Sensitivity analysis of efficiency and Malmquist productivity indices: An application to Spanish savings banks

Hypothesis testing and statistical precision in the context of non-parametric efficiency and productivity measurement have been investigated since the early 1990s. Recent contributions focus on this matter through the use of resampling methods—i.e., bootstrapping techniques. However, empirical evidence is still practically non-existent. This gap is more noticeable in the case of banking efficiency studies, where the literature is immense. In this work, we explore productivity growth and productive efficiency for Spanish savings banks over the (initial) post-deregulation period 1992–1998 using Data Envelopment Analysis (DEA) and bootstrapping techniques. Results show that productivity growth has occurred, mainly due to improvement in production possibilities, and that mean efficiency has remained fairly constant over time. The bootstrap analysis yields further evidence, as for many firms productivity growth, or decline, is not statistically significant. With regard to efficiency measurement, the bootstrap reveals that the disparities in the original efficiency scores of some firms are lessened to a great extent.     

Linear programming approaches to the measurement and analysis of productive efficiency

Invited by J. T. Pastor     

Strategic groups based on marginal rates: An application to the Spanish banking industry

This paper uses Data Envelopment Analysis (DEA) to identify strategic groups (SGs) in the Spanish banking industry. The concept of SG relies on the fact that firms grouped together value inputs and outputs in the same way. As such, they take identical direction when, due to external influences, changes are required. Weights obtained from DEA are extremely useful in the valuation of inputs and outputs. Specifically, by comparing DEA weights pair-wise, i.e. quantifying the variables’ marginal rates (MR), we can obtain a very good representation of the existent trade-off and the relative importance of the two variables.The paper uses MRs obtained through DEA models and, simultaneously, proposes feasible ways to overcome two usual problems with DEA virtual weights, namely: (1) the multiplicity of weights for efficient DMUs; and (2) the inexistence of dual variables for inefficient DMUs.From the empirical point of view, once the MRs are determined, the second stage is to perform Cluster Analysis. We apply Cluster Analysis in two ways: (1) on the basis of the MRs; and (2) following the traditional application by running Cluster Analysis with the original variables. The results obtained show the advantages of using MRs instead of the standard application of Cluster Analysis.Summing up, the concept of SG is reinforced if we use refined methods to determine the existence of SGs. The results of the application of DEA models to observe the presence of SG in the Spanish banking industry offer interesting views on it.     

An application of multiobjective programming to the study of workers’ satisfaction in the Spanish labour market

In this paper, a multiobjective scheme is used to study the satisfaction levels of Spanish workers. Data obtained from the European Community Household Panel (ECHP) are used to build a multiobjective model on the basis of a previous statistical and econometric analysis of these data. Then, a Reference Point-based method is implemented to determine the profile of the most satisfied worker in Spain nowadays. Finally, a combined Goal Programming – Reference Point approach is used to determine policies which can be carried out in order to increase workers’ satisfaction levels.     

Bayesian analysis of herding behaviour: an application to Spanish equity mutual funds

This paper proposes a dynamic Bayesian rolling window estimation procedure applied to the three‐factor model of Fama and French to analyse herding behaviour in the style exposures of mutual funds. This procedure allows a user to dynamically select the length of the estimation window by means of weighted likelihood functions that discount the loss of information because of time. This method is very flexible and allows us to consider different approaches of detecting herding behaviour by taking into account the uncertainty associated in the estimation of the style coefficients. In particular, the paper first determines the convergence behaviour following the traditional LSV herding measure and then refines this method by removing the influence exerted by market conditions, such as market volatility and returns, on this convergence. This process is empirically illustrated by an application to Spanish equity mutual funds. Copyright © 2014 John Wiley & Sons, Ltd.     

Measuring teaching efficiency in higher education: An application of data envelopment analysis to economics graduates from UK Universities 1993

Data envelopment analysis (DEA) is applied to 2547 Economics graduates from UK Universities in 1993 in order to assess teaching efficiency. Following a methodology developed by [Education Economics 10(2) (2002) 183–207], each individual’s efficiency is decomposed into two components: one attributable to the university at which the student studied, and the other attributable to the student himself. From the former component, a measure of each institution’s teaching efficiency is derived and compared to efficiency scores derived from a conventional DEA applied using each Economics department as a decision making unit (DMU). The results suggest that efficiencies derived from DEAs performed at an aggregate level include both institution and individual components, and are therefore misleading. Thus the unit of analysis in a DEA is highly important. Moreover, an analysis at the individual level can give institutions insight into whether it is the students’ own efforts or the institution’s efficiency which are a constraint on increased efficiency. This has implications for the choice of strategy for improving efficiency.     

