Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools

Public sector output provision is influenced not only by discretionary inputs but also by exogenous environmental factors. In this paper, we extended the literature by developing a conditional DEA estimator of allocative efficiency that allows a decomposition of overall cost efficiency into allocative and technical components while simultaneously controlling for the environment. We apply the model to analyze technical and allocative efficiency of Dutch secondary schools. The results reveal that allocative efficiency represents a significant 37 percent of overall cost efficiency on average, although technical inefficiency is still the dominant part. Furthermore, the results show that the impact of environment largely differs between schools and that having a more unfavorable environment is very expensive to schools. These results highlight the importance of including environmental variables in both technical and allocative efficiency analysis.     

A DEA approach to derive individual lower and upper bounds for the technical and allocative components of the overall profit efficiency

In this paper, we propose a slack-based data envelopment analysis approach to be used in economic efficiency analyses when the objective is profit maximization. The focus is on the measurement of the technical component of the overall efficiency with the purpose of guaranteeing the achievement of the Pareto efficiency. As a result, we will be able to estimate correctly the allocative component in the sense that this latter only reflects the improvements that can be accomplished by reallocations along the Pareto-efficient frontier. Some new measures of technical and allocative efficiency in terms of both profit ratios and differences of profits are defined. We do not make any assumption on the way the technical efficiency is to be measured, that is, we do not use, for example, either a hyperbolic measure or a directional distance function, which allows us to extend this approach and derive individual lower and upper bounds for these efficiency components. To do it, we use novel models of minimum distance to the frontier. This broadens the range of possibilities for the explanation of the overall efficiency in terms of technical and allocative inefficiencies.     

Developing a decomposable measure of profit efficiency using DEA

In for-profit organizations efficiency measurement with reference to the potential for profit augmentation is particularly important as is its decomposition into technical, and allocative components. Different profit efficiency approaches can be found in the literature to measure and decompose overall profit efficiency. In this paper, we highlight some problems within existing approaches and propose a new measure of profit efficiency based on a geometric mean of input/output adjustments needed for maximizing profits. Overall profit efficiency is calculated through this efficiency measure and is decomposed into its technical and allocative components. Technical efficiency is calculated based on a non-oriented geometric distance function (GDF) that is able to incorporate all the sources of inefficiency, while allocative efficiency is retrieved residually. We also define a measure of profitability efficiency which complements profit efficiency in that it makes it possible to retrieve the scale efficiency of a unit as a component of its profitability efficiency. In addition, the measure of profitability efficiency allows for a dual profitability interpretation of the GDF measure of technical efficiency. The concepts introduced in the paper are illustrated using a numerical example.     

Efficient firm groups: Allocative efficiency in cooperative games

The concept of efficiency in groups postulates that a coalition of firms has to record a smaller distance toward the aggregate technology frontier compared with the sum of individual distances. Efficiency analysis (either allocative or technical) is defined with respect to cooperative firm game in order to provide operational distance functions, the so-called pseudo-distance functions. These pseudo-distances belong to the core interior of the allocative firm game, in other terms, any given firm coalition may always improve its allocative efficiency. We prove that such a result is impossible for technical efficiency, i.e., the technical efficiency cannot increase for all possible coalitions.     

Estimating output gains by means of Luenberger efficiency measures

In this paper we propose a new measure of input allocative efficiency that we estimate using directional distance functions. Our new measure compares the gain in output if a firm reduces technical inefficiency for the direct production possibility set and the gain in output if the firm reduces technical inefficiency for the indirect production possibility set. Because the directional distance function uses a translated origin, the gain in output from an optimal reallocation of inputs can be estimated for non-radial expansions in output. We estimate efficiency for Japanese banks during 1992–1999. The gains in outputs from reducing allocative inefficiency by reallocating inputs are greater than the gains in outputs that can be attained by reducing technical inefficiency.     

Technical and allocative efficiency in European banking

This paper specifies an empirical framework for estimating both technical and allocative efficiency using the translog cost-share system, thus providing a solution to the issue known in the literature as the Greene problem. The model is applied to a large panel of European banks and the results are compared with those of a model that does not include an allocative inefficiency term and also with those obtained by using a consistent Bayesian technique. Our results suggest that models which include only technical efficiency, significantly overestimate it, while parameter estimates from the model that includes both technical and allocative efficiency are very close to the ones obtained from the Bayesian approach, thus enhancing our confidence in the proposed methodology. Finally, the fact that allocative efficiency of banks in our sample improves more than technical efficiency underlines the importance of including an allocative inefficiency component in parametric efficiency models.     

