between the two groups of banks are interest revenue to total earning assets, and profit before taxes to loans plus securities, which are higher for the domestic banks.AMS classification: 91B28     

Bank productivity and performance groups: A decomposition approach based upon the Luenberger productivity indicator

The purpose of this paper is twofold. First, in the framework of the strategic groups’ literature, it analyZes changes in productivity and efficiency of Spanish private and savings banks over an eight-year period (1998-2006). Second, by adapting the decomposition of the Malmquist productivity indices suggested by Färe et al. (1994), it proposes similar components decomposing the Luenberger productivity indicator. Initially, productivity is decomposed into technological and efficiency changes. Thereafter, this efficiency change is decomposed into pure efficiency, scale and congestion changes. Empirical results demonstrate that productivity improvements are partially due to technological innovation. Furthermore, it is shown how the competition between private and savings banks develops in terms of the analyzed productivity and efficiency components. While private banks enjoy better efficiency change, savings banks contribute more to technological progress. Consequently, the Luenberger components are used as cluster analysis inputs. Thus, economic interpretations of the resulting performance groups are made via key differences in productivity components. Finally, following the strategic groups’ literature, supplementary insights are gained by linking these performance groups with banking ratios.     

An epsilon-based measure of efficiency in DEA – A third pole of technical efficiency

In DEA, we have two measures of technical efficiency with different characteristics: radial and non-radial. In this paper we compile them into a composite model called “epsilon-based measure (EBM).” For this purpose we introduce two parameters which connect radial and non-radial models. These two parameters are obtained from the newly defined affinity index between inputs or outputs along with principal component analysis on the affinity matrix. Thus, EBM takes into account diversity of input/output data and their relative importance for measuring technical efficiency.     

The sources of productivity change in Spanish banking

In this paper we examine the pattern of productivity change in Spanish banking over the period 1986–1993. Two sectors dominate Spanish banking, commercial banks and the faster-growing savings banks. We begin by examining productivity change separately within each sector. However since the two sectors are gradually becoming more competitive, we continue by merging the two sectors, and by examining productivity change in the industry. The merging procedure follows a methodology originally proposed by Charnes, Cooper and Rhodes (1981), in which intra-sectoral managerial inefficiency is eliminated prior to merging. This procedure allows us to distinguish differences in managerial efficiency within each sector from differences in the institutional efficiency of the two sectors. It also enables us to decompose potential productivity change into institutional efficiency change, technical change, and the impact of scale economies. We find the commercial banks to have had a slightly lower rate of productivity growth, but a slightly higher rate of potential productivity growth. We attribute this phenomenon to differences in both managerial efficiency and institutional efficiency, to differences in the rate of technical progress, and to the adverse impact of diseconomies of scale in the commercial banking sector.     

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.     

基于区间数DEA的贷款定价模型研究

在贷款的买方市场或充分竞争的金融环境中,贷款利率不会由银行自己说了算,因此建立银企双方共同接受的贷款利率定价模型在现实中尤为重要。本文采用区间数的形式反映存款利息支出率、违约风险补偿率等定价指标的不确定性,以已结清贷款最小定价效率、最大定价效率组成的贷款定价效率区间为目标,以新贷款的贷款利率为决策变量,通过逆向求解区间数DEA模型反推出新贷款的贷款利率区间,建立了基于区间数DEA的贷款定价模型。本文的创新与特色一是以已结清贷款的存款利息支出率、目标利润率等指标为输入,以已结清贷款的贷款利率为输出,利用DEA模型求得已结清贷款的实际最小效率及最大效率。二是以银企双方均可接受的贷款定价效率区间为目标、以新贷款的存款利息支出率等用区间数形式表示的贷款成本为投入,反推出贷款利率的取值区间。三是通过区间数形式来反映违约风险补偿率、目标利润率等定价指标的不确定性,改变了现有研究将目标利润、贷款费用、违约损失等变量看作常数来定价的不合理现状。研究表明:存款利息支出率、费用支出率、违约风险补偿率及目标利润率均与贷款利率成正比。企业提高在贷款银行中的资金结算比率、存贷比率可以降低贷款利率。     

A multi-objective approach to determine alternative targets in data envelopment analysis

The choice for radial projections of classic data envelopment analysis (DEA) models, resulting in a number of projections onto the Pareto-inefficient portion of the frontier, has been seen lately as a disadvantage in DEA. The search for a non-radial projection method resulted in developments such as preference structure models. These models consider a priori preference incorporation, using weights in the search for the most preferred efficient target, although presenting some implementation difficulties. In this paper, we propose a multi-objective approach that determines the bases for a posteriori preference incorporation, through individual projections of each variable (input or output) as an objective function, thus allowing one to obtain a target at every extreme-efficient point on the frontier. This multi-objective approach is shown to be equivalent to the preference structure models, yet presenting some advantages, such as the mapping of the possible weights, assigned to partial efficiencies of an observed unit, in order to reach a specific target.