Effects of heterogeneity on bank efficiency scores

Bank efficiency estimates often serve as a proxy of managerial skill since they quantify sub-optimal production choices. But such deviations can also be due to omitted systematic differences among banks. In this study, we examine the effects of heterogeneity on bank efficiency scores. We compare different specifications of a stochastic cost and alternative profit frontier model with a baseline specification. After conducting a specification test, we discuss heterogeneity effects on efficiency levels, ranks and the tails of the efficiency distribution. We find that heterogeneity controls influence both banks’ optimal costs and profits and their ability to be efficient. Differences in efficiency scores are important for more than only methodological reasons. First, different ways of accounting for heterogeneity result in estimates of foregone profits and additional costs that are significantly different from what we infer from our general specification. Second, banks are significantly re-ranked when their efficiency is estimated with a specification other than the preferred, general specification. Third, the general specification gives the most reliable estimates of the probability of distress, although differences to the other specifications are low.     

Comparing frontier methods for economic–environmental trade-off analysis

This paper uses a mechanistic frontier approach as a reference to evaluate the ability of conventional parametric (SFA) and non-parametric (DEA) frontier approaches for analyzing economic–environmental trade-offs. Conventional frontier approaches are environmentally adjusted through incorporating the materials balance principle. The analysis is worked out for the Flemish pig finishing case, which is both representative and didactic. Results show that, on average, SFA and DEA yield adequate economic–environmental trade-offs. Both methods are good estimators for technical efficiency. Cost allocative and environmental allocative efficiency scores are less robust, due to the well-known methodological advantages and disadvantages of SFA and DEA. For particular firms, SFA, DEA and the mechanistic approach may yield different economic–environmental trade-offs. One has therefore to be careful when using conventional frontier approaches for firm-specific decision support. The mechanistic approach allows for optimizing performances per average present finisher, which is the production unit in pig finishing. Conventional frontier methods do not allow for this optimization since the number of average present finishers varies along the production functions. Since the mechanistic production function is based on underlying growth, feed uptake and mortality functions, additional firm-specific indicators can also be calculated at each point of the production function.     

Regional concentration and efficiency in Mexican manufacturing

This paper explores the link between industrial location, concentration, and economic efficiency in Mexican manufacturing. Using a linear programming approach, the authors calculate indices of overall, technical, allocative, and scale efficiency for Mexican manufacturing industries by state to test whether, in 1985, those regions with high levels of industrial concentration were suffering from the costs of congestion. The evidence suggests that, at least at the aggregate level, there continued to be a positive relationship between industry concentration and efficiency in production. There is also evidence that overall efficiency was related to scale efficiency, although highly industrialized regions on the production frontier often operated at inefficient scales. In particular, the most concentrated regions (the Federal District, the state of Mexico, Jalisco, and Nuevo León) consistently display decreasing returns to scale, indicating that the process of industrial concentration may be leading to diseconomies of scale. Finally, an econometric analysis suggests that scale, urbanization, and agglomeration economies are positively related to overall and technical efficiency at the regional level, while foreign ownership is negatively related. Agglomeration economies at the industry level were not significant. The paper also makes a methodological contribution. It is the first application of a distance-function production methodology to measuring regional efficiency in a developing country. It demonstrates how to conduct distance-function efficiency analysis using the newly developed GAMS mathematical programming environment. These tools should be of considerable interest to applied microeconomists.     

Quantile regression for robust bank efficiency score estimation

We discuss quantile regression techniques as a robust and easy to implement alternative for estimating Farell technical efficiency scores. The quantile regression approach estimates the production process for benchmark banks located at top conditional quantiles. Monte Carlo simulations reveal that even when generating data according to the assumptions of the stochastic frontier model (SFA), efficiency estimates obtained from quantile regressions resemble SFA-efficiency estimates. We apply the SFA and the quantile regression approach to German bank data for three banking groups, commercial banks, savings banks and cooperative banks to estimate efficiency scores based on a simple value added function and a multiple-input–multiple-output cost function. The results reveal that the efficient (benchmark) banks have production and cost elasticities which differ considerably from elasticities obtained from conditional mean functions and stochastic frontier functions.     

