Efficiency estimation and error decomposition in the stochastic frontier model: A Monte Carlo analysis

Critics of the deterministic approach to efficiency measurement argue that no allowance is made for measurement error and other statistical noise. Without controlling for measurement error, the resulting measure of efficiency will be distorted due to the contamination of noise. The stochastic frontier models purportedly allow both inefficiency and measurement error. Some proponents argue that the stochastic frontier models should be used despite the limitations because of the superior conceptual treatment of noise. However, the ultimate value of the stochastic frontier depends on its ability to properly decompose noise and inefficiency. This paper tests the validity of the stochastic frontier cross-sectional models using a Monte Carlo analysis. The results suggest that the technique does not accurately decompose the total error into inefficiency and noise components. Further, the results suggest that at best, the stochastic frontier is only as good as the deterministic model.     

动态异方差随机前沿模型的Bayesian推断

随机前沿模型中如果忽略单边干扰项的异质性(heterogeneity)往往导致错误的效率估计.从个体特征的影响和方差的时变性两方面对单边干扰项进行考虑,提出异方差动态随机前沿模型.利用Gibbs抽样方法对动态异方差随机前沿模型进行Bayesian分析.导出了模型参数的后验条件分布,对中小样本的模拟实验显示在最小后验均方误差准则下得到的参数估计值非常接近真值.对电力公司的实际数据进行分析显示对数无效率项的方差有一定的时变性.     

On the influence of model setting on stochastic frontier analysis

This article deals with the comparison of technical efficiency results through various stochastic frontier analysis models. Effects of model type, possible frontier shift, distribution of inefficiency term, different output variable, and estimator selection were explored. For this purpose, aggregated annual data within the EU construction sector from 2000 to 2015 were used for the efficiency estimation. The resulting efficiency values were compared by correlation coefficients. Among others, it has been shown that estimator selection may strongly affect efficiency estimate for particular models.     

Group and individual heterogeneity in a stochastic frontier model: Container terminal operators

Container ports are a major component of international trade and the global supply chain. Hence, the improvement of port efficiency can have a significant impact on the wider maritime economy. This paper deconstructs a representation in the existing literature that neglects the heterogeneity of individual and group-specific terminal operators. In its place, we present a hierarchical model to make a connection between efficiency and terminal operator group characteristics. The paper develops a stochastic frontier model that controls not only individual heterogeneity but also group-specific variations. The model decomposes the total stochastic derivation from the frontier into inefficiency, individual heterogeneity, group-specific variations, and noise components, with the estimation being performed using Markov chain Monte Carlo simulations. The validity of the model is tested with a panel of container terminal operator data from 1997-2004. Our findings show that terminal operator groups are important in promoting terminal efficiency at the global level, and that the operators with stevedore backgrounds show a higher efficiency than carriers.     

Efficiency distribution and the cost frontier

Efficiency measures derived from data envelopment analysis models are employed here to estimate the parametric forms of the efficiency distribution. Possible uses of this method in evaluating cost efficiency in a stochastic framework are also discussed. © 1998 John Wiley & Sons, Ltd.     

A stochastic frontier approach to running performance

^** Email: e.sterken{at}eco.rug.nl Long-distance running performance depends on age of the runnerand race distance. In this paper we apply a stochastic frontierapproach to estimate optimal running performance across distancesfrom 5000 m up to and including the marathon. We present agecorrection factors for 5000, 10000 and 15000 m, half-marathonand marathon distances for women and men. Two conclusions emerge:(1) official age grading tables are too optimistic for olderrunners and (2) running performance–age curves differacross distances.     

Group-specific stochastic production frontier models with parametric specifications

This paper develops a stochastic frontier model that not only focuses more on group-specific temporal variations in technical efficiency rather than individual temporal variations, but also allows for a parametric function of the time-varying coefficient of the efficiency factor. We derived the concentrated least squares estimator and its asymptotic properties. When applied to the Penn World data set, the group-specific models yield much more variation in the temporal patterns of efficiency across countries. This application demonstrates the feasibility of applying a group-specific stochastic frontier model with a parametric function of temporal pattern to a real empirical analysis.     

Measures of inefficiency in data envelopment analysis and stochastic frontier estimation

This paper discusses recent work in developing scalar measures of inefficiency which (a) comprehend all inefficiencies, including non-zero slacks, and (b) are readily interpretable and easily used in a wide variety of contexts. The opening section of the paper discusses some of the varied contexts in which uses of DEA are now being reported. This provides background for some of these measures. The closing section turns to simulation studies of DEA-regression combinations and possible inefficiency measures. Serious problems of bias in SF (Stochastic Frontier) regression approaches are identified. Extensions and modifications are suggested which can make a development of other inefficiency measures worthwhile for SF extensions to input-specific and multiple output evaluations.     

A comparison of chance-constrained DEA and stochastic frontier analysis: bank efficiency in Taiwan

We employed both chance-constrained data envelopment analysis (CCDEA) and stochastic frontier analysis (SFA) to measure the technical efficiency of 39 banks in Taiwan. Estimated results show that there are significant differences in efficiency scores between chance-constrained DEA and stochastic frontier production function. The advanced setting of the chance-constrained mechanism of DEA does not change the instinctive differences between DEA and SFA approaches. We further find that the ownership variable is still a significant variable to explain the technical efficiency in Taiwan, irrespective of whether a DEA, CCDEA or SFA approach is used.     

