The Dynamics of Efficiency Improving Input Allocation

A dynamic theory of efficiency improving input reallocations is presented which relaxes the assumption that decision-making units have the ability to reorganize their activities instantaneously to achieve efficient input allocations. Explicit account is taken of the decision-making unit’s gradual transition to an efficient input allocation. A balanced panel data set covering 906 U.S. agricultural banks is constructed for the period 1996–2000 and we find that these banks are allocatively efficient but technically inefficient. The explicit solution for the optimal input use finds evidence of gradual transitions for two of the three inputs, with the labor input transition being the slowest. The efficiency improving path finds the firm transitions toward an efficient allocation by simultaneously improving on technical efficiency instantaneously and on allocative efficiency intertemporally, which suggests a non-linear path toward the most efficient allocation.     

Rural hospital performance and its correlates

The cost, technical, allocative and scale efficiencies of a sample of rural U.S. hospitals are calculated via linear programming models. Tobit analysis is used to assess possible correlates of each of the efficiency measures. A large amount of dispersion in operating efficiency is found within our data set; the majority of the dispersion is due to technical inefficiency. In general, for-profit hospitals are found to outperform not-for-profit and public hospitals. Demand characteristics, quality of care, and the mix of services offered are also found to influence performance.     

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 %.     

Productivity drivers and market dynamics in the Spanish first division football league

This paper analyses efficiency drivers of a representative sample of Spanish football clubs by means of the two-stage data envelopment analysis (DEA) procedure proposed by Simar and Wilson (J Econ, 136:31–64, 2007). In the first stage, the technical efficiency of football clubs is estimated using a bootstrapped DEA model in order to establish which of them are the most efficient; the ranking is based on total productivity in the period 1996–2004. In the second stage, the Simar and Wilson (J Econ, 136:31–64, 2007) procedure is used to bootstrap the DEA scores with a truncated bootstrapped regression. Policy implications of the main findings are also considered.     

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.     

Determination of the efficiency of the world railway companies by method of DEA and comparison of their efficiency by Tobit analysis

This paper attempts to measure the performance of railway companies that produce passenger and freight services around the world. The data covering 10 years from 2000 to 2009 is analyzed first via the data envelopment analysis method in order to obtain technical efficiency and allocative efficiency scores of 31 railway companies for the purpose of the study. In the analysis conducted by use of the CCR model, while total 17 firms were efficient in the first year, this figure reaches to 18 companies for the last year with one more addition. While only two companies seem efficient in the first year, this figure goes down to one for the last year. With input oriented and variable return analysis conducted by use of the BCC model, the firms having technical efficiency at the beginning of the period were 20 in number. At the end of the period, the figure reaches to 24. Next, the outputs of DEA are correlated by Tobit regression and tried to determine decisiveness of the outputs on the efficiency. It has been seen that the same output composition used with Tobit analysis gives more compliant results with the allocative efficiency scores rather than with the technical efficiency scores.     

Hospital efficiency and equity in health care delivery: A study based in China

Hospital efficiency and equity in health care delivery are two enduring research topics. Yet little research has been done to examine the relationship between them. This paper studies the impact of hospital efficiency on equity in health care delivery based on a proprietary dataset of hospital characteristics and 630,000 inpatient records from 149 public hospitals in a representative Chinese city. To measure the hospitals' efficiencies, this study takes the hospitals' operational features and case-mix indexes into account, and computes the efficiency levels using data envelopment analysis with bootstrapping. Through regressions that control for a variety of the patients’ personal characteristics (e.g., age, disease, residence, hospital visit frequency), this study shows that the gap between hospitalization expenses of urban and rural inpatients in more efficient hospitals is smaller than those in less efficient hospitals. Thus efficiency enhances equity in expenditure between urban and rural patients. But the dwindling urban-rural gap in expenditure is achieved by raising the spending of rural patients, thereby undermining their access to health care. This pattern is more conspicuous in large and sophisticated high-tier hospitals. Further analysis shows that hospital efficiency impacts equity of health care delivery by inducing different lengths of stay and uncovered parts of total expenditure for urban and rural groups. The findings imply that an efficiency-oriented health care policy may lead to social benefit loss.     

Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons

This paper presents a new formula for decomposing cost efficiency into technical, price, and allocative efficiencies in an environment marked by the fact that unit input prices differ among certain enterprises. We employed this formula in comparing cost efficiency between Japanese and US electric power companies, and found a significant difference in the price-based efficiency. However, negligible differences were found in the technical and allocative efficiencies.     

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.     

Profit efficiency in the European Union banking industry: a directional technology distance function approach

We employ the directional technology distance function approach and present estimates of profit efficiency in the 25 European Union (EU) member states over the period 1998–2008. This method decomposes profit efficiency into its technical and allocative components. We investigate potential efficiency differences across the old EU region and the new EU member states, across countries and across banks of different size. Our results indicate a significant level of profit inefficiency for the EU region, which is predominantly attributed to allocative inefficiency. Our findings also suggest that banks operating in the old EU region are, on average, more profit efficient than credit institutions in the new EU member states. Overall, we observe considerable variation of efficiency scores across countries and different patterns in efficiency change over time, as well as a negative relationship between bank size and efficiency.     

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.     

