Estimation of technical inefficiency effects using panel data and doubly heteroscedastic stochastic production frontiers

In previous studies, measures of technical inefficiency effects derived from stochastic production frontiers have been estimated from residuals which are sensitive to specification errors. This study corrects for this inaccuracy by extending the doubly heteroscedastic stochastic cost frontier suggested by Hadri (1999) to the model for technical inefficiency effects. This model is a stochastic frontier production function for panel data as proposed by Battese and Coelli (1995). The study uses, for illustration of the techniques, data on 101 mainly cereal farms in England. We find that the correction for heteroscedasticity is supported by the data. Both point estimates and confidence intervals for technical efficiencies are provided. The confidence intervals are constructed by extending the “Battese-Coelli” method reported by Horrace and Schmidt (1996) by allowing the technical inefficiency to be time varying and the disturbance terms to be heteroscedastic. The confidence intervals reveal the precision of technical efficiency estimates and show the deficiencies of making inferences based exclusively on point estimates. First version received: March 2000/Final version received: Oct. 2001 RID="*" ID="*"  The authors are grateful to the Economic and Social Research Council for access to their Data Archive which has provided the data for this research. We are indebted to Badi Baltagi and two anonymous referees for their helpful comments and suggestions. The usual caveat applies.     

Maximum entropy: a stochastic frontier approach for electricity distribution regulation

The literature on incentive-based regulation in the electricity sector indicates that the size of this sector in a country constrains the choice of frontier methods as well as the model specification itself to measure economic efficiency of regulated firms. The aim of this study is to propose a stochastic frontier approach with maximum entropy estimation, which is designed to extract information from limited and noisy data with minimal statements on the data generation process. Stochastic frontier analysis with generalized maximum entropy and data envelopment analysis—the latter one has been widely used by national regulators—are applied to a cross-section data on thirteen European electricity distribution companies. Technical efficiency scores and rankings of the distribution companies generated by both approaches are sensitive to model specification. Nevertheless, the stochastic frontier analysis with generalized maximum entropy results indicate that technical efficiency scores have similar distributional properties and these scores as well as the rankings of the companies are not very sensitive to the prior information. In general, the same electricity distribution companies are found to be in the highest and lowest efficient groups, reflecting weak sensitivity to the prior information considered in the estimation procedure.

     

Is it efficient to analyse efficiency rankings?

When production functions are estimated as frontier functions, the deviations from the frontier can be interpreted as individual inefficiency estimates. Unfortunately, it has recently been shown that efficiency differences across individuals are very often statistically insignificant. In this paper, we will analyse the consequences of the consideration of confidence statements for the reliability of efficiency rankings. The stochastic frontier and confidence intervals derived by Horrace and Schmidt are compared to the COLS approach and bootstrap confidence intervals. The membership function is proposed as a simple Monte-Carlo approximation for the probability for an individual to be the most efficient in the sample. First version received: May 1998/final version accepted: July 1999     

Specification and testing of count data recreation demand functions

This article examines the effects of alternative formulations of count data recreation demand models on parameter estimates, model selection, and consumer surplus. The results indicate that large parameter and consumer surplus differences exists across the various count model formulations. More importantly, the results show that distributional assumptions, heteroscedastic functional forms, and overdispersion can have a substantial effect on consumer surplus estimates.     

Health expenditure models: A comparison using panel data

In this article, we focus on the estimation of outpatient expenditures with panel data. We model the logarithm of expenditures and consider five different models. The first two are two-part and sample selection cross-section models. Two-part panel data models turn out to be inappropriate for dealing with expenditures. We thus estimate sample selection models with panel data: one without a lagged dependent variable and two with a lagged dependent variable. These two latter models differ in their assumptions on the variance of the residuals. Modelling heteroscedasticity may indeed be important to avoid the bias due to the retransformation problem. We show that lagged dependent variables are important factors for heteroscedasticity. For the models with state dependence, we provide a new solution to the initial conditions problem by controlling for generalised residuals. We establish that panel data models highly improve the correlation explained by the model in the time-series dimension without damaging the fit in the cross-section dimension. For all indicators of fit, the model with state dependence and heteroscedasticity seems to dominate the others.     

COST FUNCTIONS AND COST EFFICIENCY IN ELECTRICITY DISTRIBUTION: A STOCHASTIC FRONTIER APPROACH*

The paper develops a cost frontier model of electricity distribution and estimates it on data for the 12 regional electricity companies of England and Wales. It is found that some significant cost drivers in cross-section estimation are insignificant when the model is estimated on panel data, highlighting the well-known drawbacks of cross-section estimation. Panel data estimation suggests that the main determinants of distribution operating costs are the number of customers in the area and simultaneous maximum demand. These results and the efficiency rankings of the companies are not sensitive to changes in error distribution assumptions and sample size. There is also significant evidence of economies of scale. There is a small but significant effect on cost efficiency from privatization, but this is as likely to be due to the changes in accounting policies at the time of privatization as any real effect.     