A comparison of chance-constrained DEA and stochastic frontier analysis: bank efficiency in Taiwan

We employed both chance-constrained data envelopment analysis (CCDEA) and stochastic frontier analysis (SFA) to measure the technical efficiency of 39 banks in Taiwan. Estimated results show that there are significant differences in efficiency scores between chance-constrained DEA and stochastic frontier production function. The advanced setting of the chance-constrained mechanism of DEA does not change the instinctive differences between DEA and SFA approaches. We further find that the ownership variable is still a significant variable to explain the technical efficiency in Taiwan, irrespective of whether a DEA, CCDEA or SFA approach is used.     

Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm

In this article, we study the bi-level linear programming problem with multiple objective functions on the upper level (with particular focus on the bi-objective case) and a single objective function on the lower level. We have restricted our attention to this type of problem because the consideration of several objectives at the lower level raises additional issues for the bi-level decision process resulting from the difficulty of anticipating a decision from the lower level decision maker. We examine some properties of the problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0–1 linear programming problem. The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming. This approach further enables characterization of the whole Pareto frontier in the bi-objective case. Two illustrative numerical examples are included to show the viability of the proposed methodology.     

Sensitivity and stability analysis on the first and second levels of efficiency score relative to data error

In data envelopment analysis (DEA), efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for a category DMUs and finds the stability radius for all efficient DMUs. By means of combining some classic DEA models and with the condition that the efficiency scores of efficient DMUs remain unchanged, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalizes the conventional sensitivity analysis approach in which the inputs of efficient DMUs increase and their outputs decrease, while the inputs of inefficient DMUs decrease and their outputs increase. We find the maximum quantity of perturbations of data so that all first level efficient DMUs remain at the same level.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

A modified super-efficiency DEA model for infeasibility

The super-efficiency data envelopment analysis (DEA) model is obtained when a decision making unit (DMU) under evaluation is excluded from the reference set. This model provides for a measure of stability of the “efficient” status for frontier DMUs. Under the assumption of variable returns to scale (VRS), the super efficiency model can be infeasible for some efficient DMUs, specifically those at the extremities of the frontier. The current study develops an approach to overcome infeasibility issues. It is shown that when the model is feasible, our approach yields super-efficiency scores that are equivalent to those arising from the original model. For efficient DMUs that are infeasible under the super-efficiency model, our approach yields optimal solutions and scores that characterize the extent of super-efficiency in both inputs and outputs. The newly developed approach is illustrated with two real world data sets.     

An efficiency measurement framework for multi-stage production systems

We develop an efficiency measurement framework for systems composed of two subsystems arranged in series that simultaneously computes the efficiency of the aggregate system and each subsystem. Our approach expands the technology sets of each subsystem by allowing each to acquire resources from the other in exchange for delivery of the appropriate (intermediate or final) product, and to form composites from both subsystems. Managers of each subsystem will not agree to ‘`vertical integration’' initiatives unless each subsystem will be more efficient than what each can achieve by separately applying conventional efficiency analysis. A Pareto Efficient frontier characterizes the acceptable set of efficiencies of each subsystem from which the managers will negotiate to select the final outcome. Three proposals for the choice for the Pareto efficient point are discussed: the one that achieves the largest equiproportionate reduction in the classical efficiencies; the one that achieves the largest equal reduction in efficiency; and the one that maximizes the radial contraction in the aggregate consumption of resources originally employed before integration. We show how each choice for the Pareto efficient point determines a derived measure of aggregate efficiency. An extensive numerical example is used to illustrate exactly how the 2 subsystems can significantly improve their operational efficiencies via integration beyond what would be predicted by conventional analysis.     

