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.     

Comparing frontier methods for economic–environmental trade-off analysis

This paper uses a mechanistic frontier approach as a reference to evaluate the ability of conventional parametric (SFA) and non-parametric (DEA) frontier approaches for analyzing economic–environmental trade-offs. Conventional frontier approaches are environmentally adjusted through incorporating the materials balance principle. The analysis is worked out for the Flemish pig finishing case, which is both representative and didactic. Results show that, on average, SFA and DEA yield adequate economic–environmental trade-offs. Both methods are good estimators for technical efficiency. Cost allocative and environmental allocative efficiency scores are less robust, due to the well-known methodological advantages and disadvantages of SFA and DEA. For particular firms, SFA, DEA and the mechanistic approach may yield different economic–environmental trade-offs. One has therefore to be careful when using conventional frontier approaches for firm-specific decision support. The mechanistic approach allows for optimizing performances per average present finisher, which is the production unit in pig finishing. Conventional frontier methods do not allow for this optimization since the number of average present finishers varies along the production functions. Since the mechanistic production function is based on underlying growth, feed uptake and mortality functions, additional firm-specific indicators can also be calculated at each point of the production function.     

Effects of heterogeneity on bank efficiency scores

Bank efficiency estimates often serve as a proxy of managerial skill since they quantify sub-optimal production choices. But such deviations can also be due to omitted systematic differences among banks. In this study, we examine the effects of heterogeneity on bank efficiency scores. We compare different specifications of a stochastic cost and alternative profit frontier model with a baseline specification. After conducting a specification test, we discuss heterogeneity effects on efficiency levels, ranks and the tails of the efficiency distribution. We find that heterogeneity controls influence both banks’ optimal costs and profits and their ability to be efficient. Differences in efficiency scores are important for more than only methodological reasons. First, different ways of accounting for heterogeneity result in estimates of foregone profits and additional costs that are significantly different from what we infer from our general specification. Second, banks are significantly re-ranked when their efficiency is estimated with a specification other than the preferred, general specification. Third, the general specification gives the most reliable estimates of the probability of distress, although differences to the other specifications are low.     

Determinants of bank efficiency: The case of Brazil

This paper analyzes the efficiency of the Brazilian banking sector over the post-privatization period of 2000–2007. We employ a Bayesian stochastic frontier approach, which provides exact efficiency estimates and confidence intervals and thus, allows an accurate comparison across institutions and bank groups. The results suggest that large banks are the most cost and profit efficient, supporting the concentration process observed in recent years. Foreign banks have achieved a good performance through either the establishment of new affiliates and the acquisition of local banks. The remaining public banks have had improvements in cost efficiency, but are relatively profit inefficient. Finally, we observe a positive impact of capitalization on efficiency.     

Estimation of Stochastic Frontier Cost Function Using Data Envelopment Analysis: an Application to the AT&T Divestiture

This study develops a new use of data envelopment analysis for estimating a stochastic frontier cost function that is assumed to have two different error components: a one-sided disturbance (representing technical and allocative inefficiencies) and a two-sided disturbance (representing an observational error). The two error components are handled by data envelopment analysis in combination with goal programming/constrained regression. The approach proposed in this study can avoid several statistical assumptions used in conventional methods for estimating a stochastic frontier function. As an important application, this study uses the estimation technique to obtain an AT&T stochastic frontier cost function. As a result, this study measures technical and allocative efficiencies of AT&T production process and review its natural monopoly issue. The estimated stochastic frontier cost function is also compared with the other cost function models used for previous studies concerning the divestiture of the telephone industry.     

Cost efficiency and scale economies in general dental practices in the US: a non-parametric and parametric analysis of Colorado data

This paper uses both the non-parametric method of data envelopment analysis (DEA) and the econometric method of stochastic frontier analysis (SFA) to study the production technology and cost efficiency of the US dental care industry using practice level data. The American Dental Association 2006 survey data for a number of general dental practices in the state of Colorado in the US are used for the empirical analysis. The findings suggest that the cost efficiency score is between 0.79 and 0.87, on average, and the cost inefficiency is mostly due to allocative rather than technical inefficiency. The optimal output level for a dental practice to fully exploit the economies of scale is estimated to be at $1.68 million. Average cost at this level of output is 50.6 cents for each dollar of gross billing generated. The DEA and SFA approaches provide generally consistent results.     

Stochastic production frontiers and panel data: A latent variable framework

This paper deals with the issue of estimating production frontier and measuring efficiency from a panel data set. First, it proposes an alternate method for the estimation of a production frontier on a short panel data set. The method is based on the so-called mean-and-covariance structure analysis which is closely related to the generalized method of moments. One advantage of the method is that it allows us to investigate the presence of correlations between individual effects and exogenous variables without the requirement of some available instruments uncorrelated with the individual effects as in instrumental variable estimation. Another advantage is that the method is well suited to a panel data set with a short number of periods. Second, the paper considers the question of recovering individual efficiency levels from the estimates obtained from the mean-and-covariance structure analysis. Since individual effects are here viewed as latent variables, they can be estimated as factor scores, i.e., weighted sums of the observed variables. We illustrate the proposed methods with the estimation of a stochastic production frontier on a short panel data of French fruit growers.     

Distribution of cost and profit efficiency: Evidence from Indian banking

This paper uses the nonparametric DEA methodology to estimate cost and profit efficiency of Indian banks during the post-reform period. The results show considerable variation in average levels of profit efficiency across various ownership categories of banks. In general, state owned banks are found to be more efficient than their private counter parts. Further, efficiency tends to be low among the small banks (assets up to Rs. 50 billion), indicating that at the existing scale of operations, these banks are operating far below the efficient frontier. We also examine the distribution of efficiency using nonparametric kernel density estimates. The analysis reveals a rightward-shift of the efficiency distribution over the years. A major part of this shift comes from the state owned banks. Based on the conditional distribution, the study finds strong evidence of ownership explaining the efficiency differential of banks. Additionally, bank size and product-mix are also found to be important, although to a lesser extent.     