New estimating equation approaches with application in lifetime data analysis

Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with censored data. However, MLE may produce substantial bias and even fail to obtain valid confidence intervals when data size is not large enough or there is censoring data. In this paper, based on nonlinear combinations of order statistics, we propose new estimation equation approaches for a class of probability distributions, which are particularly effective for skewed distributions with small sample sizes and censored data. The proposed approaches may possess a number of attractive properties such as consistency, sufficiency and uniqueness. Asymptotic normality of these new estimators is derived. The construction of new estimation equations and their numerical performance under different censored schemes are detailed via Weibull distribution and generalized exponential distribution.     

因子分析在居民消费结构的变动分析中的应用

以往在研究居民消费结构方面,使用较多的方法是恩格尔系数和线性支出系统,但在进行消费结构变动分析时,由于指标多,且指标体系中各指标之间存在着此消彼涨、此低彼高的现象。笔者认为因子分析模型正是解决这一问题的有力工具,并利用它对浙江城镇居民消费结构变动进行了实证分析。     

时间效益分析法在教学质量评价中的应用

文章在回顾教学质量评价方法的基础上 ,介绍了时间效益分析方法的基本原理并应用此方法 ,利用同一地区两所学校 95年中考成绩和 98年高考成绩对两所学校的教学质量进行了分析比较。文章最后还采用齐次马尔可夫链分析法和协方差分析方法对这两所学校的教学质量进行了评价 ,三种方法得出了相同的结论 ,从而验证了时间效益分析方法的可行性     

An interactive approach to improve estimates of value efficiency in data envelopment analysis

Management Science 45 (1) (1999) 103–115 presents an approach for incorporating preference information in data envelopment analysis (DEA). In their paper, they develop value efficiency, an extension of the concept of efficiency in DEA. The paper presented an approach to estimate lower bounds for the value efficiency scores––efficiency measures that reflect the decision-maker’s (DM’s) preferences. In this paper, we develop some related concepts, and present two refinements: (1) Some bounds on the value efficiency scores that may be obtained without any DM involvement; and (2) A way of precisely measuring value efficiency scores with minimal DM involvement. The approach can also be used to explore whether certain underlying assumptions are met.     

An MCDM approach to production analysis: An application to irrigated farms in Southern Spain

The analysis of the decision-making process in agricultural enterprises is approached with the development of a methodology based upon two stages: firstly we enlarge our knowledge of the system under study by performing grouping operation - cluster analysis - of the farm enterprises. The result of this stage is to classify farms according to crop pattern, which is the basis for the second stage of analysis: the system is studied by solving a weighted goal programming to approach the weights given by different farmers to the objectives of the decision process. This methodology is applied to two nearby but different irrigation units in Southern Spain, and we found that there was an important degree of heterogeneity in production plans explained by differences in objective weights.     

Bayesian detection of clusters in efficiency score maps: An application to Brazilian energy regulation

An original application of an approach first used in epidemiology investigation was developed and implemented in energy regulation benchmarking. Using Brazilian electricity energy distribution utilities, the proposed methodology applies spatial Bayesian analysis to estimate the number of clusters and the utilities in each cluster. By dividing the utilities into smaller, but geographically closer groups, it can be argued that local determinants of production or environmental components are accounted in the benchmarking model. Thus, the proposed method requires the spatial location of the utilities and their cost efficiencies, estimated previously by the regulator. Results show two detected clusters with high and low efficiencies located in the east and west of Brazil. After applying the regulator model to the detected groups, significant changes in cost efficiencies were estimated for a few utilities. This is important information that can be used by the regulator to estimate future cost incentives.     

A new multicriteria approach for the analysis of efficiency in the Spanish olive oil sector by modelling decision maker preferences

The efficiency in production is often analysed as technical efficiency using the production frontier function. Efficiency scores are usually based on distance computations to the frontier in an m + s-dimensional space, where m inputs produce s outputs. In addition, efficiency improvements consider the total consumption of each input. However, in many cases, the “consumption” of each input can be divided into input-consumption sections (ICSs), and trade-off among the ICSs is possible. This share framework can be used for computing efficiency. This analysis provides information about both the total optimal consumption of each input, as does data envelopment analysis, and the most efficient allocation of the “consumption” among the ICSs. This paper studies technical efficiency using this approach and applies it to the olive oil sector in Andalusia (Spain). A non-parametrical methodology is presented, and an input-oriented Multi-Criteria Linear Programming model (MLP) is proposed. The analysis is developed at global, input and ICSs levels, defining the extent of satisfaction achieved at all these levels for each company, in accordance with their own preferences. The companies’ preferences are modelled with their utility function and their set of weights. MLP offers more detailed information to assist decision makers than other models previously proposed in the literature. In addition to this application, it is concluded that there is room for improvement in the olive oil sector, particularly in the management of the skilled labour. Additionally, the solutions with two opposite scenarios indicate that the model is suitable for the intended decision making process.     