Risk forecasting models and optimal portfolio selection

This study analyses, from an investor's perspective, the performance of several risk forecasting models in obtaining optimal portfolios. The plausibility of the homoscedastic hypothesis implied in the classical Markowitz model is dicussed and more general models which take into account assymetry and time varying risk are analysed. Specifically, it studies whether ARCH-type based models obtain portfolios whose risk-adjusted returns exceed those of the classical Markowitz model. The same analysis is performed with models based on the Lower Partial Moment (LPM) which take into account the assymetry in the distribution of returns. The results suggest that none of the models achieve a clearly superior average performance. It is also found that models based on semivariance perform as well as those based on the variance, but not better than, even if the evaluation criterion is based on the Reward-to-Semivariance ratio. When attention turns to the analysis of worst case performance, the results are clearly different. Models which employ LPM with a high degree of risk aversion (n>2) as the risk measure are consistently superior to those which employ a symmetric measure, either homoscedastic or heteroscedastic.     

Estimating market power using a composed error model

We present a maximum likelihood based composed error model to estimate market powers of firms. In our model, the stochastic part of the supply relation includes two random components: the conventional two‐sided error term and a random term, which is capturing firm‐specific conducts. Moreover, we provide a generalization of scaled Stevenson stochastic frontier model in the context of doubly truncated normal distributions. We estimate the market powers of Chicago based airlines as an empirical example that is showing the applicability of our estimation procedure.     

A stochastic frontier model of the productive efficiency of Korean container terminals

A central objective of port privatization and/or deregulation policies is stimulating greater efficiency by engendering a more competitive market and commercial approach to management. Korea provides a prime example of a nation that is implementing such policies. Also, its ports play a pivotal role in world shipping, particularly in the ever-burgeoning container market. The success of these policies in increasing the productive efficiency of Korean container terminals is assessed. The UK container terminal sector provides a useful benchmark for comparison since privatization and deregulation have formed an integral part of UK port reforms for nearly 20 years and the effect on efficiency, having had time to mature, will be much easier to gauge. The stochastic frontier model is justified as the chosen methodology for estimating productive efficiency levels and is applied to cross-sectional data under a variety of distributional assumptions. A panel data model is also estimated. Results are consistent and suggest (1) The degree of private sector involvement in sample container terminals is positively related to productive efficiency and (2) Improved productive efficiency has followed the implementation of privatization and deregulation policies within the Korean sector. Even though not categorical, these conclusions are important because the market for container throughput is internationally competitive and if policies which promote competition between Korean container terminals lead to greater productive efficiency, this will inevitably make the sector as a whole more competitive internationally.     

Predicting technical effciency in stochastic production frontier models in the presence of misspecification: a Monte-Carlo analysis

This paper provides a theoretical explanation for the sensitivity of technical efficiency measures to the choice of functional specification in stochastic production frontier models. It is shown that inappropriate functional specifications translate into a misspecification in the conditional mean of the stochastic frontier regression model. This misspecification, in turn, results in estimates of technical efficiency, confidence intervals and production elasticities being biased, even asymptotically. Monte-Carlo simulations reveal that the severity of the bias depends on the functional specification and the percentage contribution of the variance of technical inefficiency to the total variance of the composed errors.     

Modelling Exogenous Variables in Human Capital Formation through a Heteroscedastic Stochastic Frontier

The objective of this paper is to suggest the use of a stochastic frontier model in which the inefficiency component is heteroscedastic in the measurement of technical efficiency in Human Capital Formation in the Italian University System. The heteroscedastic frontier model enables one to consider the effect of students’ individual characteristics and the influences of the resources and organization of the specific faculty on efficiency. The suggested model is applied to the case of Florence University graduates. The results show that the model specification is strongly supported by the data. Moreover, the suggested specification explains variation in technical efficiency in terms of graduate-specific factors. The technical efficiency scores obtained are comparable across faculties.

Cost efficiency of the Chinese banking sector: A comparison of stochastic frontier analysis and data envelopment analysis

This paper investigates the consistency of efficiency scores obtained from the stochastic frontier analysis and data envelopment analysis methods. We estimate cost efficiency and economies of scale based on an unbalanced panel data set of Chinese banks over the period 1994 to 2007. The results suggest moderate consistency between parametric and non-parametric frontier methods in efficiency scores rankings, identification of best and worst practise banks, the stability of efficiency scores over time and correlation between frontier efficiency and accounting based performance measures. Based on the findings, we conclude that the use of multiple frontier techniques for efficiency analysis is to be strongly recommended and that this methodological cross-checking analysis will result in more robust and convincing assessments of bank performance.     

Consistency in performance rankings: the Peru water sector

Regulators can utilize a number of alternative methodologies for comparing firm efficiency, but these approaches need to be robust to be accepted by stakeholders. This study evaluates the consistency of water-utility performance rankings for Peruvian water utilities. The results indicate that data envelopment analysis (DEA) and stochastic frontier analysis (SFA) yield similar rankings in this case. In addition, the techniques have comparable success for identifying the best and worst performing utilities. However, these rankings based on sophisticated statistical techniques are not highly correlated with those developed by the Peruvian water regulator (SUNASS). This result does not invalidate the performance rankings obtained by the regulator, since those rankings are based on more dimensions of utility performance. However, they illustrate the importance of developing sound techniques for identifying weak utilities. Improvements in sector performance require that benchmarking be given greater attention than in the past.     

