Fuzzy Pair-wise Dominance and Implications for Technical Efficiency Performance Assessment

Classically, the concept of efficiency measurement is based on the definition of a frontier that envelops the observed production plans. The efficiency score itself is based on the distance of an observed production plan from this frontier. The frontier along with the required technological assumptions (such as convexity) needed for its definition may be replaced with the concept of pair-wise dominance. This concept leads to a classification scheme for all production plans instead of a ranking based on efficiency scores. Also, the traditional assumption of deterministic or crisp production plans may be substituted with the weaker assumption of fuzzy production plans as proposed by fuzzy set theory. This paper merges these two concepts and defines a new classification scheme based on fuzzy dominance.     

Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia

This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.

     

Weight restrictions in DEA: misplaced emphasis?

Measuring productive efficiency is an important research strand within fields of economics, management science and operations research. One definition of efficiency is the proportional scaling needed for observations of inefficient units to be projected onto an efficient production function and another definition is a ratio index of weighted outputs on weighted inputs. When linear programming is used to estimate efficiency the two definitions give identical results due to the fundamental duality of linear programming. Empirical applications of DEA using linear programming showed a prevalence of zero weights leading to questioning the consequence for the efficiency score estimate based on the ratio definition. Early literature on weight restrictions is exclusively based on the ratio efficiency. It was stated that variables with zero weights had no influence on the efficiency score, in spite of the alleged importance of the variables. This has been one motivation for introducing restrictions on weights. Another empirical result was that often there were too many efficient units. This problem could also be overcome by introducing weight restrictions. Weight restrictions were said to introduce values for inputs and outputs. The paper makes a critical examinations of these claims based on defining efficiency relative to a frontier production function.     

异质性的技术俱乐部与中国地区工业增长——基于潜类别随机前沿模型的研究

本文利用中国1999~2007年30个省份工业的面板数据,以各省份的人力资本水平、对外开放程度作为类别的条件变量,通过建立潜类别随机前沿模型,考虑技术俱乐部的异质性,从而分析了我国的工业经济增长过程。结果表明,我国30个省份存在两个技术俱乐部,使用不同的技术前沿,生产函数存在巨大差异,并且俱乐部A的技术效率高于俱乐部B。技术进步是各省份工业产出变化最重要的决定因素,且B俱乐部要高于A俱乐部。投入变动起着很重要的作用,而效率变化的作用却非常小。     

A Stochastic Frontier Production Function with Flexible Risk Properties

This paper considers a stochastic frontier production function which has additive, heteroscedastic error structure. The model allows for negative or positive marginal production risks of inputs, as originally proposed by Just and Pope (1978). The technical efficiencies of individual firms in the sample are a function of the levels of the input variables in the stochastic frontier, in addition to the technical inefficiency effects. These are two features of the model which are not exhibited by the commonly used stochastic frontiers with multiplicative error structures.An empirical application is presented using cross-sectional data on Ethiopian peasant farmers. The null hypothesis of no technical inefficiencies of production among these farmers is accepted. Further, the flexible risk models do not fit the data on peasant farmers as well as the traditional stochastic frontier model with multiplicative error structure.     

Efficiency and Technological Change in the U.S. Brewing Industry

This study demonstrates that the measurement of technological change and economic efficiency are tightly linked. Efficiency measures may depend on carefully controlling for technological change, while tests of technological change may be sensitive to empirical model specifications. Moreover, the study underlines Solow's (1994) and Romer's (1994) admonition that econometricians should pay attention to industry and institutional evidence in building models of technological change. The empirical results presented here suggest that there has been substantial technological change in the U.S. brewing industry from 1950 to 1992. This occurred in the form of a dramatic shift in technology beginning with the introduction of super breweries in about 1972. There has also been a substantial increase in scale economies, which undoubtedly caused many inefficiently small firms to exit the industry during the 1960s and 1970s. Further results suggest that a more complete specification of technological change and the stochastic nature of the frontier production function leads to higher and more tenable estimates of efficiency.     

Productive Efficiency of the Swine Industry in Hawaii: Stochastic Frontier vs. Data Envelopment Analysis

Improving productive efficiency is an increasingly important determinant of the future of the swine industry in Hawaii. This paper examines the productive efficiency of a sample of swine producers in Hawaii by estimating a stochastic frontier production function and the constant returns to scale (CRS) and variable returns to scale (VRS) output-oriented DEA models. The technical efficiency estimates obtained from the two frontier techniques are compared. The scale properties are also examined under the two approaches. The industry's potential for increasing production through improved efficiency is also discussed.     

Estimating heterogeneous capacity and capacity utilization in a multi-species fishery

We use a stochastic production frontier model to investigate the presence of heterogeneous production and its impact on fleet capacity and capacity utilization in a multi-species fishery. We propose a new fleet capacity estimate that incorporates complete information on the stochastic differences between vessel-specific technical efficiency distributions. Results indicate that ignoring heterogeneity in production technologies within a multi-species fishery as well as the complete distribution of a vessel’s technical efficiency score, may lead to erroneous fleet-wide production profiles and estimates of capacity. Our new estimate of capacity enables out-of-sample production predictions which may be useful to policy makers.     

