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.     

Estimating indirect allocative inefficiency and productivity change

Building on the method used in previous indirect production studies, we construct an indicator of indirect output allocative inefficiency. Our indicator equals the difference between a revenue-constrained directional input distance function and a directional input distance function that depends on outputs, rather than revenue. The indicator measures the overuse of inputs that occurs when firms do not choose a revenue maximizing mix of outputs. Adding a time dimension allows productivity change to be measured. In an empirical illustration of our method we find that Japanese banks use, between 2% and 7%, too many inputs because bank outputs are inefficiently allocated.     

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.     

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.     

An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’

As a measure of overall technical inefficiency, the Directional Distance Function (DDF) introduced by Chambers, Chung, and Färe ties the potential output expansion and input contraction together through a single parameter. By duality, the DDF is related to a measure of profit inefficiency, which is calculated as the normalized deviation between optimal and actual profit at market prices. As we show, in the most usual case, the associated normalization represents the sum of the actual revenue and the actual cost of the assessed firm. Consequently, the corresponding profit inefficiency measure associated with the DDF has no obvious economic interpretation. In contrast, in this paper we allow outputs to expand and inputs to contract by different proportions. This results in a modified DDF that retains most of the properties of the original DDF. The corresponding dual problem has a much simpler interpretation as the lost profit on (average) outlay that can be decomposed into a technical and an allocative inefficiency component. In addition, an overall measure of technical inefficiency at the industry level is introduced resorting to the direction corresponding to the average input–output bundle.     

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.     

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.     

Specification and estimation of multiple output technologies: A primal approach

This paper addresses specification and estimation of multiple-outputs and multiple-inputs production technology in the presence of technical inefficiency. The primary focus is on the primal formulations. Several competing specifications such as production function, input (output) distance function, input requirement function are considered. We show that all these specifications come from the same transformation function and are algebraically identical. We also show that: (i) unless the transformation function is separable (i.e., outputs are separable from inputs), the input (output) ratios in the input (output) distance function can not be treated as exogenous (uncorrelated with technical inefficiency) resulting inconsistent estimates of the input (output) distance function parameters. (ii) Even if input (output) ratios are exogenous, estimation of the input (output) distance function will result in inconsistent parameter estimates if outputs (inputs) are endogenous. We address endogeneity and instrumental variable issues in details in the context of flexible (translog) functional forms. Estimation of several specifications using both single and system approaches are discussed using Norwegian dairy farming data.     

Hospital efficiency with risk adjusted mortality as undesirable output: the Turkish case

We analyze the operational performance of 202 Turkish rural general hospitals. To help improve performance on both input and output space, we adopt a directional distance approach. We treat a mortality based measure as a “needs indicator”. We derive pure technical, scale and output congestion inefficiency measures and show how they vary across size classes. We show that “reducing mortality” involves sacrificing some good outputs. This is a trade off that holds at the potential output level. Second stage regressions of the inefficiency scores against hospital and rural district level variables, pinpoint critical areas for performance improvement. In particular we show the relative scarcity of nurses is linked to output congestion.     

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.     

The weighted Russell measure of technical efficiency

Theoretical consideration of technical efficiency has existed since Koopmans [10] defined it for production possibilities for which it is not possible to increase any output without simultaneously increasing any input, ceteris paribus. The nonparametric approach to efficiency measurement known as Data Envelopment Analysis is based on the index of Farrell [9], which measures radial reduction in all inputs consistent with observed output. Even after Farrell efficiency is achieved, however, there may exist additional slack in individual inputs, suggesting that the Farrell index does not necessarily measure Koopmans inefficiency. To solve this problem, the non-radial Russell measure was introduced. This paper shows that problems may arise with the Russell measure due to restrictive assumptions on the implicit weighting of inputs and outputs. This paper develops a new measure, the Weighted Russell measure, that relaxes this assumption. Using simulated data, the new measure is shown to be preferred to existing methods. In addition, the new method is applied to analyze the performance of New York State school districts.     

Network DEA efficiency in input–output models: With an application to OECD countries

We undertake network efficiency analysis within an input–output model that allows us to assess potential technical efficiency gains by comparing technologies corresponding to different economies. Input–output tables represent a network where different sectoral nodes use primary inputs (endowments) to produce intermediate input and outputs (according to sectoral technologies), and satisfy final demand (preferences). Within the input–output framework it is possible to optimize primary inputs allocation, intermediate production and final demand production by way of non-parametric data envelopment analysis (DEA) techniques. DEA allows us to model the different subtechnologies corresponding to alternative production processes, to assess efficient resource allocation among them, and to determine potential output gains if inefficiencies were dealt with. The proposed model optimizes the underlying multi-stage technologies that the input–output system comprises identifying the best practice economies. The model is applied to a set of OECD countries.     