The scale of hospital production in different settings: one size does not fit all

This paper analyses the productive efficiency of 141 public hospitals from 1998 to 2004 in two Canadian provinces; one a small province with a few small cities and a generally more rural population and the other a large province that is more urban in nature, with a population who mainly live in large cities. The relative efficiencies of the hospitals, the changes in productivity during this time period, and the relationship between efficiency and the size or scale of the hospitals are investigated using data envelopment analysis. The models for the production of health care use case mix adjusted hospital discharges as the output, and nursing hours as inputs. We find clear differences between the two provinces. Making use of ‘own’ and ‘meta’ technical efficiency frontiers, we demonstrate that efficient units in the larger and more urban province are larger than non-efficient units in that province. However, efficient hospitals in the smaller and more rural province are smaller than non-efficient hospitals in that province. Overall, efficient hospitals in the larger more urban province are larger than efficient hospitals in the smaller more rural province. This has interesting policy implications—different hospitals may have different optimal sizes, or different efficient modes of operation, depending on location, the population they serve, and the policies their respective provincial governments wish to implement. In addition, there are lessons to be learned by comparing the hospitals across the two provinces, since the inefficient hospitals in the small rural province predominantly use hospitals from the large urban province as benchmarks, such that substantially larger improvement potential can be identified by inter-provincial rather than intra-provincial benchmarking analysis.     

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。     

Distorted prices and producer efficiency: the case of Romania

This research aims at shedding empirical light on the relative efficiency of small-scale maize producers in Romania. Farmers in transition countries still face heavily distorted price systems resulting from imperfect market conditions and socioeconomic and institutional constraints. To capture such distortions we formulate a stochastic shadow-cost frontier model to investigate the systematic input-specific allocative inefficiency. We further adjust the underlying cost frontier by incorporating shadow price corrections and subsequently reveal evidence on farm specific technical inefficiency. Different models are estimated due to the imposition of curvature correctness and the effects on the individual efficiency estimates are shown. The empirical results show a relative high technical efficiency of the small-scale farmers but relatively poor scores on systematic input price efficiency. The usage of extension services as well as agricultural training on the farm level are found to have a positive effect on the technical efficiency level of the farms. All model specifications further agree on the negative effect on efficiency with respect to the use of insecticides. The imposition of functional concavity on the shadow cost frontier leads to relative differences in the efficiency estimates of up to 240%.      

Comparisons of Economic Inefficiency Between Output and Input Measures of Technical Inefficiency Using the Fourier Flexible Cost Function

The current paper constructs a Fourier flexible cost function, which is commonly known to be a more general function form than the typical translog form, and can globally approximate a true (but unknown) cost function. Both allocative and technical inefficiencies are considered using the Fourier function in the context of the parametric approach. The former is modeled using shadow input prices and the latter is formulated either by adding an extra term of scale parameter (when the Farrell's (1957) input technical inefficiency is assumed), or by correcting all the terms involving output quantities by a scale parameter (when the Farrell's output technical inefficiency is assumed). It is found that sample banks could save up to 23% of total costs, within the range of 3 and 69% uncovered by the previous works, in which allocative inefficiency plays a more important role than technical inefficiency. Furthermore, the cost of misallocated labor input alone constitutes more than 80% of total allocative inefficiency. Financial deregulation starting from 1991 in Taiwan appears to have improved economic efficiency of the banking industry.     

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.     

Indirect productivity measurement

Caves, Christensen and Diewert [1982a] showed that the Törnqvist productivity index is superlative in a considerably more general sense than had been previously believed. We examine the allocative and technical efficiency hypotheses on which their finding rests. We show that the allocative efficiency hypothesis can be modified, which makes the Törnqvist index superlative in a wider sense than even Caves, Christensen and Diewert showed, since it is consistent with a type of allocative efficiency other than the standard cost minimization and revenue maximization hypotheses considered by Caves, Christensen and Diewert. We also show that if the technical efficiency hypothesis is relaxed, the CCD result may no longer hold, and the distance functions that form the basis of the Malmquist productivity indexes, and hence of the Törnqvist productivity index, must be calculated. We then show how to calculate the underlying distance functions, and we argue that there are real advantages to doing so.The refereeing process of this paper was handled through N.R. Adam.     

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.     

Economic Efficiency and Productivity Growth in the Post-Privatization Chilean Hydroelectric Industry

Chiles hydroelectric industry was privatized in 1985, but required to operate within a regulatory framework designed to achieve a competitive outcome. A centralized dispatch center was established to ensure production at minimum cost, subject to constraints on minimum release and minimum reservoir stock. A reluctance to rapidly reduce the industry work force may also have existed. We develop a constrained cost-minimization model for thermal and hydro generation to obtain the shadow price of water and to determine the qualitative effect of these constraints on allocative efficiency. Using panel data from 1986–1997, we assess the economic efficiency of the hydro industry by estimating a stochastic distance frontier and price equations from the dual cost-minimization problem. We find dramatic increases in technical change and productivity change, with positive efficiency change for all years but the last. We also observe a dramatic decline in allocative inefficiencies over our sample period. The share of hydro generation from run-of-river and thermal plants relative to reservoir plants has increased, presumably in reaction to the water release and reservoir stock constraints, reducing the relative over-utilization of capital to water from the pre-1985 regime. Further, the over-utilization of labor to capital and water has fallen over time. However, considerable allocative inefficiencies remain, consistent with our finding of industry-wide scale economies. Substantial cost savings would result if technical and allocative efficiency were eliminated.JEL Classification: L94, D24     

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.