Alternate approaches to solving the Holt et al. model and to performing sensitivity analysis

The staircase structure of the recurrence relations for the Holt et al. model can be used to develop simple and efficient computational approaches for obtaining the optimal solution. The computational approaches are noniterative. We deal with finite planning horizon cases in which one or more terminal boundary conditions are not specified. The computation time varies linearly with the number of periods in the planning horizon. A framework is also developed for sensitivity analysis on the terminal values and for generation of alternate production plans. The alternate plans provide considerable flexibility to the decision maker because they can be evaluated in the context of (a) constraints not included in the model, (b) plant capacity, (c) actual costs, and (d) implications beyond the planning horizon. The results should be of interest for real world applications as well as for research because the Holt et al. model continues to be used as a benchmark to evaluate the performance of other aggregate production planning models.     

An application of vertex packing to data analysis in the evaluation of pavement deterioration

The analysis of data concerning the deterioration of pavement over time yielded a problem of aggregating the data in a manner that preserved independence of the aggregated data points and maximized the number of points. We show that this problem can be modeled as a maximum cardinality vertex packing problem on a proper internal graph and thus can be solved very efficiently by a greedy algorithm.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

An application of sensitivity analysis to a linear programming problem

Summary In an ordinary linear programming problem with a given set of statistical data, it is not known generally how reliable is the optimal basic solution. Our object here is to indicate a general method of reliability analysis for testing the sensitivity of the optimal basic solution and other basic solutions, in terms of expectation and variance when sample observations are available. For empirical illustration the time series data on input-output coefficients of a single farm producing three crops with three resources is used. The distributions of the first, second, and third best solutions are estimated assuming the vectors of net prices and resources to be constant and the coefficient matrix to be stochastic. Our method of statistical estimation is a combination of the Pearsonian method of moments and the maximum likelihood method.In our illustrative example we observe that the skewness of the distribution of the first best solution exceeds that of the distributions of the second and third best solution. We have also analyzed the time paths for the three ordered solutions to see how far one could apply the idea of a regression model based on inequality constraints. A sensitivity index for a particular sample is suggested based on the spread of the maximum and minimum values of the solutions.

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Zusammenfassung Im allgemeinen ist bei Linear-Programming-Problemen mit statistischen Einflüssen die Zuverlässigkeit der optimalen Basislösung nicht bekannt. Unser Ziel ist es, eine allgemeine Methode anzugeben, um die Empfindlichkeit der optimalen Basislösung und anderer Basislösungen durch den Erwartungswert und die Varianz bei gegebener Stichprobe zu testen. Zur Illustration wird eine Zeitreihe der input-output-Koeffizienten einer einzigen Farm benutzt, die drei Getreidesorten erzeugt, wobei drei Ressourcen benützt werden. Es werden die Verteilungen der ersten drei besten Lösungen geschätzt bei vorausgesetzten konstanten Nettopreisen und Ressourcen und stochastischer Koeffizientenmatrix. Die verwendete Methode der statistischen Schätzung ist eine Kombination der Pearsonschen Momentenmethode und der Maximum-Likelihood-Methode.In unserem Beispiel stellen wir fest, daß die Schiefe der Verteilung der besten Lösung größer ist als die der Verteilung der zweit- und drittbesten Lösungen. Ferner wurden die Zeitläufe der ersten drei geordneten Lösungen analysiert, um festzustellen, wie weit sich die Idee eines Regressionsmodells, das auf Ungleichungsrestriktionen basiert, anwenden läßt. Für eine Stichprobe wird ein Empfindlichkeitsindex empfohlen, der sich aus der Spannweite der maximalen und minimalen Werte der Lösungen ableitet.

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Research partly supported by the NSF project No. 420-04-70 at the Department of Economics, Iowa State University, Ames.The results of this paper are closely related in some theoretical aspects to the following papers. Sengupta, J. K., G. Tintner andC. Millham. On some theorems of stochastic linear programming with applications, Management Science, vol. 10, October 1963, pp. 143–159. Sengupta, J. K., G. Tintner andB. Morrison. Stochastic linear programming with applications to economic models, Economica, August 1963, pp. 262–276. Sengupta, J. K.: On the stability of truncated solutions of stochastic linear programming (to be published in Econometrica, October, 1965).     

An application of the Hurwitz theorem to the root analysis of the characteristic equation

In this work we show that a classical result of A. Hurwitz is still very effective in studying the root analysis of the characteristic equation for a linear functional differential equation. A conjecture was made by Funakubo et al. (2006) [3] regarding the asymptotic stability condition of the zero solution of a linear integro-differential equation of Volterra type. We applied the Hurwitz theorem to the characteristic equation in question and showed the existence of a root with positive real part and solved the conjecture. The Hurwitz theorem is expected to work well for the root analysis in critical cases.