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.     

Assessing dynamic inefficiency of the Spanish construction sector pre- and post-financial crisis

This paper undertakes the full decomposition of dynamic cost inefficiency into technical, scale and allocative inefficiency based on the dynamic directional distance function. The empirical application estimates dynamic inefficiency in the Spanish construction industry before and during the current financial crisis over the period 2001–2009. Static inefficiency measures are biased in a context of a significant economic crisis with large investments and disinvestments as they do not account for costs in the adjustment of quasi-fixed factors. Allocative inefficiency is smaller, while technical inefficiency is larger when using the dynamic compared to the static framework. Results further indicate that overall dynamic cost inefficiency is very high with technical inefficiency being the largest component, followed by allocative and scale inefficiency. Moreover, overall dynamic cost inefficiency is significantly larger before the beginning of the financial crisis than during the financial crisis. Larger firms are less technically and scale inefficient than smaller firms on average, but have more problems in choosing the mix of inputs that minimizes their long-term costs. Firms that went bankrupt, on average, have a higher overall dynamic cost inefficiency and scale inefficiency than continuing firms.     

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.     

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.     

Statistical inference for DEA estimators of directional distances

In productivity and efficiency analysis, the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set. The most familiar non-parametric methods use Farrell–Debreu, Shephard, or hyperbolic radial measures. These approaches require that inputs and outputs be non-negative, which can be problematic when using financial data. Recently, Chambers et al. (1998) have introduced directional distance functions which can be viewed as additive (rather than multiplicative) measures efficiency. Directional distance functions are not restricted to non-negative input and output quantities; in addition, the traditional input and output-oriented measures are nested as special cases of directional distance functions. Consequently, directional distances provide greater flexibility. However, until now, only free disposal hull (FDH) estimators of directional distances (and their conditional and robust extensions) have known statistical properties (Simar and Vanhems, 2012). This paper develops the statistical properties of directional d estimators, which are especially useful when the production set is assumed convex. We first establish that the directional Data Envelopment Analysis (DEA) estimators share the known properties of the traditional radial DEA estimators. We then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance, estimation of confidence intervals, and bias correction. The methods are illustrated in some empirical examples.     

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.     

Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs

The paper focuses upon situations in which decision-making units carry out their production activities with some inputs or outputs unobservable (or possibly omitted), and when there are a priori known constraints on the relative significance of otherwise observable (or explicitly considered) inputs and outputs. For such settings, the paper proposes a modification that alters traditional construction of the production possibility set and isolates the role of the unobservable (or omitted) variables in production by means of restrictions on virtual inputs and outputs being converted into production trade-offs. In effect, the proposed procedure induces unit-specific production possibility sets that derive from production trade-offs framed for units assessed separately to reflect their specific observed production conditions. The modification is implemented within a weighted slacks-based measure with restricted direction of slacks in order to make technical efficiency measurement more informative and consistent with the operating conditions under which production activities are accomplished. These ideas are illustrated and models implemented in a case study of bank branch performance measurement.     

Data Envelopment Analysis with Preference Structure

It is important to consider the decision making unit (DMU)'s or decision maker's preference over the potential adjustments of various inputs and outputs when data envelopment analysis (DEA) is employed. On the basis of the so-called Russell measure, this paper develops some weighted non-radial CCR models by specifying a proper set of ‘preference weights’ that reflect the relative degree of desirability of the potential adjustments of current input or output levels. These input or output adjustments can be either less or greater than one; that is, the approach enables certain inputs actually to be increased, or certain outputs actually to be decreased. It is shown that the preference structure prescribes fixed weights (virtual multiplier bounds) or regions that invalidate some virtual multipliers and hence it generates preferred (efficient) input and output targets for each DMU. In addition to providing the preferred target, the approach gives a scalar efficiency score for each DMU to secure comparability. It is also shown how specific cases of our approach handle non-controllable factors in DEA and measure allocative and technical efficiency. Finally, the methodology is applied with the industrial performance of 14 open coastal cities and four special economic zones in 1991 in China. As applied here, the DEA/preference structure model refines the original DEA model's result and eliminates apparently efficient DMUs.