Efficiency measurement with multiple outputs and multiple inputs

This paper discusses modeling technical and allocative inefficiencies in both cost minimizing and profit maximizing frameworks with special emphasis on multiple inputs and multiple outputs. Both primal and dual models are considered for this purpose. In the primal approach we use a separable output and input function (the constant elasticity of transformation output function and Cobb-Douglas input function). The dual models assume translog cost or profit functions. Technical inefficiency is assumed to be random in the cross-sectional models, and fixed firm-specific parameter in the panel data models. Allocative inefficiencies are always treated as input-specific parameters. We derive exact relations linking technical inefficiency and allocative inefficiencies to cost and profit when the underlying technology is represented by a flexible functional form such as the translog. It is shown that appending a one-sided homoscedastic error term to model technical inefficiency, or neglecting technical inefficiency altogether in a translog profit tunciton results in model misspecification and inconsistent parameter estimates.     

Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis

In the stochastic frontier literature, it is a widely held view that allocative inefficiency can be lumped together with technical inefficiency in the estimation of cost frontiers. Therefore, a one-sided error term in the cost function is believed to capture the cost of overall (technical plus allocative) inefficiency. In this paper we challenge that view through a detailed Monte Carlo investigation. The results show that failure to include the cost of allocative inefficiency explicitly in the cost function biases the estimates of: (i) the cost function parameters, (ii) returns to scale, (iii) input price elasticities, and (iv) cost-inefficiency.     

Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach

In the early 1980’s Kopp and Diewert proposed a popular method to decompose cost efficiency into allocative and technical efficiency for parametric functional forms based on the radial approach initiated by Farrell. We show that, relying on recently proposed homogeneity and duality results, their approach is unnecessary for self-dual homothetic production functions, while it is inconsistent in the non-homothetic case. By stressing that for homothetic technologies the radial distance function can be correctly interpreted as a technical efficiency measure, since allocative efficiency is independent of the output level and radial input reductions leave it unchanged, we contend that for non-homothetic technologies this is not the case because optimal input demands depend on the output targeted by the firm, as does the inequality between marginal rates of substitution and market prices—allocative inefficiency. We demonstrate that a correct definition of technical efficiency corresponds to the directional distance function because its flexibility ensures that allocative efficiency is kept unchanged through movements in the input production possibility set when solving technical inefficiency, and therefore the associated cost reductions can be solely—and rightly—ascribed to technical-engineering-improvements. The new methodology allowing for a consistent decomposition of cost inefficiency is illustrated resorting to simple examples of non-homothetic production functions.     

A Consistent Approach to Cost Efficiency Measurement*

Consistent specifications of the allocative inefficiency function in ‘cost plus input share equations’ systems may be difficult, if not impossible, to find because most plausible ones violate certain reasonable a priori conditions. Moreover, the models to which they lead give rise to highly non‐linear likelihood functions that are very hard to estimate. In an effort to confront these difficulties, this paper adapts an idea first suggested by Greene (1993) that allocative inefficiency ought to be related to input prices and allocative distortions in the input share equations. The system of ‘cost plus input demand equations’ that emerges is estimated by standard seemingly unrelated regression (SUR) techniques using data from private and state firms that operated in Greek manufacturing during the 1979–88 period. Among other findings, the estimates show that overall inefficiency for private and state firms was 63.5% and 102.2%, respectively in comparison with the least inefficient firms in their class. In relative terms these figures imply that state firms were almost 61% less efficient than private firms were. Technical and allocative reasons amounting to 64% and 36%, respectively, accounted for this excess inefficiency of state firms, in addition to differences in the utilization of labour, capital and debt. Lastly, it is found that the magnitudes of technical and allocative inefficiencies depend critically upon a self‐consistent specification of the allocative inefficiency function.     

Theory and Application of Directional Distance Functions

In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are dual to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.     

