Stochastic non-smooth envelopment of data for multi-dimensional output

The proposed method of Stochastic Non-smooth Envelopment of Data (StoNED) for measuring efficiency has to date mainly found application in the analysis of production systems which have exactly one output. Therefore, the objective of this paper is to examine the applicability of StoNED when a ray production function models a production technology with multi-dimensional input and output. In addition to a general analysis of properties required by a ray production function for StoNED to be applicable, we conduct a Monte Carlo simulation in order to evaluate the quality of the frontier and efficiencies estimated by StoNED. The results are compared with those derived via Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA). We show that StoNED provides competitive estimates in regard to other methods and especially in regard to the real functional form and efficiency.     

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.     

The StoNED age: the departure into a new era of efficiency analysis? A monte carlo comparison of StoNED and the “oldies” (SFA and DEA)

Based on the seminal paper of Farrell (J R Stat Soc Ser A (General) 120(3):253–290, 1957), researchers have developed several methods for measuring efficiency. Nowadays, the most prominent representatives are nonparametric data envelopment analysis (DEA) and parametric stochastic frontier analysis (SFA), both introduced in the late 1970s. Researchers have been attempting to develop a method which combines the virtues—both nonparametric and stochastic—of these “oldies”. The recently introduced Stochastic non-smooth envelopment of data (StoNED) by Kuosmanen and Kortelainen (J Prod Anal 38(1):11–28, 2012) is such a promising method. This paper compares the StoNED method with the two “oldies” DEA and SFA and extends the initial Monte Carlo simulation of Kuosmanen and Kortelainen (J Prod Anal 38(1):11–28, 2012) in several directions. We show, among others, that, in scenarios without noise, the rivalry is still between the “oldies”, while in noisy scenarios, the nonparametric StoNED PL now constitutes a promising alternative to the SFA ML.     

The directional profit efficiency measure: on why profit inefficiency is either technical or allocative

The directional distance function encompasses Shephard’s input and output distance functions and also allows nonradial projections of the assessed firm onto the frontier of the technology in a preassigned direction. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit maximizing behavior, it seems natural to choose as the directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the directional profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical, for firms situated within the interior of the technology, or allocative, for firms lying on the frontier. We implement and illustrate the analytical model by way of Data Envelopment Analysis techniques, and introduce the necessary optimization programs for profit inefficiency measurement.     

Managerial and program inefficiency for European meat manufacturing firms: A dynamic multidirectional inefficiency analysis approach

This paper proposes a dynamic multidirectional inefficiency analysis approach within the context of Data Envelopment Analysis to measuring input- and investment-specific managerial and program inefficiency for groups of firms characterized by different technologies. Dynamic managerial inefficiency refers to the distance to the firms’ group-specific dynamic frontier of best practices, and dynamic program inefficiency measures the difference between the group-specific dynamic frontier and the pooled dynamic frontier. The empirical application focuses on panel data of large meat processing firms in Eastern, Western and Southern Europe over the period 2005–2012. The results show that Eastern European firms have the highest dynamic managerial inefficiency for all inputs, but have the smallest values for dynamic program inefficiency. Western European firms perform worst in terms of program inefficiency for all inputs, while Southern European firms are the best with regard to dynamic managerial inefficiency. The results also reveal that regardless the dynamic inefficiency dimension considered, investments is the most inefficient input, followed by labor, and materials.     

Interpreting inefficiency ratings: An application of bank branch operating efficiencies

Data Envelopment Analysis is an analytical tool for evaluating the relative technical efficiency of a set of organizations with the same multiple inputs and outputs. This paper examines the correct interpretation of inefficiency scores in the Additive model of Data Envelopment Analysis. A contrived numerical example is offered to demonstrate that certain computational statements appearing in recent literature are not entirely correct. As rectification, a region of stability is defined that identifies sufficient conditions for altering a technical inefficiency classification to that of technical efficiency. Finally, this region of stability technique is applied to bank branch operating efficiencies to demonstrate managerial interpretations and policy implications.     

Model uncertainty and efficiency measurement in stochastic frontier analysis with generalized errors

Journal of Productivity Analysis - Advanced efficiency measurement methods usually fall within Stochastic Frontier Analysis (SFA), Data Envelopment Analysis (DEA), or their derivatives. Although...     

A multiplicative model for efficiency analysis

This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.     

Using DEA to Identify and Manage Congestion

This paper deals with identifying and managing congestion. For this purpose, DEA (Data Envelopment Analysis) is used to identify congestion when the data show it to be present, estimate its amounts, and separate it from other forms of inefficiency. DEA is also used to identify where improvements may be made in the management of congestion and to estimate input decreases and output increases that may be made after managerial inefficiencies in managing congestion are eliminated. The treatment here differs from the usual approaches that are restricted to identifying sources and amounts of technical inefficiency and congestion to be eliminated. The focus is directed rather to efficiency of performances in the presence of inefficiencies imposed by, say, labor contracts or government regulations and policies. Other developments include a use of rates of substitution formulated in terms of slack variables that help to avoid instabilities associated with the very small values that are often encountered in the use of dual variables to determine the rates of substitution. These rates of substitution are intended for use in guiding allocations (or reallocations) of inputs between different plants (or other entities) in ways that can further improve performance without reducing the congesting inputs that are to be employed. Hence modifications are needed to extend the usual restrictions to movements on the efficiency frontier so that frontiers associated with congestion and other inefficiencies can be dealt with.     

