The “wrong skewness” problem in stochastic frontier models: A new approach

Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generalizing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and nondegenerate efficiency measures. We discuss the statistical properties of the model, and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958–2005 and show that for a number of years our model suggests technical efficiencies well below the frontier while the classical one estimates no inefficiency in those years.     

Work effort,technical efficiency and productivity growth

This paper develops a model to examine labor-use efficiency associated with the effieciency wage theory and technical effieciency associated with the frontier production model. The generalixed modelcombines these two approaches and derives measures of technical and labor-use efficiency as well as their effects on productivity growth. It also seperates technical inefficiency from industry heterogenity. the model is applied to estimate loss of output due to technical and labor-use inefficiency for 18 two-digit U.S manufacturing industries using time series and cross-sectional data.     

Work effort, technical efficiency and productivity growth

This paper develops a model to examine labor-use efficiency associated with the effieciency wage theory and technical effieciency associated with the frontier production model. The generalixed modelcombines these two approaches and derives measures of technical and labor-use efficiency as well as their effects on productivity growth. It also seperates technical inefficiency from industry heterogenity. the model is applied to estimate loss of output due to technical and labor-use inefficiency for 18 two-digit U.S manufacturing industries using time series and cross-sectional data.     

企业技术效率的影响分析

 本文以上海市166家大中型企业五年的面板数据为研究对象,设定两种不同的生产函数和两种误差分布,利用随机前沿方法分别进行了技术效率的估计。我们发现不同测算方法的结果差异不大,且对企业的评价具有一致性。结果表明上海市工业企业的技术效率整体水平不高。通过研究影响企业技术效率的外生性因素,发现企业的所有制结构、规模、R&D经费支出与R&D人员投入、资本密集程度和企业的垄断程度等因素都对上海市工业企业的技术效率水平具有显著影响。基于研究结果,我们给出了提高企业技术效率的一些建议。     

A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms

This article investigates farm-level efficiency of U.S. dairy farmers by estimating their technical and allocative efficiency. Technical inefficiency is assumed to be composed of a deterministic component that is a function of some farm-specific characteristics and a random component. By doing this we extend the stochastic frontier methodology in which determinants of technicial inefficiency are explicitly introduced in the model. Given the inputs, variations in efficiency of farms are then explained by both deterministic and random components of technical inefficiency. The empirical results indicate that (a) levels of education of the farmer are important factors determining technical inefficiency and (b) large farms are more efficient (technically) than small and medium-sized farms. Both technical and allocative inefficiency are found to decrease with increase in the level of education of the farmer.     

A copula regression model for estimating firm efficiency in the insurance industry

This article considers the estimation of insurers’ cost-efficiency in a longitudinal context. The current practice ignores the tails of the cost distribution, where the most and least efficient insurers belong to. To address this issue, we propose a copula regression model to estimate insurers’ cost frontier. Both time-invariant and time-varying efficiency are adapted to this framework and various temporal patterns are considered. In our method, flexible distributions are allowed for the marginals, and the subject heterogeneity is accommodated through an association matrix. Specifically, when fitting to the insurance data, we perform a GB2 regression on insurers total cost and employ a t-copula to capture their intertemporal dependencies. In doing so, we provide a nonlinear formulation of the stochastic panel frontier and the parameters are easily estimated by likelihood-based method. Based on a translog cost function, the X-efficiency is estimated for US property-casualty insurers. An economic analysis provides evidences of economies of scale and the consistency between the cost-efficiency and other performance measures.     

动态面板空间随机前沿模型的参数估计及应用

生产效率一般会受到空间相关性和时间滞后效应的影响,不易准确测算。本文考虑时空双重滞后特征,提出一种动态面板数据空间随机前沿模型,针对模型的内生性问题,借鉴已有的估计方法,本文提出一种广义矩估计方法（Generalized Method of Moments,GMM）,并证明了参数估计的一致性。在应用分析中,利用本文所提出的理论模型实证分析了我国战略性新兴产业发展的效率,该理论模型能够客观、科学地测算技术效率,实证结论验证了理论模型的应用效果。     