Measuring technical and allocative efficiencies for banks in the transition countries using the Fourier flexible cost function

The transition economies are known to have quite different market structures from the market economies. State-owned banks accounts for a major part of the financial sector in East European countries before the transition period. Since the input prices of the sector are frequently under the control of those governments, the misallocated resources may incur the loss of economic efficiency. This paper attempts to gauge the technical and allocative efficiency using unbalanced panel data of 340 banks from 14 transition countries under the framework of the Fourier flexible shadow cost function. Accommodating technical and allocative efficiencies simultaneously, as suggested by Atkinson and Cornwell (Int Econ Rev 35:231–243, 1994a) and Kumbhakar and Wang (J Econom 134:317–340, 2006a), avoids potential specification errors and leads to consistent parameter estimates. The average total cost savings resulting from greater technical and allocative efficiency are around 28.31 and 7.13%, respectively. Foreign-owned banks are found to be the most economically efficient. The enforcement of financial liberalization does gradually improve upon the sample banks’ technical efficiency. The allocative inefficiency arises from over capitalization and excess funds. Scale diseconomies appear to prevail in the sample states with a few exceptions.     

A test for the existence of allocative inefficiency in firms

This paper is concerned with the problem of testing for the presence of allocative inefficiency in firms for models in which the cost function is stochastic, the possibility of technical inefficiency is allowed, and the efficient input cost share equations are stochastic. The test exploits the relationships among the disturbances in the cost and share equations to derive implications of the existence of allocative inefficiency. This leads to the use of a Wald-type statistic to take account of the one-sided nature of the alternative. Some empirical experience is reported.     

Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

Estimating DEA technical and allocative inefficiency using aggregate cost or revenue data

In this paper, we address the question of Data Envelopment Analysis (DEA) evaluation of efficiency when aggregate cost or revenue data must be used. We show that the DEA technical inefficiency measure using total revenues as the single output variable or total costs as the single input variable equals the aggregate technical and allocative inefficiency. We employ this result to estimate allocative inefficiency and construct statistical tests of the null hypothesis of no allocative inefficiency analogous to those of the null hypothesis of no scale inefficiency. We illustrate our method using revenue and personnel data for the top U.S. public accounting firms over 1995–1998. Our empirical results indicate the existence of statistically significant allocative inefficiency in the public accounting industry.

Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach

In this paper, we propose simulation-based Bayesian inference procedures in a cost system that includes the cost function and the cost share equations augmented to accommodate technical and allocative inefficiency. Markov chain Monte Carlo techniques are proposed and implemented for Bayesian inferences on costs of technical and allocative inefficiency, input price distortions and over- (under-) use of inputs. We show how to estimate a well-specified translog system (in which the error terms in the cost and cost share equations are internally consistent) in a random effects framework. The new methods are illustrated using panel data on U.S. commercial banks.     

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.     

Estimating X-Efficiency in Taiwanese Banking Using a Translog Shadow Profit Function

A multiproducttranslog normalized shadow profit function is used to examineX-efficiency and related issues with respect to Taiwan's bankingsector. The model developed here is theoretically more appropriatecompared to that proposed by Berger, Hancock, and Humphrey (1993);as the former is obtained within the framework of profit maximization.Parameter estimates from our parametric translog profit functionare shown to be robust against different model specifications.More than half of all potential profits are estimated to be lostdue to economic inefficiency. The relatively more important roleof technical inefficiency, compared with that of allocative inefficiency,implies that deficient output revenues outweigh excessive inputcosts. Translog evidence indicates that larger banks tend tobe more technically efficient than smaller ones. The data showstrong technical progress during the sample period, while themodel failing to include X-inefficiency yields no technical advance.     

On the Determinants of School District Efficiency: Competition and Monitoring

A number of researchers have asserted that inefficiency in the U.S. school system arises from a lack of incentives for public schools to behave efficiently. This paper uses a Shephard input distance function to model educational production, and a switching-regressions estimation to explore the relationship between school district efficiency and two existing incentive mechanisms—competition and voter monitoring. We find evidence that ease of monitoring enhances both technical and allocative efficiency of urban school districts, and that increased competition reduces allocative inefficiency in communities above a competitive threshold. We find no evidence that competition is related to technical inefficiency.     

Assessing French nursing home efficiency: An indirect approach via budget-constrained DEA models

In this paper, data envelopment analysis (DEA) techniques are applied to the French nursing home industry in order to address two policy issues. The first involves nursing home size and returns to scale, while the second deals with the potential effects of a change in nursing home reimbursement from a flat rate to one based on the severity of case-mix. To accomplish this, our analysis expands on the existing nursing home literature to analyze technical and allocative efficiency along with budget-constrained models rather than the more common direct input-based distance function. Technical efficiency is evaluated via an indirect output distance function while allocative output efficiency is computed with a cost indirect revenue function. The findings suggest that system-wide efficiency and equity may result from coming reforms since payments would more accurately reflect resource use.     

