The Components of Output Growth: A Stochastic Frontier Analysis

This paper uses Bayesian stochastic frontier methods to decompose output change into technical, efficiency and input changes. In the context of macroeconomic growth exercises, which typically involve small and noisy data sets, we argue that stochastic frontier methods are useful since they incorporate measurement error and assume a (flexible) parametric form for the production relationship. These properties enable us to calculate measures of uncertainty associated with the decomposition and minimize the risk of overfitting the noise in the data. Tools for Bayesian inference in such models are developed. An empirical investigation using data from 17 OECD countries for 10 years illustrates the practicality and usefulness of our approach.     

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.     

Panel estimators and the identification of firm-specific efficiency levels in parametric,semiparametric and nonparametric settings

The paper analyzes a number of competing approaches to modeling efficiency in panel studies. The specifications considered include the fixed effects stochastic frontier, the random effects stochastic frontier, the Hausman–Taylor random effects stochastic frontier, and the random and fixed effects stochastic frontier with an AR(1) error. I have summarized the foundations and properties of estimators that have appeared elsewhere and have described the model assumptions under which each of the estimators have been developed. I discuss parametric and nonparametric treatments of time varying efficiency including the Battese–Coelli estimator and linear programming approaches to efficiency measurement. Monte Carlo simulation is used to compare the various estimators and to assess their relative performances under a variety of misspecified settings. A brief illustration of the estimators is conducted using U.S. banking data.     

Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach

We propose a kernel-based Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The primary feature of this framework is that the unknown distribution of inefficiency is approximated by a transformed Rosenblatt-Parzen kernel density estimator. To justify the kernel-based model, we conduct a Monte Carlo study and also apply the model to a panel of U.S. large banks. Simulation results show that the kernel-based model is capable of providing more precise estimation and prediction results than the commonly-used exponential stochastic frontier model. The Bayes factor also favors the kernel-based model over the exponential model in the empirical application.

     

Consistent estimation of technical and allocative efficiencies for a semiparametric stochastic cost frontier with shadow input prices

Conventional parametric stochastic cost frontier models are likely to suffer from biased inferences due to misspecification and the ignorance of allocative efficiency (AE). To fill up the gap in the literature, this article proposes a semiparametric stochastic cost frontier with shadow input prices that combines a parametric portion with a nonparametric portion and that allows for the presence of both technical efficiency (TE) and AE. The introduction of AE and the nonparametric function into the cost function complicates substantially the estimation procedure. We develop a new estimation procedure that leads to consistent estimators and valid TE and AE measures, which are proved by conducting Monte Carlo simulations.     

A quantile-based approach for relative efficiency measurement

Two popular approaches for efficiency measurement are a non-stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Institutions and Bank Performance: A Stochastic Frontier Analysis*

This article investigates the impact of institutions on bank efficiency and technology, using a stochastic frontier analysis of a data set of 7,959 banks across 136 countries over 10 years. The results confirm the importance of well‐developed institutions for the efficient operation of commercial banks. Furthermore, the insights reveal the impact of institutional reforms in improving bank efficiency. The results are robust to adjustments in country‐specific effects, achieved by including country dummies, as well as across different risk profiles. Moreover, they provide empirical evidence in support of the public view of the banking sector.     

Confidence statements for efficiency estimates from stochastic frontier models

This paper is an empirical study of the uncertainty associated with technical efficiency estimates from stochastic frontier models. We show how to construct confidence intervals for estimates of technical efficiency levels under different sets of assumptions ranging from the very strong to the relatively weak. We demonstrate empirically how the degree of uncertainty associated with these estimates relates to the strength of the assumptions made and to various features of the data.     

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.     

Estimation of stochastic frontier models based on multimodel inference

In most empirical studies, once the best model has been selected according to a certain criterion, subsequent analysis is conducted conditionally on the chosen model. In other words, the uncertainty of model selection is ignored once the best model has been chosen. However, the true data-generating process is in general unknown and may not be consistent with the chosen model. In the analysis of productivity and technical efficiencies in the stochastic frontier settings, if the estimated parameters or the predicted efficiencies differ across competing models, then it is risky to base the prediction on the selected model. Buckland et al. (Biometrics 53:603?C618, 1997) have shown that if model selection uncertainty is ignored, the precision of the estimate is likely to be overestimated, the estimated confidence intervals of the parameters are often below the nominal level, and consequently, the prediction may be less accurate than expected. In this paper, we suggest using the model-averaged estimator based on the multimodel inference to estimate stochastic frontier models. The potential advantages of the proposed approach are twofold: incorporating the model selection uncertainty into statistical inference; reducing the model selection bias and variance of the frontier and technical efficiency estimators. The approach is demonstrated empirically via the estimation of an Indian farm data set.     

Input- and Output-Oriented Technical Efficiency of Ukrainian Collective Farms, 1989–1992: Bayesian Analysis of a Stochastic Production Frontier Model

We propose estimation of a stochastic production frontier model within a Bayesian framework to obtain the posterior distribution of single-input-oriented technical efficiency at the firm level. All computations are carried out using Markov chain Monte Carlo methods. The approach is illustrated by applying it to production data obtained from a survey of Ukrainian collective farms. We show that looking at the changes in single-input-oriented technical efficiency in addition to the changes in output-oriented technical efficiency improves the understanding of the dynamics of technical efficiency over the first years of transition in the former Soviet Union.     

