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.     

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.     

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.     

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.     

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.     

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.     

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.     

An enhanced DEA model for decomposition of technical efficiency in banking

Past studies about the application of data envelopment analysis (DEA) to banking performance often follow the concept of technical efficiency (TE) and/or the productivity defined by the TE. In this paper, we propose an enhanced DEA model, based on a modification of the directional distance function by simultaneously but disproportionately seeking the maximum expansion of each desirable output and contraction of each undesirable output for efficiency measurement, which allows us to decompose the TE into operating efficiency (OPE) and risk management efficiency (RME). The OPE characterizes the ability of a bank to expand the room for profits through its regular business activities, while the RME describes a bank’s ability in risk management activities for sustaining operations. To illustrate the usefulness of the proposed model, a case study of Taiwan’s domestic commercial banks is presented. The major findings are that operating inefficiency is the main source of technical inefficiency, although banks with a higher OPE generally also have a higher RME. Banks subordinate to financial holding companies are more efficient in both OPE and RME than stand-alone banks.     

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.     

Cost efficiency and scale economies in general dental practices in the US: a non-parametric and parametric analysis of Colorado data

This paper uses both the non-parametric method of data envelopment analysis (DEA) and the econometric method of stochastic frontier analysis (SFA) to study the production technology and cost efficiency of the US dental care industry using practice level data. The American Dental Association 2006 survey data for a number of general dental practices in the state of Colorado in the US are used for the empirical analysis. The findings suggest that the cost efficiency score is between 0.79 and 0.87, on average, and the cost inefficiency is mostly due to allocative rather than technical inefficiency. The optimal output level for a dental practice to fully exploit the economies of scale is estimated to be at $1.68 million. Average cost at this level of output is 50.6 cents for each dollar of gross billing generated. The DEA and SFA approaches provide generally consistent results.     

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.     

Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA

In this paper, we show how Data Envelopment Analysis (DEA) may be used to measure and decompose revenue inefficiency, taking into account all sources of technical waste in the context of an application to assess the Spanish quality wine sector, in particular Designation of Origin (DO) wines. We try to go beyond the standard approaches, which use Shephard distance functions or directional distance functions, to provide decomposition that incorporates slacks as a source of technical inefficiency. To accomplish this, we will base our analysis on a recent approach introduced in Cooper et al. (2011a). In particular, we show how an output-oriented version of the Weighted Additive model can be used to properly identify revenue, technical, and allocative inefficiencies in Spanish DOs. In the application, we conclude that the main source of revenue inefficiency in this sector is technical waste, and that Cava can be highlighted as the DO that performs as a benchmark for more numbers of units.     

On the measurement of technical efficiency in the public sector

Existing measures of technical inefficiency obtained through linear programming models in the public sector do not properly control for environmental variables that affect production. It will be shown that the consequences of not controlling for these fixed factors are biased estimates of technical efficiency. This paper extends the mathematical programming approach to frontier estimation known as Data Envelopment Analysis to allow for environmental variables. This modified model will be then contrasted with the existing model that purportedly controls for exogeneous factors to measure public sector efficiency with simulated data. The results provide evidence that the existing Data Envelopment Analysis model will overestimate the level of technical inefficiency and that the modified model developed in this paper does a better job controlling for exogenous factors. The modified model is also applied to analyze the technical efficiency of school districts.     

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.     

Efficiency measurement in the stochastic frontier model

Deterministic models of technical efficiency assume that all deviations from the production frontier are due to inefficiency. Critics argue that no allowance is made for measurement error and other statistical noise so that the resulting efficiency measure will be contaminated. The stochastic frontier model is an alternative that allows both inefficiency and measurement error. Advocates argue that the stochastic frontier models should be used despite other potential limitations because of the superior conceptual treatment of noise. As will be demonstrated in this paper, however, the assumed shape of the error distributions is used to identify a key production function parameter. Therefore, the stochastic frontier models, like the deterministic models, cannot produce absolute measures of efficiency. Moreover, we show that rankings for firm-specific inefficiency estimates produced by traditional stochastic frontier models do not change from the rankings of the composed errors. As a result, the performance of the deterministic models is qualitatively similar to that of the stochastic frontier models.     

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.     

Dynamic effects in inefficiency: Evidence from the Colombian banking sector

Firms face a continuous process of technological and environmental changes that requires them to make managerial decisions in a dynamic context. However, costs and constraints prevent firms from making instant adjustments towards optimal conditions and may cause inefficiency to persist in time. We propose a dynamic inefficiency specification that captures differences in the adjustment costs among firms and non-persistent effects of inefficiency heterogeneity. The model is fitted to a ten year sample of Colombian banks. The new specification improves model fit and have effects on efficiency estimations. Overall, Colombian banks present high inefficiency persistence but important differences between institutions are found. In particular, merged banks present low adjustment costs that allow them to recover rapidly efficiency losses derived from merging processes.     

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.     

Decomposing profit inefficiency in DEA through the weighted additive model

An issue that has received little attention in the Data Envelopment Analysis literature is the decomposition of profit inefficiency by means of measures that account all sources of technical inefficiency. In this paper we introduce a new way to measure and decompose profit inefficiency through weighted additive models. All our results are derived from a new Fenchel-Mahler inequality using duality theory.     

Determinants of bank efficiency: The case of Brazil

This paper analyzes the efficiency of the Brazilian banking sector over the post-privatization period of 2000–2007. We employ a Bayesian stochastic frontier approach, which provides exact efficiency estimates and confidence intervals and thus, allows an accurate comparison across institutions and bank groups. The results suggest that large banks are the most cost and profit efficient, supporting the concentration process observed in recent years. Foreign banks have achieved a good performance through either the establishment of new affiliates and the acquisition of local banks. The remaining public banks have had improvements in cost efficiency, but are relatively profit inefficient. Finally, we observe a positive impact of capitalization on efficiency.