Estimating output allocative efficiency and productivity change: Application to Japanese banks

A new measure of output allocative efficiency is developed by comparing the input technical efficiency of a firm for the direct input requirement set and the indirect input requirement set proposed by Shephard [Indirect Production Functions, Verlag Anton Hain, Meisenheim Am Glan]. The ratio of the direct and indirect input quasi-distance functions serves as the measure of output allocative efficiency. As such, it measures the ratio of potential to actual inputs if the firm had chosen the revenue maximizing output mix. Using panel data on Japanese banks operating during 1992–1996 productivity growth is measured and decomposed into changes in output allocative efficiency, changes in input technical efficiency, and technical change. During the period, Japanese banks experienced productivity declines averaging 2% per year and could have used only 78–93% of actual inputs if they had chosen the revenue maximizing output mix.     

Profitability of a sample of Portuguese bank branches and its decomposition into technical and allocative components

The efficiency literature, both using parametric and non-parametric methods, has been focusing mainly on cost efficiency analysis rather than on profit efficiency. In for-profit organisations, however, the measurement of profit efficiency and its decomposition into technical and allocative efficiency is particularly relevant. In this paper a newly developed method is used to measure profit efficiency and to identify the sources of any shortfall in profitability (technical and/or allocative inefficiency). The method is applied to a set of Portuguese bank branches first assuming long run and then a short run profit maximisation objective. In the long run most of the scope for profit improvement of bank branches is by becoming more allocatively efficient. In the short run most of profit gain can be realised through higher technical efficiency.     

Resource allocation based on cost efficiency

In this paper, we consider a resource allocation (RA) problem and develop an approach based on cost (overall) efficiency. The aim is to allocate some inputs among decision making units (DMUs) in such way that their cost efficiencies improve or stay unchanged after RA. We formulate a multi-objective linear programming problem using two different strategies. First, we propose an RA model which keeps the cost efficiencies of units unchanged. This is done assuming fixed technical and allocative efficiencies. The approach is based on the assumption that the decision maker (DM) may not have big changes in the structure of DMUs within a short term. The second strategy does not impose any restrictions on technical and allocative efficiencies. It guarantees that none of the cost efficiencies of DMUs get worse after RA, and the improvement for units is possible if it is feasible and beneficial. Two numerical examples and an empirical illustration are also provided.     

Evolution of bank efficiency in Brazil: A DEA approach

This paper investigates cost, technical and allocative efficiencies for Brazilian banks in the recent period (2000–2007). We use Data Envelopment Analysis (DEA) to compute efficiency scores. Brazilian banks were found to have low levels of economic (cost) efficiency compared to banks in Europe and in the US. For the period with high macroeconomic volatility (2000–2002) the economic inefficiency in Brazilian banks can be attributed mainly to technical inefficiency rather than allocative inefficiency. State-owned banks are significantly more cost efficient than foreign, private domestic and private with foreign participation. There is no evidence of differences in economic efficiency due to type of activity and bank size. These results may provide some useful guidance for financial regulators and bank managers.     

Evaluating public school district performance via DEA gain functions

Existing measures of input allocative efficiency may be biased when estimated via data envelopment analysis (DEA) because of the possibility of slack in the constraints defining the reference technology. In this paper we derive a new measure of input allocative efficiency and compare it to existing measures. We measure efficiency by comparing the actual outputs of a decision-making unit relative to Koopmans’ efficient subset of the direct and indirect output possibility sets. We estimate the existing measures and our new measure of input allocative efficiency for a sample of public school districts operating in Texas.     

Assessing the technical and allocative efficiency of hospital operations in Greece and its resource allocation implications

In this paper, we seek to develop a research framework concerning the assessment of the efficiency of public sector hospital operations. Public hospitals are increasingly under pressure to improve their operations both in terms of resources they use and also in terms of the quantity and quality of their outcomes. The assessment of efficiency entails both the notions of technical and allocative efficiency as they yield complementary information about the management effectiveness of individual hospitals. Technical efficiency has a diagnostic purpose as it yields comparative information about the effectiveness with which individual units convert their input resources into outputs. On the other hand allocative efficiency has a planning orientation since the objective of the assessment is to gauge efficiency improvements by means of resource reallocation. A linear programming based model is proposed for assessing allocative efficiency in the light of uncertainty about the prices of input factors. The empirical part of the paper is based on data from Greek public hospitals. Results and policy implications are discussed based on data from 98 general hospitals based on information from 1992. It was found that significant inefficiencies are present in the operations of Greek hospitals that account approximately for 100 MEcu in 1992 prices.     

