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 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.     

Fixed and Random Effects in Stochastic Frontier Models

Received stochastic frontier analyses with panel data have relied on traditional fixed and random effects models. We propose extensions that circumvent two shortcomings of these approaches. The conventional panel data estimators assume that technical or cost inefficiency is time invariant. Second, the fixed and random effects estimators force any time invariant cross unit heterogeneity into the same term that is being used to capture the inefficiency. Inefficiency measures in these models may be picking up heterogeneity in addition to or even instead of inefficiency. A fixed effects model is extended to the stochastic frontier model using results that specifically employ the nonlinear specification. The random effects model is reformulated as a special case of the random parameters model. The techniques are illustrated in applications to the U.S. banking industry and a cross country comparison of the efficiency of health care delivery.JEL classification: C1, C4     

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.     

What is the environmental performance of firms overseas? An empirical investigation of the global gold mining industry

Using a large plant level data set, this paper carries out an econometric analysis of the environmental performance of multinational firms in the gold mining industry worldwide. The aim of the analysis is to determine if, by looking at the actual environmental performance of firms (as opposed to inferring such behavior from location decisions), we can shed any light on important questions in the literature on firm location decisions: Do pollution havens exist in the gold mining industry? Do foreign controlled gold mines perform environmentally worse or better than their domestic counterparts? We develop different ways of measuring environmental performance within the context of a Bayesian stochastic production frontier approach. In particular, we derive different ways of measuring technical and environmental efficiency. When we implement these methods in our empirical work, we find that results are robust across different models and ways of measuring efficiency. We find that gold mines exhibit a wide range of environmental efficiencies; some are clearly more efficient than others. However, and most importantly for our questions, we find that this variation in efficiencies cannot be systematically related to mine characteristics such as whether they are foreign or domestically controlled or whether they are located in developed versus developing countries.     

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。     

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.     

A Monte Carlo study of ranked efficiency estimates from frontier models

Parametric stochastic frontier models yield firm-level conditional distributions of inefficiency that are truncated normal. Given these distributions, how should one assess and rank firm-level efficiency? This study compares the techniques of estimating (a) the conditional mean of inefficiency and (b) probabilities that firms are most or least efficient. Monte Carlo experiments suggest that the efficiency probabilities are easier to estimate (less noisy) in terms of mean absolute percent error when inefficiency has large variation across firms. Along the way we tackle some interesting problems associated with simulating and assessing estimator performance in the stochastic frontier model.     

Market conditions and the effect of diversification on mutual fund performance: should funds be more concentrative under crisis?

This paper investigates the non-monotonic and non-linear effect of diversification on mutual fund performance. We apply a frontier-based efficiency measure, the stochastic frontier approach, to estimate fund efficiency and the benefit of diversification. The empirical results indicate that concentration strategy may not be appropriate for fund managers, and the benefit of diversification disappears or negatively affects performance when a fund holds too large a number of different stocks. Moreover, this paper examines whether market conditions moderate the relation between diversification and fund performance. The result shows that the benefit of diversification increases within low market return, high market volatility, and financial crisis, implying that the number of stocks needed to achieve a well-diversified portfolio increases under such market conditions.     

Aspects of statistical analysis in DEA-type frontier models

In Grosskopf (1995) and Banker (1995) different approaches and problems of statistical inference in DEA frontier models are presented. This paper focuses on the basic characteristics of DEA models from a statistical point of view. It arose from comments and discussions on both papers above. The framework of DEA models is deterministic (all the observed points lie on the same side of the frontier), nevertheless a stochastic model can be constructed once a data generating process is defined. So statistical analysis may be performed and sampling properties of DEA estimators can be established. However, practical statistical inference (such as test of hypothesis, confidence intervals) still needs artifacts like the bootstrap to be performed. A consistent bootstrap relies also on a clear definition of the data generating proces and on a consistent estimator of it: The approach of Simar and Wilson (1995) is described. Finally, some trails are proposed for introducing stochastic noise in DEA models, in the spirit of the Kneip-Simar (1995) approach.     

Adjustment and unobserved heterogeneity in dynamic stochastic frontier models

Stochastic frontier models with autocorrelated inefficiency have been proposed in the past as a way of addressing the issue of temporal variation in firm-level efficiency scores. They are justified using an underlying model of dynamic firm behavior. In this paper we argue that these models could have radically different implications for the expected long-run efficiency scores in the presence of unobserved heterogeneity. The possibility of accounting for unobserved heterogeneity is explored. Random- and correlated random-effects dynamic stochastic frontier models are proposed and applied to a panel of US electric utilities.     