The efficiency of health and education expenditures in the Philippines

This paper attempts to measure the efficiency of provinces in the Philippines in utilizing public resources for health and education where only 1% of the total budget is spent for health and 3% is allocated for education. With such budget constraints, it is important to examine the efficiency of spending on social services as small changes can have a major impact in achieving the Millennium Development Goals. Efficiency is defined as the deviation from the frontier which represents the maximum output attainable from each input level. This efficiency frontier is estimated using the data envelopment analysis, free disposal hull and Malmquist-DEA. We use expenditures for social services for input and primary and secondary enrollment rates, literacy rate per province, and life expectancy for outputs. An analysis of efficiency scores shows that provinces where the level of inequality is higher (as measured by the Gini coefficient) as well as those who receive a larger portion of their budget as grants are among the least efficient. This research can help in the budget allocation and rationalization among Philippine provinces.     

Computing nonperforming loan prices in banking efficiency analysis

Within the framework of banking efficiency analysis, we propose a methodology for computing unobservable shadow prices for nonperforming loans (NPL). Our approach is to include NPL as an undesirable output variable in a distance function stochastic frontier analysis. We conduct a panel study of US and European banks during the most recent financial crisis by adopting a semi-nonparametric Fourier specification, which ensures convergence to the true values of both the estimated function and the related efficiency. Computing NPL prices has several advantages, such as identifying approaching crises, quantifying the responsibilities of governments and banks for credit risk and determining appropriate regulatory interventions.

     

Explaining inefficiency in nonparametric production models: the state of the art

The performance of economic producers is often affected by external or environmental factors that, unlike the inputs and the outputs, are not under the control of the Decision Making Units (DMUs). These factors can be included in the model as exogenous variables and can help to explain the efficiency differentials, as well as improve the managerial policy of the evaluated units. A fully nonparametric methodology, which includes external variables in the frontier model and defines conditional DEA and FDH efficiency scores, is now available for investigating the impact of external-environmental factors on the performance. In this paper, we offer a state-of-the-art review of the literature, which has been proposed to include environmental variables in nonparametric and robust (to outliers) frontier models and to analyse and interpret the conditional efficiency scores, capturing their impact on the attainable set and/or on the distribution of the inefficiency scores. This paper develops and complements the approach of B?din et al. (2012) by suggesting a procedure that allows us to make local inference and provide confidence intervals for the impact of the external factors on the process. We advocate for the nonparametric conditional methodology, which avoids the restrictive “separability” assumption required by the two-stage approaches in order to provide meaningful results. An illustration with real data on mutual funds shows the usefulness of the proposed approach.     

Improving PRETREE's predictive capabilities

Compared to compensatory type choice models (e.g., logit), hierarchical choice models have been used much less frequently in the real world. This has happened even though there is a lot of evidence to suggest that the hierarchical structure is closer to the actual process by which individuals make choices. In this paper, we have considered one of the original hierarchical models (PRETREE). The PRETREE model has been heavily cited in the marketing and psychometric literatures. We wish to examine PRETREE at the aggregate level making n-way (market share) predictions.A primary strength of the PRETREE model was its apparent ability to capture violations of the property of the “independence of irrelevant alternatives” (IIA). We prove that there are limitations to this argument. We suggest a method to overcome these limitations; this change resulted in substantial improvement in the predictive abilities of the model, when the modified PRETREE is applied to real world data. The predictions are at an aggregate level on a hold-out sample.The above modification to PRETREE will hopefully not only renew but also increase interest in applying a hierarchical approach to modeling real-world problems on choice.     

Deriving the DEA frontier for two-stage processes

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model provides not only an overall efficiency score for the entire process, but as well yields an efficiency score for each of the individual stages. Due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores, as in the standard DEA approach, does not necessarily yield a frontier projection. The current paper develops an approach for determining the frontier points for inefficient DMUs within the framework of two-stage DEA.     