Estimating technical efficiency with non-neutral shift of the frontier

In the literature, technical efficiency is measured as the ratio of the observed output to potential output. Although there is no a priori theoretical reasoning, in the stochastic framework of measuring technical efficiency, potential output has been conventionally assumed as a neutral shift from observed output, owing solely to a larger intercept term in the frontier production function and without change in the input response coefficients. The objective of this paper is to propose and apply a method to measure technical efficiency without the above assumption. Furthermore, this methodology does not require the restrictive assumption of a particular distribution for the efficiency-related error term, as has been the case until now in the stochastic production function literature. A random sample of farmers from Madurai district in Tamil Nadu, India, was used. The analysis revealed substantial variation in the farm-specific input response coefficients between farms, which means that the contributions of individual inputs to the output differ from farm to farm, because the methods of application of the individual inputs vary. The frontier production function, which defines the potential of a technology, is determined by the highest values of the coefficients of each individual input which may come from one or more farms. Farm-specific frontier functions generally showed a considerable potential for improving the technical.performance of each input.     

空间ZISF的估计及蒙特卡罗模拟

在随机前沿模型中引入空间效应和技术无效率项的非连续性并构建了空间零无效率随机前沿模型,使用极大似然估计和JLMS方法得出参数和技术效率的估计。蒙特卡罗模拟表明:(1)逆似然比检验能以较高的准确率识别真实模型;(2)本方法在参数估计和技术效率的估计两方面均表现较好;(3)若真实模型为空间零无效率随机前沿模型但误用了空间随机前沿模型,参数估计和技术效率的估计两方面均表现较差。空间零无效率随机前沿模型有其存在的必要性。     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an unobserved set of DMUs. The model provides posterior predictive data for the unobserved DMUs to augment the frontier in the DEA that provides a posterior predictive distribution for the efficiency scores. We explore the method on a multiple-input and multiple-output DEA model. The data for the example are from a comprehensive examination of how nursing homes complete a standardized mandatory assessment of residents.     

Semiparametric Smooth Coefficient Stochastic Frontier Model With Panel Data

ABSTRACT

We investigate the semiparametric smooth coefficient stochastic frontier model for panel data in which the distribution of the composite error term is assumed to be of known form but depends on some environmental variables. We propose multi-step estimators for the smooth coefficient functions as well as the parameters of the distribution of the composite error term and obtain their asymptotic properties. The Monte Carlo study demonstrates that the proposed estimators perform well in finite samples. We also consider an application and perform model specification test, construct confidence intervals, and estimate efficiency scores that depend on some environmental variables. The application uses a panel data on 451 large U.S. firms to explore the effects of computerization on productivity. Results show that two popular parametric models used in the stochastic frontier literature are likely to be misspecified. Compared with the parametric estimates, our semiparametric model shows a positive and larger overall effect of computer capital on the productivity. The efficiency levels, however, were not much different among the models. Supplementary materials for this article are available online.     

Measuring the efficiency of public services: the limits of analysis

Summary.  Policy makers are increasingly seeking to develop overall measures of the effi-ciency of public service organizations. For that, the use of 'off-the-shelf' statistical tools such as data envelopment analysis and stochastic frontier analysis have been advocated as tools to measure organizational efficiency. The analytical sophistication of such methods has reached an advanced stage of development. We discuss the context within which such models are deployed, their underlying assumptions and their usefulness for a regulator of public services. Four specific model building issues are discussed: the weights that are attached to public service outputs; the specification of the statistical model; the treatment of environmental influences on performance; the treatment of dynamic effects. The paper concludes with recommendations for policy makers and researchers on the development and use of efficiency measurement techniques.     

Weighted Estimator for the Linear Transformation Models with Multivariate Failure Time Data

In this article, a simple and efficient weighted method is proposed to improve the estimation efficiency for the linear transformation models with multivariate failure time data. Asymptotic properties of the estimators with a closed-form variance-covariance matrix are established. In addition, a goodness-of-fit test is developed to evaluate the adequacy of the model. The performance of proposed method and the comparison on the efficiency between the proposed method and the working independence method (Lu, 2005) are conducted in finite-sample situation by simulation studies. Finally a real data set from the Busselton Population Health Surveys is illustrated to validate the proposed methodology. The related proofs of the theorems are given in the Appendix.     