Efficiency measurement in the stochastic frontier model

Deterministic models of technical efficiency assume that all deviations from the production frontier are due to inefficiency. Critics argue that no allowance is made for measurement error and other statistical noise so that the resulting efficiency measure will be contaminated. The stochastic frontier model is an alternative that allows both inefficiency and measurement error. Advocates argue that the stochastic frontier models should be used despite other potential limitations because of the superior conceptual treatment of noise. As will be demonstrated in this paper, however, the assumed shape of the error distributions is used to identify a key production function parameter. Therefore, the stochastic frontier models, like the deterministic models, cannot produce absolute measures of efficiency. Moreover, we show that rankings for firm-specific inefficiency estimates produced by traditional stochastic frontier models do not change from the rankings of the composed errors. As a result, the performance of the deterministic models is qualitatively similar to that of the stochastic frontier models.     

Non-crossing quantile regression via doubly penalized kernel machine

Quantile regression provides a more complete statistical analysis of the stochastic relationships among random variables. Sometimes quantile regression functions estimated at different orders can cross each other. We propose a new non-crossing quantile regression method using doubly penalized kernel machine (DPKM) which uses heteroscedastic location-scale model as basic model and estimates both location and scale functions simultaneously by kernel machines. The DPKM provides the satisfying solution to estimating non-crossing quantile regression functions when multiple quantiles for high-dimensional data are needed. We also present the model selection method that employs cross validation techniques for choosing the parameters which affect the performance of the DPKM. One real example and two synthetic examples are provided to show the usefulness of the DPKM.     

A New Approach to Censored Quantile Regression Estimation

Quantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly censored data. In this article, we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data. Supplementary material for this article is available online.     

Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse

We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.     

中国城市公共交通行业技术效率实证研究

本文选取1999-2004年间中国城市公共交通行业的面板数据,在Cobb-Douglas函数的基础上运用随机边界法对我国城市公共交通行业的技术效率进行了考察,并从时间、地域、交通工具类型和客运规模方面,分析了该行业的效率差异及其产生原因,旨在为该行业的未来发展和管制改革提供决策依据。研究结果表明,我国城市公共交通行业技术效率情况为:近几年虽有小幅上升,但基数总体不高;东部地区技术效率偏高;客运量大和拥有轨道交通的省市的技术效率较高。     

Unified Noncrossing Multiple Quantile Regressions Tree

In this article, we consider the estimation problem of a tree model for multiple conditional quantile functions of the response. Using the generalized, unbiased interaction detection and estimation algorithm, the quantile regression tree (QRT) method has been developed to construct a tree model for an individual quantile function. However, QRT produces different tree models across quantile levels because it estimates several QRT models separately. Furthermore, the estimated quantile functions from QRT often cross each other and consequently violate the basic properties of quantiles. This undesirable phenomenon reduces prediction accuracy and makes it difficult to interpret the resulting tree models. To overcome such limitations, we propose the unified noncrossing multiple quantile regressions tree (UNQRT) method, which constructs a common tree structure across all interesting quantile levels for better data visualization and model interpretation. Furthermore, the UNQRT estimates noncrossing multiple quantile functions simultaneously by enforcing noncrossing constraints, resulting in the improvement of prediction accuracy. The numerical results are presented to demonstrate the competitive performance of the proposed UNQRT over QRT. Supplementary materials for this article are available online.     

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.     

Estimation of additive quantile regression

We consider the nonparametric estimation problem of conditional regression quantiles with high-dimensional covariates. For the additive quantile regression model, we propose a new procedure such that the estimated marginal effects of additive conditional quantile curves do not cross. The method is based on a combination of the marginal integration technique and non-increasing rearrangements, which were recently introduced in the context of estimating a monotone regression function. Asymptotic normality of the estimates is established with a one-dimensional rate of convergence and the finite sample properties are studied by means of a simulation study and a data example.     

Weighted quantile regression for longitudinal data using empirical likelihood

This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood (EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.     

The impact of liberalization on the productive efficiency of Indian commercial banks

We examine the productive efficiency of 70 Indian commercial banks during the early stages (1986–1991) of the ongoing period of liberalization. We use data envelopment analysis to calculate radial technical efficiency scores. We then use stochastic frontier analysis to attribute variation in the calculated efficiency scores to three sources: a temporal component, an ownership component, and a random noise component. We find publicly-owned Indian banks to have been the most efficient, followed by foreign-owned banks and privately-owned Indian banks. We also find a temporal improvement in the performance of foreign-owned banks, virtually no trend in the performance of privately-owned Indian banks, and a temporal decline in the performance of publicly-owned Indian banks. We attempt to explain these patterns in terms of the government's evolving regulatory policies.     

Bayesian analysis of quantile regression for censored dynamic panel data

This paper develops a Bayesian approach to analyzing quantile regression models for censored dynamic panel data. We employ a likelihood-based approach using the asymmetric Laplace error distribution and introduce lagged observed responses into the conditional quantile function. We also deal with the initial conditions problem in dynamic panel data models by introducing correlated random effects into the model. For posterior inference, we propose a Gibbs sampling algorithm based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the mixture representation provides fully tractable conditional posterior densities and considerably simplifies existing estimation procedures for quantile regression models. In addition, we explain how the proposed Gibbs sampler can be utilized for the calculation of marginal likelihood and the modal estimation. Our approach is illustrated with real data on medical expenditures.