A multiplier bound approach to assess relative efficiency in DEA without slacks

In this paper, we propose a new approach to deal with the non-zero slacks in data envelopment analysis (DEA) assessments that is based on restricting the multipliers in the dual multiplier formulation of the used DEA model. It guarantees strictly positive weights, which ensures reference points on the Pareto-efficient frontier, and consequently, zero slacks. We follow a two-step procedure which, after specifying some weight bounds, results in an “Assurance Region”-type model that will be used in the assessment of the efficiency. The specification of these bounds is based on a selection criterion among the optimal solutions for the multipliers of the unbounded DEA models that tries to avoid the extreme dissimilarity between the weights that is often found in DEA applications. The models developed do not have infeasibility problems and we do not have problems with the alternate optima in the choice of weights that is made. To use our multiplier bound approach we do not need a priori information about substitutions between inputs and outputs, and it is not required the existence of full dimensional efficient facets on the frontier either, as is the case of other existing approaches that address this problem.     

Super-efficiency DEA in the presence of infeasibility

It is well known that super-efficiency data envelopment analysis (DEA) approach can be infeasible under the condition of variable returns to scale (VRS). By extending of the work of Chen (2005), the current study develops a two-stage process for calculating super-efficiency scores regardless whether the standard VRS super-efficiency mode is feasible or not. The proposed approach examines whether the standard VRS super-efficiency DEA model is infeasible. When the model is feasible, our approach yields super-efficiency scores that are identical to those arising from the original model. For efficient DMUs that are infeasible under the super-efficiency model, our approach yields super-efficiency scores that characterize input savings and/or output surpluses. The current study also shows that infeasibility may imply that an efficient DMU does not exhibit super-efficiency in inputs or outputs. When infeasibility occurs, it can be necessary that (i) both inputs and outputs be decreased to reach the frontier formed by the remaining DMUs under the input-orientation and (ii) both inputs and outputs be increased to reach the frontier formed by the remaining DMUs under the output-orientation. The newly developed approach is illustrated with numerical examples.     

Comparing efficiency across markets: An extension and critique of the methodology

The use of non-parametric frontier methods for the evaluation of product market efficiency in heterogeneous markets seems to have gained some popularity recently. However, the statistical properties of these frontier estimators have been largely ignored. The main point is that non-parametric frontier estimators are biased and that the degree of bias depends on specific sample properties, most importantly sample size and number of dimensions of the model. To investigate the effect of this bias on comparing market efficiency, this contribution estimates the efficiency for several datasets for two main product categories. Following (Zhang, Y., Bartels, R., 1998. The effect of sample size on the mean efficiency in DEA with an application to electricity distribution in Australia, Sweden and New Zealand. Journal of Productivity Analysis, 9(3), 187-204.), these results comprise re-estimates for the larger samples limiting their size to that of the smaller samples when the model dimensions for different samples are identical. Furthermore, sample sizes are adjusted to mitigate the eventual differences in dimensions in specification. This allows comparing market efficiency for different markets on a more equal footing, since it reduces the bias effect to a minimum making the comparison of market efficiency possible. However, the article also points out the critical limitations of this [Zhang, Y., Bartels, R., (1998). The effect of sample size on the mean efficiency in DEA with an application to electricity distribution in Australia, Sweden and New Zealand. Journal of Productivity Analysis 9 (3), 187–204] approach in certain respects. Apart from reporting these negative results, we also offer some suggestions for future work.     

A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations

This paper analyses the mechanisms through which binding finance constraints can induce debt-constrained firms to improve technical efficiency to guarantee positive profits. This hypothesis is tested on a sample of firms belonging to the Italian manufacturing. Technical efficiency scores are computed by estimating parametric production frontiers using the one stage approach as in Battese and Coelli [Battese, G., Coelli, T., 1995. A model for technical efficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20, 325–332]. The results support the hypothesis that a restriction in the availability of financial resources can affect positively efficiency.     

Collective adjustment of pension rights in ALM models

Collective adjustment of pension rights is a way to keep defined benefit systems tenable. In asset liability management (ALM) models presented in the literature these decisions are modeled both at the aggregate level of the liabilities as a whole and at a more detailed level. In this paper we compare the approximate aggregate approach to the accurate detailed approach for the average earnings scheme with conditional indexation. We prove that the aggregate approach leads to one-sided errors. Moreover, we show that for semi-realistic data these biases are considerable.