Specification of Distance Functions Using Semi- and Nonparametric Methods with an Application to the Dynamic Performance of Eastern and Western European Air Carriers

In this paper we examine the productive performance of a group of three East European carriers and compare it to thirteen of their West European competitors during the period 1977–1990. We first model the multiple output/multiple input technology with a stochastic distance frontier using recently developed semiparametric efficient methods. The endogeneity of multiple outputs is addressed in part by introducing multivariate kernel estimators for the joint distribution of the multiple outputs and potentially correlated firm random effects. We augment estimates from our semiparametric stochastic distance function with nonparametric distance function methods, using linear programming techniques, as well as with extended decomposition methods, based on the Malmquist index number. Both semi- and nonparametric methods indicate significant slack in resource utilization in the East European carriers relative to their Western counterparts, and limited convergence in efficiency or technical change between them. The implications are rather stark for the long run viability of the East European carriers in our sample.     

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 stochastic frontier production functions with input-oriented technical efficiency

This paper deals with estimation of input-oriented (IO) technical inefficiency using a stochastic production frontier model. Econometrically the model is similar to a class of models that arise in specifying technical inefficiency in cost-minimizing and profit-maximizing frameworks. The standard maximum likelihood (ML) method that is used to estimate output-oriented (OO) technical efficiency cannot be applied to estimate these models. We use a simulated ML approach to estimate the IO production function and compare results from the IO and OO models, mainly to emphasize the point that estimated efficiency, returns to scale, technical change, etc., differ depending on whether one uses the model with IO or OO technical inefficiency.     

Stochastic FDH/DEA estimators for frontier analysis

In this paper we extend the work of Simar (J Product Ananl 28:183–201, 2007) introducing noise in nonparametric frontier models. We develop an approach that synthesizes the best features of the two main methods in the estimation of production efficiency. Specifically, our approach first allows for statistical noise, similar to Stochastic frontier analysis (even in a more flexible way), and second, it allows modelling multiple-inputs-multiple-outputs technologies without imposing parametric assumptions on production relationship, similar to what is done in non-parametric methods, like Data Envelopment Analysis (DEA), Free Disposal Hull (FDH), etc.... The methodology is based on the theory of local maximum likelihood estimation and extends recent works of Kumbhakar et al. (J Econom 137(1):1–27, 2007) and Park et al. (J Econom 146:185–198, 2008). Our method is suitable for modelling and estimation of the marginal effects onto inefficiency level jointly with estimation of marginal effects of input. The approach is robust to heteroskedastic cases and to various (unknown) distributions of statistical noise and inefficiency, despite assuming simple anchorage models. The method also improves DEA/FDH estimators, by allowing them to be quite robust to statistical noise and especially to outliers, which were the main problems of the original DEA/FDH estimators. The procedure shows great performance for various simulated cases and is also illustrated for some real data sets. Even in the single-output case, our simulated examples show that our stochastic DEA/FDH improves the Kumbhakar et al. (J Econom 137(1):1–27, 2007) method, by making the resulting frontier smoother, monotonic and, if we wish, concave.     

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.     

Measuring Cost Efficiency in European Banking: A Comparison of Frontier Techniques

This paper investigates the consistency of efficiency frontier methods on European banking samples. We measure the cost efficiency of banks from five European countries (France, Germany, Italy, Spain, Switzerland) with three approaches: stochastic frontier approach, distribution-free approach, and data envelopment analysis. We compare means, correlation coefficients, two public policy issues, and the correlation with standard measures of performance. In general, we conclude in favor of the lack of robustness between approaches, even if there are some similarities in particular between parametric approaches. We do, however, observe some correlation between all frontier approaches and standard measures of performance.     

Technical efficiency measures for dairy farms using panel data: A comparison of alternative model specifications

This article examines the impact of fixed effects production functions vis-à-vis stochastic production frontiers on technical efficiency measures. An unbalanced panel consisting of 96 Vermont dairy farmers for the 1971–1984 period was used in the analysis. The models examined incorporated both time-variant and time-invariant technical efficiency. The major source of variation in efficiency levels across models stemmed from the assumption made concerning the distribution of the one-sided term in the stochastic frontiers. In general, the fixed effects technique was found superior to the stochastic production frontier methodology. Despite the fact that the results of various statistical tests revealed the superiority of some specifications over others, the overall conclusion of the study is that the efficiency analysis was fairly consistent throughout all the models considered.     

How to improve the performances of DEA/FDH estimators in the presence of noise?

In frontier analysis, most nonparametric approaches (DEA, FDH) are based on envelopment ideas which assume that with probability one, all observed units belong to the attainable set. In these “deterministic” frontier models, statistical inference is now possible, by using bootstrap procedures. In the presence of noise, envelopment estimators could behave dramatically since they are very sensitive to extreme observations that might result only from noise. DEA/FDH techniques would provide estimators with an error of the order of the standard deviation of the noise. This paper adapts some recent results on detecting change points [Hall P, Simar L (2002) J Am Stat Assoc 97:523–534] to improve the performances of the classical DEA/FDH estimators in the presence of noise. We show by simulated examples that the procedure works well, and better than the standard DEA/FDH estimators, when the noise is of moderate size in term of signal to noise ratio. It turns out that the procedure is also robust to outliers. The paper can be seen as a first attempt to formalize stochastic DEA/FDH estimators.      

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.