Metafrontier efficiency analysis with convex and non-convex metatechnologies by stochastic nonparametric envelopment of data

This paper suggests how stochastic nonparametric envelopment of data (StoNED) can be extended as an estimator in the metafrontier efficiency analysis. Both convex and non-convex metatechnologies are formed and a semi-nonparametric estimation technique for the corresponding metafrontiers is developed. Remaining consistent with the metafrontier theory, the resulting estimated metafrontiers always envelope the estimated group frontiers

Consistent proportional trade-offs in data envelopment analysis

Proportional trade-offs – as an enhanced form of the conventional absolute trade-offs – have recently been proposed as a method which can be used to incorporate prior views or information regarding the assessment of decision making units (DMUs) into relative efficiency measurement systems by Data Envelopment Analysis (DEA). A proportional trade-off is defined as a percentage change of the level of inputs/outputs so that the corresponding restriction is adapted with respect to the volume of the inputs and outputs of the DMUs in the analysis. It is well-known that the incorporation of trade-offs either in an absolute form or proportional form may lead in certain cases to serious problems such as infinity or even negative efficiency scores in the results. This phenomenon is often interpreted as a result of defining the set of trade-offs carelessly by the analyst. In this paper we show that this may not always be the case. The existing framework by which the trade-offs are combined mathematically to build a corresponding production technology may cause a problem rather than the definition of the trade-offs. We therefore develop analytical criteria and formulate computational methods that allow us to identify the above-mentioned problematic situations and test if all proportional trade-offs are consistent so that they can be applied simultaneously. We then propose a novel framework for aggregating local sets of trade-offs, which can be combined mathematically. The respective computational procedure is shown to be effectively done by a suggested algorithm. We also illustrate how the efficiency can be measured against an overall technology, which is formed by the union of these local sets. An empirical illustration in the context of engineering schools will be presented to explain the properties and features of the suggested approach

A linear programming approach to efficiency evaluation in nonconvex metatechnologies

The notions of metatechnology and metafrontier arise in applications of data envelopment analysis (DEA) in which decision making units (DMUs) are not sufficiently homogeneous to be considered as operating in the same technology. In this case, DMUs are partitioned into different groups, each operating in the same technology. In contrast, the metatechnology includes all DMUs and represents all production possibilities that can in principle be achieved in different production environments. Often, the metatechnology cannot be assumed to be a convex set. In such cases benchmarking a DMU against the common metafrontier requires implementing either an enumeration algorithm and solving a linear program at each of its steps, or solving an equivalent mixed integer linear program. In this paper we show that the same task can be accomplished by solving a single linear program. We also show that its dual can be used for the returns-to-scale characterization of efficient DMUs on the metafrontier

A linear programming approach to efficiency evaluation in nonconvex metatechnologies

The notions of metatechnology and metafrontier arise in applications of data envelopment analysis (DEA) in which decision making units (DMUs) are not sufficiently homogeneous to be considered as operating in the same technology. In this case, DMUs are partitioned into different groups, each operating in the same technology. In contrast, the metatechnology includes all DMUs and represents all production possibilities that can in principle be achieved in different production environments. Often, the metatechnology cannot be assumed to be a convex set. In such cases benchmarking a DMU against the common metafrontier requires implementing either an enumeration algorithm and solving a linear program at each of its steps, or solving an equivalent mixed integer linear program. In this paper we show that the same task can be accomplished by solving a single linear program. We also show that its dual can be used for the returns-to-scale characterization of efficient DMUs on the metafrontier

Efficiency and Its Impact on the Performance of European Commercial Banks

The paper empirically analyzes the impact of the degree of efficiency on key performance fig-ures of publicly traded European banks in the period from 2005 to 2009. Efficiency is meas-ured by constructing non-parametric frontiers using the technique of data envelopment analysis on the cost, revenue, and profit sides. Decomposition of overall efficiency provides a detailed insight into effective risk and performance drivers in the banking industry. The results of our paper suggest that an increase in pure technical efficiency is related to more volatile assets, which is reflected in lower market values. Allocative and scale efficiency, however, boost capi-tal market performance