Estimation of stochastic volatility in the Hull-White model

Estimation of the stochastic volatility in the Hull-White framework is considered. Stock price is taken as the observation and the estimation problem is posed for the stochastic volatility. It is first shown that it is not possible to formulate this as the usual filtering problem, and an alternative formulation is proposed. A robust filtering equation is then derived suitable for real observation data.     

Optimal dividend payments in the stochastic Ramsey model

We consider the dividend payments of a self-financing firm in the stochastic Ramsey model. The firm invests in capital stock and its production technology is given by the Cobb–Douglas function. Our objective is to maximize the expected present value of future real dividends subject to a positive constraint on the capital stock. We use the penalization method to obtain a solution for the variational inequality associated with the optimal growth problem and give a synthesis of the optimal dividend policy.     

Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics

A nonlinear stochastic dynamical model on a typical HAB algae diatom and dianoflagellate densities was created and presented in this paper. Simplifying the model through a stochastic averaging method, we obtained a two-dimensional diffusion process of averaged amplitude and phase. The singular boundary theory of diffusion process and the invariant measure theory were applied in analyzing the bifurcation of stability and the Hopf bifurcation of the stochastic system. The critical value of the stochastic Hopf bifurcation parameter was obtained and the conclusion that the position of Hopf bifurcation drifting with the parameter increase is presented as a result.     

A stochastic inventory model

Summary In some cases arising in certain industries or military installations not only the demand for a particular commodity is a stochastic variable but its supply as well. In these cases it is convenient to consider the inventory level resulting from the interaction of supply and demand as a third stochastic variable. The variation of the inventory level in time can then be considered as a stochastic process. If this process is ergodic, the total inventory cost over a certain timeT may be represented as a function of the mean inventory level. This mean level can then be manipulated in such a way as to minimize the total inventory cost.

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Zusammenfassung Es kommt vor, daß in gewissen Industriezweigen sowohl der Verbrauch, als auch die Anlieferung eines bestimmten Gutes stochastische Variable sind. In solchen Fällen ist es zweckmäßig, wenn man die aus der Zusammenwirkung von Verbrauch und Anlieferung resultierende Vorratsmenge als eine dritte stochastische Variable einführt. Man kann dann die Oszillationen der Vorratsmenge in der Zeit als einen stochastischen Prozeß auffassen. Falls dieser Prozeß ergodisch ist, können die gesamten Vorratshaltungskosten für eine bestimmte ZeitT dargestellt werden als eine Funktion der mittleren Vorratsmenge. Diese mittlere Vorratsmenge kann dann so bestimmt werden, daß sie die gesamten Vorratshaltungskosten minimalisiert.

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SHAPE Air Defence Technical Centre. Formerly with Tidewater Oil Company, Los Angeles, California, where the present problem was originally investigated.

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Vorgel. v.:J. Nitsche.     

Bayesian estimation of the half-normal regression model with deterministic frontier

A regression model with deterministic frontier is considered. This type of model has hardly been studied, partly owing to the difficulty in the application of maximum likelihood estimation since this is a non-regular model. As an alternative, the Bayesian methodology is proposed and analysed. Through the Gibbs algorithm, the inference of the parameters of the model and of the individual efficiencies are relatively straightforward. The results of the simulations indicate that the utilized method performs reasonably well.     

A stochastic back-up model

Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, pp. 52–63, 1991.     

The stochastic Heisenberg model

The stochastic Heisenberg model is a classical mechanical model for a magnet in contact with a medium at fixed temperature. The dynamics in the infinite volume limit is a well-defined Markov process. Equilibrium states exist, and in this limit there is the possibility of multiple equilibrium states at low temperature, corresponding to different directions of magnetism.     

Asymptotic behaviour of the stochastic Lotka-Volterra model

This paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process, namely the Lotka-Volterra model. The stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart. Indeed, the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations.     

Mean-field limit for the stochastic Vicsek model

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behaviour of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number N of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coupling argument to the present case in which both the particle system and the PDE are defined on a surface rather than on the whole space R^d. As part of the study we give existence and uniqueness results for both the particle system and the PDE.     

Fluctuations of the front in a stochastic combustion model

We consider an interacting particle system on the one-dimensional lattice Z modeling combustion. The process depends on two integer parameters 2?a?M<∞. Particles move independently as continuous time simple symmetric random walks except that (i) when a particle jumps to a site which has not been previously visited by any particle, it branches into a particles, (ii) when a particle jumps to a site with M particles, it is annihilated. We start from a configuration where all sites to the left of the origin have been previously visited and study the law of large numbers and central limit theorem for rt, the rightmost visited site at time t. The proofs are based on the construction of a renewal structure leading to a definition of regeneration times for which good tail estimates can be performed.     

Efficiency and total quality management in health care organizations: A dynamic frontier approach

This paper analyses hospital performance using Data Envelopment Analysis (DEA) and the Malmquist productivity index. We follow two approaches to quantify movements in productivity: (1) the traditional approach that only considers output and input variables; and (2) a more comprehensive approach that incorporates movements in quality and restricts some achievements, if quality is reduced. On the premise that the indicator for quality (nosocomial infections) is equivalent to a bad output, we explore the characteristics of, and compare the results of, the different technological ways to incorporate quality (good or bad attributes, strong or weak disposability technological assumptions). After discussing the virtues and limitations of the existing possibilities, the paper presents a better formulation that allows the preservation of TQM postulates. The decomposition in the Malmquist productivity index shows an improvement in productivity and a positive technical change, especially when quality is introduced. This paper forms part of a more extensive research work, financed by the Spanish Science and Technology Ministry (ref. SEC2003-047707).