Allocative and scale efficiency among maize farmers in Zambia: a zero efficiency stochastic frontier approach

The commonly used stochastic frontier model assumes that all firms are inefficient. In this specification, inefficiency is non-negative, and the probability of inefficiency being exactly zero is also zero. To the extent that efficiency varies widely across farms in under-developed economies, it is important to employ techniques that account for both inefficiency and full efficiency to ensure unbiased efficiency estimates. In this study, we employ a zero-inefficiency stochastic frontier model to examine allocative efficiency and scale economies, as well as key determinants of efficiency among Zambian maize farmers. The results show that, unlike the stochastic frontier model, the zero-inefficiency stochastic frontier model successfully allows for both fully efficient and inefficient firms to be accounted for in the estimation procedure. The estimates also reveal the presence of scale economies, with the zero-inefficiency stochastic frontier model better predicting scale efficiency compared to the stochastic frontier model. The findings also show that inefficiency is explained by the level of education, access to extension services, distance to markets and access to credit.     

地方财政支农投入与农业技术效率的省际差异:1995～2011年

运用参数法中的随机前沿分析法,结合我国1995—2011年的省级面板数据,选取地方财政"一般预算支出"中的"农林水事务"支出作为代理变量,分析地方财政支农投入对农业技术效率的影响,发现地方财政支农投入对于农业技术效率以及农业产出具有显著的积极作用,财政支农投入差异是我国各省市农业技术效率差异的重要根源之一。但鉴于目前我国在中央与地方的财政分配上严重倾向于中央财政,不少省市的地方财政收入很有限,财政支农投入的数量、结构、区域分布等方面都亟待调整和完善。     

SIMULATED MAXIMUM LIKELIHOOD ESTIMATION BASED ON FIRST‐ORDER CONDITIONS*

I describe a strategy for structural estimation that uses simulated maximum likelihood (SML) to estimate the structural parameters appearing in a model's first‐order conditions (FOCs). Generalized method of moments (GMM) is often the preferred method for estimation of FOCs, as it avoids distributional assumptions on stochastic terms, provided all structural errors enter the FOCs additively, giving a single composite additive error. But SML has advantages over GMM in models where multiple structural errors enter the FOCs nonadditively. I develop new simulation algorithms required to implement SML based on FOCs, and I illustrate the method using a model of U.S. multinational corporations.     

Testing commodity futures market efficiency under time-varying risk premiums and heteroscedastic prices

We propose a novel test to measure market efficiency while estimating the time-varying risk premiums of commodity futures, given that the prices are heteroscedastic. The risk premium is estimated using a state-space model with a Kalman filter modified for heteroscedasticity. Using 79 commodity futures traded on 16 exchanges during the period 2000–2014 and a Monte Carlo simulation, we demonstrate that the proposal produces robust results compared with conventional approaches. The global financial crisis has improved the efficiency and affected the trading volumes of commodity futures, but it has had no effect on the average or the volatility of risk premiums.     

A Spatial Stochastic Frontier Model with Spillovers: Evidence for Italian Regions

Efficiency measurement using stochastic frontier models is well established in applied econometrics. However, no published work seems to be available on efficiency analysis using spatial data dealing with possible spatial dependence between regions. This article considers a stochastic frontier model with decomposition of inefficiency into an idiosyncratic and a spatial, spillover component. Exact posterior distributions of parameters are derived, and computational schemes based on Gibbs sampling with data augmentation are proposed to conduct simulation‐based inference and efficiency measurement. The new method is illustrated using production data for Italian regions (1970–1993). Clearly, further theoretical and empirical research on the subject would be of great interest.     

A performance assessment of the Angolan soccer league

This article analyses the technical efficiency of the Angolan soccer league from 2008 to 2014, using a translog distance stochastic frontier model. The Greene stochastic frontier model, presented in 2005, and Kumbhakar stochastic frontier model, presented in 1990, are adopted, and the covariates used include Luanda location, funding by the oil company Sonangol, club supported by rich fans and club relegated during the period. Policy implications are then derived.     

Soccer transfers,team efficiency and the sports cycle in the most valued European soccer leagues – have European soccer teams been efficient in trading players?

The sale of soccer players is a serious issue for the sustainability of professional teams. This article discusses the efficiency of the values that 183 European soccer teams have received for the sales of their players since 2007. We estimated stochastic frontiers for these soccer teams using stochastic frontier analysis. We found that teams with higher numbers of titles, with huge past acquisitions of players, and achieving good rankings in the previous season tend to receive more transfer inflows. The efficiency of these inflows can be significantly influenced if the team exhibits a long sports history or if the team participates in the Champions League or in the Europa League.