A DEA-based incentives system for centrally managed multi-unit organisations

In multi-unit organisations such as a bank and its branches or a national body delivering publicly funded health or education services through local operating units, the need arises to incentivize the units to operate efficiently. In such instances, it is generally accepted that units found to be inefficient can be encouraged to make efficiency savings. However, units which are found to be efficient need to be incentivized in a different manner. It has been suggested that efficient units could be incentivized by some reward compatible with the level to which their attainment exceeds that of the best of the rest, normally referred to as “super-efficiency”. A recent approach to this issue (Varmaz et. al. 2013) has used Data Envelopment Analysis (DEA) models to measure the super-efficiency of the whole system of operating units with and without the involvement of each unit in turn in order to provide incentives. We identify shortcomings in this approach and use it as a starting point to develop a new DEA-based system for incentivizing operating units to operate efficiently for the benefit of the aggregate system of units. Data from a small German retail bank is used to illustrate our method

The Luenberger indicator and directions of measurement: a bottoms-up approach with an empirical illustration to German savings banks

The Luenberger productivity indicator applies directional distance functions which allow to specifying in what direction (i.e. direction of measurement) the operating units will be evaluated. In the presence of a change in the direction of measurement, the standard components of the existing Luenberger productivity indicator may provide values which are not compatible with reality. In order to eliminate this pitfall, the so-called bottoms-up approach is used to revisit the definition of the indicator and its components. We start with a list of selected sources of productivity change, namely efficiency change, technical change and direction change, then examine the best possible way of measuring each of the sources and combine them to derive a new measure of productivity change. The proposed indicator will be illustrated by means of an empirical application to a panel of 417 German saving banks over the time period 2006-2012. The example explains how the proposed approach is able to properly measure efficiency change, technical change and direction change. The results also provide conclusive evidence about the effect of the change in direction of measurement on the results of the productivity over time in a centralized management scenario

The overall Malmquist index: a new approach for measuring productivity changes over time

This paper deals with a special case of the non-homogeneity problem related to the determination of the global benchmark technology when measuring productivity changes over time. The authors propose a new way of constructing the global framework of the Malmquist index which applies the minimum extrapolation principle on the aggregation of the experienced contemporaneous technologies. The proposed index, called overall Malmquist index, preserves the role of each contemporaneous technology in the determination of the newly-proposed best practice technology, whereby an acceptable level of discrimination between non-homogeneous observations is provided. With respect to both computational and test properties, the proposed index possesses the circularity property, generates a single measure of productivity change and is immune to infeasibility under variable returns to scale. Furthermore, unlike in the global form, previously computed results by the overall Malmquist index are more stable and less sensitive to changes in the shape of the best practice technology when a new time period is incorporated. Similar to traditional indices, it can be decomposed into various components such as efficiency change, scale efficiency change, and best practice change. The suggested index will be illustrated by means of a real-world example from banking. In particular, it will be compared to the contemporaneous and global forms of the Malmquist index introduced into the literature by Färe et al. (1992) and Pastor and Lovell (2005), respectively

Efficiency and Its Impact on the Performance of European Commercial Banks

The paper empirically analyzes the impact of the degree of efficiency on key performance fig-ures of publicly traded European banks in the period from 2005 to 2009. Efficiency is meas-ured by constructing non-parametric frontiers using the technique of data envelopment analysis on the cost, revenue, and profit sides. Decomposition of overall efficiency provides a detailed insight into effective risk and performance drivers in the banking industry. The results of our paper suggest that an increase in pure technical efficiency is related to more volatile assets, which is reflected in lower market values. Allocative and scale efficiency, however, boost capi-tal market performance.Data Envelopment Analysis (DEA), Efficiency, European Banks, Bank Performance