Efficiency in Islamic and conventional banking: an international comparison

The paper investigates the efficiency of a sample of Islamic and conventional banks in 10 countries that operate Islamic banking for the period 1996–2002, using an output distance function approach. We obtain measures of efficiency after allowing for environmental influences such as country macroeconomic conditions, accessibility of banking services and bank type. While these factors are assumed to directly influence the shape of the technology, we assume that country dummies and bank size directly influence technical inefficiency. The parameter estimates highlight that during the sample period, Islamic banking appears to be associated with higher input usage. Furthermore, by allowing for bank size and international differences in the underlying inefficiency distributions, we are also able to demonstrate statistically significant differences in inefficiency related to these factors even after controlling for specific environmental characteristics and Islamic banking. Thus, for example, our results suggest that Sudan and Yemen have relatively higher inefficiency while Bahrain and Bangladesh have lower estimated inefficiency. Except for Sudan, where banks exhibits relatively strong returns to scale, most sample banks exhibit very slight returns to scale, although Islamic banks are found to have moderately higher returns to scale than conventional banks. While this suggests that Islamic banks may benefit from increased scale, we would emphasize that our results suggest that identifying and overcoming the factors that cause Islamic banks to have relatively low potential outputs for given input usage levels will be the key challenge for Islamic banking in the coming decades.     

Allocative efficiency of rural water supply – a globally flexible SGM cost frontier

This contribution investigates the efficiency of water suppliers in rural areas of East and West Germany. A non-radial measure of input specific allocative inefficiency is used to reduce the distributional dependency with respect to the inefficiency parameters. It is based on the demand system of a flexible cost function for the variable inputs labour, energy and chemicals modelled by applying a modified symmetric generalized McFadden functional form. Concavity restrictions, as required by economic theory, are imposed. The analysis reveals that efforts towards increasing suppliers’ allocative efficiency should focus on the relatively inefficient usage of the input chemicals. The input specific allocative model specification was found to be superior to the overall allocative specification.

商业银行运营特征的DEA估计研究

数据包络分析是一种评价决策单元相对效率的有效工具,商业银行是数据包络分析方法的重要应用领域。之前的文献一般都集中于对商业银行的技术效率评价进行研究,而本文对商业银行的技术效率、纯技术效率、规模效率、成本效率、投入配置效率、收益效率与产出配置效率的评价方法作了系统性的研究。     

Estimation of technical and allocative inefficiency: A primal system approach

The estimation of technical and allocative inefficiencies using a flexible (translog) cost system is found to be quite difficult, especially when both the inefficiencies are random. In this paper we use the alternative primal system consisting of the production function (translog) and the first-order conditions of cost minimization. The estimation of the primal system is more straightforward and it enables us to estimate observation-specific technical and allocative inefficiencies, and their impact on input demand and cost. We use data on steam-electric generating plants from the U.S. to estimate the model using both Cobb–Douglas and translog production functions.     

Estimating technical and allocative inefficiency relative to stochastic production and cost frontiers

Earlier papers by Aiger, Lovell and Schmidt and by Meeusen and van den Broeck have considered stochastic frontier production functions. this paper extends that work by considering the duality between stochastic frontier production and cost funstions, under the assumtions of exact cost minimization (tecchnical inefficiency only) and of inexact cost minimization (technical and allocative inefficiency). We show how to measure both types of inefficiency, and the associated cost of inefficiency. The techniques are illustrated using data on steam-electric generating plants.     

Feasible estimation of firm‐specific allocative inefficiency through Bayesian numerical methods

Both the theoretical and empirical literature on the estimation of allocative and technical inefficiency has grown enormously. To minimize aggregation bias, ideally one should estimate firm and input‐specific parameters describing allocative inefficiency. However, identifying these parameters has often proven difficult. For a panel of Chilean hydroelectric power plants, we obtain a full set of such parameters using Gibbs sampling, which draws sequentially from conditional generalized method of moments (GMM) estimates obtained via instrumental variables estimation. We find an economically significant range of firm‐specific efficiency estimates with differing degrees of precision. The standard GMM approach estimates virtually no allocative inefficiency for industry‐wide parameters. Copyright © 2009 John Wiley & Sons, Ltd.