考虑环境变量的网络DEA模型

本文放松环境同质性的假定条件,构建包含环境变量的网络DEA模型,测度环境变量对生产前沿及生产决策单元效率的影响效应。构建的模型放松了投入产出变量集合与环境变量集合间的独立性假定,并且不需要先验性的判断环境变量的作用方向,弥补了现有处理环境变量方法的不足。提出的距离函数是一种非径向非导向的效率测度类型,能够有效地测度所有潜在松弛。Monte Carlo模拟结果表明本文构建的模型能够很好的测度环境变量对整体生产过程及其子生产过程的作用效应,创新生产过程分析结果表明出口依存度与技术创新效率间存在负相关关系,不考虑环境变量作用效应下测度的省际技术创新效率排名存在较大偏误。     

Efficiency Measure from Dynamic Stochastic Production Frontier: Application to Tunisian Textile, Clothing, and Leather Industries

This paper adresses the measurement of technical efficiency of textile, clothing, and leather (TCL) industries in Tunisia through a panel data estimation of a dynamic translog production frontier. It provides a perspective on productivity and efficiency that should be instructive to a developing economy which will face substantial competitive pressure along the gradual economic liberalisation process. The importance of TCL industries in Tunisian manufacturing sector is a reason for obtaining more knowledge of productivity and efficiency for this key industry. Dynamic is introduced to reflect the production consequences of the adjustment costs, which are associated with changes in factor inputs. Estimation of a dynamic error components model is considered using the system generalized method of moments (GMM) estimator suggested by Arellano and Bover (1995), Another look at the instrumental-variable estimation of error-components models, J. Econometrics68:29-51) and Blundell and Bond (Blundell, R., Bond, S. (1998a), Initial conditions and moment restrictions in dynamic panel data models. J. Econometrics87:115-143; Blundell, R., Bond, S. (1998b), GMM estimation with persistent panel data: an application to production functions, Paper presented at the Eighth International Conference on Panel Data, Goteborg University). Our study evaluates the sensitivity of the results, particularly of the efficiency measures, to different specifications. Firm-specific time-invariant technical efficiency is obtained using the Schmidt and Sickles (Schmidt, P., Sickles, R. C. (1984). Production frontiers and panel data. J. Bus. Econ. Stat.2:367-374) approach after estimating the dynamic frontier. We stress the importance of allowing for lags in adjustment of output to inputs and of controlling for time-invariant variables when estimating firm-specific efficiency. The results suggest that the system GMM estimation of the dynamic specification produces the most accurate parameter estimates and technical efficiency measure. Mean efficiency scores is of 68%. Policy implications of the results are outlined.     

中国市场价格扭曲测度：1952-2005

理论上,可以通过考察实际生产状态与潜在最优生产状态之间的差距,反映资源利用效率与市场扭曲程度。通常可以区分三类市场扭曲：生产无效率与要素市场局部价格扭曲、产品市场价格扭曲、要素市场全局价格扭曲。本文将各种市场扭曲的影响整合在统一框架内测度,以有效分析其相对强弱程度。使用随机前沿分析技术刻画生产可能性边界（PPF）,利用中国31个省区1952-2005年面板数据建立计量模型,进行中国市场扭曲程度测度,并展开时期比较与地区比较。     

Construction of New Three-Level Response Surface Designs

Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. In this article, we present a method for constructing three-level designs in order to explore and optimize response surfaces combining orthogonal arrays and covering arrays in a particular manner. The produced designs achieve the properties of rotatability, predictive performance and efficiency for the estimation of a second-order model.     

基于潜类别随机前沿的区域创新效率及其影响因素分析

运用可根据研究对象的潜在属性内生分组的潜类别随机前沿模型,采用1999-2012年中国各省区数据,研究各省区的创新效率及影响因素。结果表明:以人力资本水平和基础设施状况为条件变量,将全国各省区分成两个技术类别,分别有各自的技术前沿和函数形式,A类别中上海市的创新效率最高,B类别中河北省的创新效率最高;平均来看,各类的创新效率均呈上升趋势,贸易开放、产业结构和金融发展对创新效率均有显著的正向作用,同时创新效率在各类内部均存在俱乐部收敛。