A new approach to estimating a profit frontier using the censored stochastic frontier model

The translog profit functional form is widely used to study technical efficiency for banks. Although this functional form is known as being flexible, it is not applicable to those banks incurring economic losses. The recently developed approach, i.e., the censored stochastic frontier model (CSFM), by Tsay et al. (2013) appears to be superior to existing approaches, since CSFM does not need to transform negative profit into positive profit before taking the natural logarithm. The transformation with respect to the profit variable tends to bias the parameter estimates of the profit frontier and the subsequent profit efficiency measure. We show that the parameter estimates of CSFM have the desirable statistical properties. Moreover, empirical results reveal that the mean profit efficiency of CSFM is more robust than those models using transformed profits across the sub-periods 1991–1998 and 1999–2009.     

生产效率的区域特征与生产率增长的分解——基于主成分分析与随机前沿超越对数生产函数的方法

运用随机前沿超越对数生产函数和2001～2006年省际面板数据,本文研究了我国各地区的全要素生产率以及生产效率的区域特征,利用提取主成分法得到的变量,对生产效率进行影响因素分析。实证结果表明,外商投资和基础设施的实际有效利用对各地区生产效率有重要的影响;前沿技术进步是全要素生产率的主导因素;东部地区前沿技术进步率与生产效率都高于中西部;西部前沿技术进步表现为分化的特征,而中部则有趋同的趋势。     

Efficiency of U.S. hospitals between 2001 and 2011

This study focuses on finding the trend of efficiency in the healthcare industry in recent years. We applied stochastic frontier analysis and data envelopment analysis methods to capture the efficiency of 1,471 hospitals and found a sign of the Baumol effect, which is detected by the decreasing trend of hospital efficiency with increasing trend of labor costs. Furthermore, we compared the results of both approaches (stochastic frontier and data envelope analyses) in capturing efficiency scores and suggest the U‐shaped curve of the size effect may indicate the practice of “cream skimming” by some small hospitals.     

Estimation and efficiency measurement in stochastic production frontiers with ordinal outcomes

We consider Bayesian estimation of a stochastic production frontier with ordered categorical output, where the inefficiency error is assumed to follow an exponential distribution, and where output, conditional on the inefficiency error, is modelled as an ordered probit model. Gibbs sampling algorithms are provided for estimation with both cross-sectional and panel data, with panel data being our main focus. A Monte Carlo study and a comparison of results from an example where data are used in both continuous and categorical form supports the usefulness of the approach. New efficiency measures are suggested to overcome a lack-of-invariance problem suffered by traditional efficiency measures. Potential applications include health and happiness production, university research output, financial credit ratings, and agricultural output recorded in broad bands. In our application to individual health production we use data from an Australian panel survey to compute posterior densities for marginal effects, outcome probabilities, and a number of within-sample and out-of-sample efficiency measures.     

Estimating production frontiers and efficiency when output is a discretely distributed economic bad

This article studies the estimation of production frontiers and efficiency scores when the commodity of interest is an economic bad with a discrete distribution. Existing parametric econometric techniques (stochastic frontier methods) assume that output is a continuous random variable but, if output is discretely distributed, then one faces a scenario of model misspecification. Therefore a new class of econometric models has been developed to overcome this problem. The Delaporte subclass of models is studied in detail, and tests of hypotheses are proposed to discriminate among parametric models. In particular, Pearson’s chi-squared test is adapted to construct a new kernel-based consistent Pearson test. A Monte Carlo experiment evaluates the merits of the new model and methods, and these are used to estimate the frontier and efficiency scores of the production of infant deaths in England. Extensions to the model are discussed.     

On maximum likelihood estimation of stochastic frontier production models

The iterative algorithm suggested by Greene (1982) for the estimation of stochastic frontier production models does not necessarily solve the likelihood equations. Corrected iterative algorithms which generalize Fair's method (1977) and solve the likelihood equations are derived. These algorithms are compared with the Newton method in an empirical case. The Newton method is more time saving than these algorithms.     

随机前沿方法的研究进展与展望

本文对随机前沿方法发展的历史沿革及其在中国的应用做了评述。围绕随机前沿方法的基本特征,首先阐述了其启蒙与产生的轨迹,然后对使用前提、分布假定、估计方法、异方差等基本问题以及效率的时变性、外生影响等研究的理论进展及相关应用做了梳理,并对全要素生产率的变化做了分解,评述了随机前沿方法在经验分析中的优势与作用,总结了国内区域与行业经济增长中随机前沿方法的应用与不足,最后对其研究发展做了展望。     

Stochastic frontier models with random coefficients

The paper proposes a stochastic frontier model with random coefficients to separate technical inefficiency from technological differences across firms, and free the frontier model from the restrictive assumption that all firms must share exactly the same technological possibilities. Inference procedures for the new model are developed based on Bayesian techniques, and computations are performed using Gibbs sampling with data augmentation to allow finite‐sample inference for underlying parameters and latent efficiencies. An empirical example illustrates the procedure. Copyright © 2002 John Wiley & Sons, Ltd.