Determinants of allocative and technical inefficiency in stochastic frontier models: An analysis of Norwegian electricity distribution firms

Recent econometric advances have made it possible to distinguish between persistent and transient technical inefficiency along with allocative inefficiency in stochastic frontier models for panel data. Kumbhakar et al. (2020) and Lai and Kumbhakar (2019) introduce a methodology that allows for the estimation of these inefficiency components and costs therefrom, while including determinants of both components of technical inefficiency. We extend these models to include technical change and determinants of allocative inefficiency (input misallocation). Including a set of variables that influence input misallocation, we are able to determine the effects of these variables on the cost of allocative inefficiency. We provide empirical evidence on the costs of all three types of inefficiency using data on 149 Norwegian electricity distribution firms between 2000 and 2016. We find that the cost of input misallocation is only slightly lower than that of technical inefficiency. Our results reject a commonly imposed modeling assumption that firms are fully allocatively efficient.     

Convexity,quality and efficiency in education

While Data Envelopment Analysis (DEA) has many attractions as a technique for analysing the efficiency of educational organisations, such as schools and universities, care must be taken in its use whenever its assumption of convexity of the prevailing technology and associated production possibility set may not hold. In particular, if the convexity assumption does not hold, DEA may overstate the scope for improvements in technical efficiency through proportional increases in all educational outputs and understate the importance of improvements in allocative efficiency from changing the educational output mix. The paper therefore examines conditions under which the convexity assumption is not guaranteed, particularly when the performance evaluation includes measures related to the assessed quality of the educational outputs. Under such conditions, there is a need to deploy other educational efficiency assessment tools, including an alternative non-parametric output-orientated technique and a more explicit valuation function for educational outputs, in order to estimate the shape of the efficiency frontier and both technical and allocative efficiency.     

Decomposing technical inefficiency using the principle of least action

In for-profit organizations, profit efficiency decomposition is considered important since estimates on profit drivers are of practical use to managers in their decision making. Profit efficiency is traditionally due to two sources – technical efficiency and allocative efficiency. The contribution of this paper is a novel decomposition of technical efficiency that could be more practical to use if the firm under evaluation really wants to achieve technical efficiency as soon as possible. For this purpose, we show how a new version of the Measure of Inefficiency Proportions (MIP), which seeks the minimization of the total technical effort by the assessed firm, is a lower bound of the value of technical inefficiency associated with the directional distance function. The targets provided by the new MIP could be beneficial for firms since it specifies how firms may become technically efficient simply by decreasing one input or increasing one output, suggesting that each firm should focus its effort on a specific dimension (input or output). This approach is operationalized in a data envelopment analysis framework and applied to a dataset of airlines.     

Resolving a strange case of efficiency

In a recent paper in the Journal of the Operational Research Society, Tone proposes an alternative to the Farrell cost efficiency index to avoid the ‘strange case’ problem in which firms with identical inputs and outputs but with input prices differing by some factor (eg, one has input prices twice another) will have the same Farrell cost efficiency. We provide an alternative cost efficiency indicator that avoids this problem, allows for decomposition into technical and allocative efficiency, and is easily estimated using DEA type models.     

Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis

This paper replaces ordinary DEA formulations with stochastic counterparts in the form of a series of chance constrained programming models. Emphasis is on technical efficiencies and inefficiencies which do not require costs or prices, but which are nevertheless basic in that the achievement of technical efficiency is necessary for the attainment of ‘allocative’, ‘cost’ and other types of efficiencies.     

Allocative efficiency in branch banking

Bank branch efficiency and organization change is analyzed using data from 50 savings bank branches in Sweden. First, technical and allocative efficiencies are analyzed, using non-priced and priced inputs. Secondly, by grouping the branches according to their organizational designation, efficiency is examined by level of service. Trends in performance over two time periods are also analyzed.     

Measuring Technical,Allocative and Overall Efficiencies Using a DEA Algorithm

This study presents an effectively-designed algorithm for measuring technical, allocative and overall efficiencies, using data envelopment analysis (DEA). The specially designed DEA code takes advantage of unique features related to the DEA algorithm. Computational efficiency of the proposed DEA algorithm is confirmed by a Monte Carlo simulation study.     

A generalized DEA model for centralized resource allocation

In this paper, we introduced a new generalized centralized resource allocation model which extends Lozano and Villa’s and Asmild et al.’s models to a more general case. In order to uncover the sources of such total input contraction in the generalized centralized resource allocation model, we applied the structural efficiency to further decompose it into three components: the aggregate technical efficiency, the aggregate allocative efficiency and re-transferable efficiency components. The proposed models are not only flexible enough for the central decision-maker to adjust the inputs and outputs to achieve the total input contraction but also identify the sources of such total input contraction, thereby giving rise to an important interpretation and understanding of the generalized centralized resource allocation model. Finally, an empirical example is used to illustrate the approach.