Estimation of a non-neutral stochastic frontier production function

This article proposed a hybrid of a stochastic frontier regression. The proposed model and estimation differ from the conventional model of Aigner, Lovell, and Schmidt. The model combines a stochastic frontier regression and a truncated regression to estimate the production frontier with non-neutral shifting of the average production function. The truncated regression identifies the sources of efficiency. The article presents empirical evidence of non-neutral effects of the firm's characteristics—the age of the firms, the export ratio, and the R&D expenditure—on the frontier production function and production efficiency in the Taiwan's electronics industry.We would like to express appreciation to George E. Battese, the associate editor, and anonymous referees for various comments and suggestions. The research was partially supported by the University Research Council of Vanderbilt University, and the Sun Yat-Sen Institute for Social Sciences and Philosophy of Academia Sinica, Taiwan. Residual errors are ours alone.     

Beyond profitability: effects of acquisitions on technical efficiency in the Italian pasta industry

Unlike traditional studies on the impact of ownership changes—which use either profitability measures or stock prices—this paper investigates the impact of acquisitions on acquired firms' technical efficiency. Using a panel of Italian firms in the pasta industry for the 1981–1997 period, I estimate a stochastic production frontier with exogenous factors affecting efficiency in a translog specification with non‐neutral technical progress. The main result is that acquired firms experience, within the 6 years period following the acquisition, an increase in technical efficiency of the order of 10%. This result is statistically significant and proves to be robust with respect to the inclusion of size and calendar year effects as explanatory variables of firms' inefficiency. These findings contribute to the debate on the welfare gains of ownership changes by providing evidence that mergers and acquisitions lead to cost savings, due to the reduction of acquired firms' X‐inefficiency. Copyright © 2002 John Wiley & Sons, Ltd.     

Are all Scales Optimal in DEA? Theory and Empirical Evidence

Policy recommendations concerning optimal scale of production units may have serious implications for the restructuring of a sector. The piecewise linear frontier production function framework (DEA) is becoming the most popular one for assessing not only technical efficiency of operations, but also for scale efficiency and calculation of optimal scale sizes. The main purpose of the present study is to investigate if neoclassical production theory gives any guidance as to the nature of scale properties in the DEA model, and empirically explore such properties. Theoretical results indicate that the DEA model may have more irregular properties than usually assumed in neoclassical production theory, concerning shape of optimal scale curves and the M-locus. The empirical results indicate that optimal scale may be found over almost the entire size variations in outputs and inputs, thus making policy recommendations about efficient scale difficult. It seems necessary to establish the nature of optimal scale before any practical conclusions can be drawn. Proposals for indexes characterizing the nature of optimal scale are provided.     

The measurement of productive efficiency: A robust minimax approach

Some applied aspects of robustness are formulated and empirically tested so as to generalize the Farrell efficiency measure for the frontier production function. A minimax method is used to develop a Chebyshev efficiency measure along with a stochastic production frontier. The relative insensitivity of such a measure in respect of sample size variations and outliers are illustrated by an empirical application to educational production functions.     

Productive efficiency of French grain producers: A latent variable model

In this article we propose to implement a covariance structure analysis to deal with the estimation of a stochastic frontier production function on panel data and the measurement of a time-varying technical efficiency. First, this method solves the potential problem of correlations between input quantities and individual effects. Second, individual effects and efficiency measures can be recovered as a byproduct of the analysis through the so-called factor scores. We implement this approach by fitting to a balanced panel of French grain producers, a parsimonious version of the Cornwell, Schmidt, and Sickles [1990]'s model where technical efficiencies are individual-specific linear functions of time. A specification search shows that this model is preferred to the traditional production function. Results shed light on the temporal pattern of efficiency in the French grain production sector.The authors thank Jacques Mairesse, Quang Vuong, two referees, the editor, and session participants at the Econometric Society European Meeting, Cambridge, September 1991, at the Second European Workshop on Efficiency and Productivity Analysis, Louvain-la-Neuve, October 1991, at the Conference on Current Issues in Productivity, Newark, December 1991, and at the ENSAE-EHESS seminar, Paris, March 1992, for helpful comments and suggestions.     

Does school ownership matter? An unbiased efficiency comparison for regions of Spain

The programme for international student assessment (PISA) 2006 Report (OECD, PISA 2006: science competencies for tomorrow’s world, Organisation for Economic Co-operation and Development, Paris in 2007) showed significant differences among Spanish students attending publicly financed schools. Publicly financed schools include entirely public schools and schools that are privately managed but publicly funded. Families with a lower socioeconomic status may self-select into public schools, so a direct efficiency comparison between the two school types could lead to flawed conclusions because of the possible school selection bias. In this paper, we suggest using a propensity score matching approach in order to correctly analyze the impact of school ownership on student performance. After tackling the self-selection problem, we use a stochastic parametric distance function framework to compare student efficiency and productivity in both school types across ten Spanish regions using PISA 2006 data. Furthermore, we propose two original measures to analyze the impact of school ownership on academic performance across regions: the average treatment effect on the treated on the production frontier and the average treatment effect on the treated assuming school inefficiency. We find that, on average, private government-dependent schools are more productive than public schools, although efficiency results across regions are highly divergent.     

Regulation and technological change in the American meat industry

The effects of regulation upon technological change in the American meat industry in the period between 1950 and 1978 are examined in terms of the relationship between three alternative models — neoclassical, X-efficiency, and technological exogeneity —and the behavior of regulatory agencies. The paper is based upon patent data, equipment approvals by the United States Department of Agriculture and interviews with meat equipment and meat processing firms. Each theory was found to account for some of the observed transactions between regulation and technological change. Conversely, no single theory encompasses all observed effects.Regulations have added to the cost of developing new products. Increased uncertainty in the late 1970s over the standards sought by regulatory agencies have similarly increased the uncertainties of the profitability of R&D in selected product lines. This uncertainty was also found to be inducing firms to substitute product development via mergers for their own R&D. The Humane Slaughter Act was the proximate spur for technological advances that lead to a rationalization of production processes. The innovations that resulted from this act and from other regulatory standards highlighted, in accordance with the X-efficiency framework, technological opportunities that existed prior to and independent of changes in regulatory standards. Much of the momentum for technological change in the industry was shaped by an initial set of technological advances and the subsequent working through of production bottlenecks in an interrelated production system. These advances were largely independent of and unaffected by regulatory standards.Indeed, there is reason to believe that regulatory standards may themselves have an element of endogeneity in terms of the feasible set of best practice techniques. Thus at any particular time, technological change may serve to generate a production frontier towards which a regulatory agency might seem to propel an industry.Overall, our judgment is that regulation had little discernible impact on the pace of technological change related to the production and distribution of ground beef in the period between 1950 and 1978. If there has been any net effect, regulation probably served more to stimulate than to inhibit technological change.     

污染排放约束下中国农业水资源效率的区域差异与影响因素

应用数据包络分析（DEA）构建了非径向方向性距离函数模型,采用全要素水资源效率的测度思路,对污染排放约束下中国分省及区域的农业水资源效率进行了测度,并采用Bootstrap断尾回归模型对污染排放下农业水资源效率的影响因素进行了实证研究。2011年、2012年全国农业平均用水效率分别为0.693、0.671,全国一半以上的省份未达到生产前沿。在八大区域中,北部沿海和黄河中游地区的农业水资源效率最高,西北和东北地区的农业水资源效率处于低水平。在诸多影响因素中,农田水利建设和环境规制对于提升我国农业水资源效率具有显著的促进作用,而水资源丰裕程度对其则具有显著的负面影响。     

Separating Technical Change from Time-Varying Technical Inefficiency in the Absence of Distributional Assumptions

This paper proposes an alternative model for separating technical change from time-varying technical inefficiency. The proposed formulation uses the general index, developed by Baltagi and Griffin (1988), to model technical change in the production frontier function and a quadratic function of time, as in Cornwell, Schmidt and Sickles (1990), to capture the temporal pattern of technical inefficiency. In such a setting, all parameters associated with the rate of technical change and the temporal pattern of technical inefficiency are identified separately. Moreover, the proposed formulation is independent of any distributional assumption concerning the one-sided error term associated with technical inefficiency, and it can be estimated in a single stage with non-linear FGLS. Empirical results based on a translog production frontier, and estimates of technical inefficiency and technical change are presented for the UK dairy sector over the period 1982–1992.     

Technical efficiency during economic reform in Nicaragua: evidence from farm household survey data

This paper employs a translog stochastic frontier model to examine technical efficiency of maize and bean farmers in two selected regions of Nicaragua using farm-level survey data for the 1994–1995 crop year. The average technical efficiency levels are 69.8 and 74.2% for maize and beans, respectively. The results from the maize and beans translog frontier functions show that farmers’ human capital represented by the level of schooling, access to formal credit and farming experience represented by age contribute positively to production efficiency, while farmers’ participation in non-farm employment tends to reduce production efficiency.     

Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England

The presence of outliers in the data has implications for stochastic frontier analysis, and indeed any performance analysis methodology, because they may lead to imprecise parameter estimates and, crucially, lead to an exaggerated spread of efficiency predictions. In this paper we replace the normal distribution for the noise term in the standard stochastic frontier model with a Student’s t distribution, which generalises the normal distribution by adding a shape parameter governing the degree of kurtosis. This has the advantages of introducing flexibility in the heaviness of the tails, which can be determined by the data, as well as containing the normal distribution as a limiting case, and we outline how to test against the standard model. Monte Carlo simulation results for the maximum simulated likelihood estimator confirm that the model recovers appropriate frontier and distributional parameter estimates under various values of the true shape parameter. The simulation results also indicate the influence of a phenomenon we term ‘wrong kurtosis’ in the case of small samples, which is analogous to the issue of ‘wrong skewness’ previously identified in the literature. We apply a Student’s t-half normal cost frontier to data for highways authorities in England, and this formulation is found to be preferred by statistical testing to the comparator normal-half normal cost frontier model. The model yields a significantly narrower range of efficiency predictions, which are non-monotonic at the tails of the residual distribution.

     

A multiplicative model for efficiency analysis

This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.