The closest strong efficient targets in the FDH technology: an enumeration method

This paper is concerned with the identification of the closest strong efficient target of a Decision Making Unit (DMU) in the Free Disposal Hull (FDH) technology in Data Envelopment Analysis (DEA). The paper uses the geometrical properties of the FDH Production Possibility Set (PPS) to design and test an enumeration algorithm to obtain the minimum distance from a DMU to the strong efficient frontier of the PPS, corresponding to each of the various returns to scale assumptions. The proposed method solves some simple optimization problems whose optimal solutions are obtained by calculating a limited number of ratios. Then, an attempt will be made to mitigate the problem of the lack of unit and translation invariance of the selected distances by considering weighted norms. Finally, the applicability of the presented method is illustrated by a numerical example using real data.

     

Nonparametric least squares methods for stochastic frontier models

When analyzing productivity and efficiency of firms, stochastic frontier models are very attractive because they allow, as in typical regression models, to introduce some noise in the Data Generating Process . Most of the approaches so far have been using very restrictive fully parametric specified models, both for the frontier function and for the components of the stochastic terms. Recently, local MLE approaches were introduced to relax these parametric hypotheses. In this work we show that most of the benefits of the local MLE approach can be obtained with less assumptions and involving much easier, faster and numerically more robust computations, by using nonparametric least-squares methods. Our approach can also be viewed as a semi-parametric generalization of the so-called “modified OLS” that was introduced in the parametric setup. If the final evaluation of individual efficiencies requires, as in the local MLE approach, the local specification of the distributions of noise and inefficiencies, it is shown that a lot can be learned on the production process without such specifications. Even elasticities of the mean inefficiency can be analyzed with unspecified noise distribution and a general class of local one-parameter scale family for inefficiencies. This allows to discuss the variation in inefficiency levels with respect to explanatory variables with minimal assumptions on the Data Generating Process.     

基于DEA评价模型的我国国际机场效率分析

文章以2011年我国民航运输量排名前30位的国际机场为样本,每个机场分别选取3个投入指标和产出指标,进行模型构建和数据分析。总样本数为180个,通过数据包络分析(Data Envelopment Analysis,DEA)方法和常用的评估技术有效和规模有效的CCR模型。评估我国国际机场总体的运营效率值和我国机场的效率优化,分析影响我国不同区域机场效率差异的相关因素,并指出运营无效的主要原因及提高效率的途径。结果显示我国大多数机场属于运营无效,其中,机场运营无效源于纯技术无效或规模无效。最后针对不同类型机场给出了提高效率的建议。     

我国大陆主要集装箱港口相对有效性评价

以数据包络分析(DEA)的BC2模型为基础,选取泊位长度、堆场面积和桥吊数量为输入项,吞吐量为输出项,从定量角度对我国大陆主要集装箱港口的相对有效性进行了评价。结合评价结果,对各港口的有效和无效原因做了初步的分析。     

Construct a composite indicator based on integrating Common Weight Data Envelopment Analysis and principal component analysis models: An application for finding development degree of provinces in Iran

Balanced development of regions requires the fair distribution of facilities and services. Hence, it is necessary to find and estimate the development degree of regions for policy makers. This paper presents an integrated Common Weight Data Envelopment Analysis (CWDEA) – Principal Component Analysis (PCA) model to find out the development degree of provinces in Iran. First, 131 suitable indicators are selected and then, the indicators are classified in fourteen different classes. In classical DEA model, each Decision Making Unit (DMU) is free to set its weights to reach the efficient frontier. In this paper, to restrict flexibility in indicator weights, development degree of provinces in each class is calculated using CWDEA model. Since, the proposed CWDEA model is not capable of fully ranking of provinces with all indicators, hence, the development degrees generated by CWDEA model are considered as indicators of PCA and the final ranks are obtained using PCA model. The results of proposed CWDEA-PCA model show that Yazd, Semnan and Bushehr are top three provinces in Iran.     

A Simulation Study of Joint Uses of Data Envelopment Analysis and Statistical Regressions for Production Function Estimation and Efficiency Evaluation

A previous paper by Arnold, Bardhan, Cooper and Kumbhakar (1996) introduced a very simple method to estimate a production frontier by proceeding in two stages as follows: Data Envelopment Analysis (DEA) is used in the first stage to identify efficient and inefficient decision-making units (DMUs). In the second stage the thus identified DMUs are incorporated as dummy variables in OLS (ordinary least squares) regressions. This gave very satisfactory results for both the efficient and inefficient DMUs. Here a simulation study provides additional evidence. Using this same two-stage approach with Cobb-Douglas and CES (constant elasticity-of-substitution) production functions, the estimated values for the coefficients associated with efficient DMUs are found to be not significantly different from the true parameter values for the (known) production functions whereas the parameter estimates for the inefficient DMUs are significantly different. A separate section of the present paper is devoted to explanations of these results. Other sections describe methods for estimating input-specific inefficiencies from the first stage use of DEA in the two-stage approaches. A concluding section provides further directions for research and use.     

Identifying technically efficient fishing vessels: a non‐empty,minimal subset approach

Stochastic frontier models are often employed to estimate fishing vessel technical efficiency. Under certain assumptions, these models yield efficiency measures that are means of truncated normal distributions. We argue that these measures are flawed, and use the results of Horrace ( 2005 ) to estimate efficiency for 39 vessels in the Northeast Atlantic herring fleet, based on each vessel's probability of being efficient. We develop a subset selection technique to identify groups of efficient vessels at pre‐specified probability levels. When homogeneous production is assumed, inferential inconsistencies exist between our methods and the methods of ranking the means of the technical inefficiency distributions for each vessel. When production is allowed to be heterogeneous, these inconsistencies are mitigated. Copyright © 2007 John Wiley & Sons, Ltd.     

Disentangling the efficiency drivers in country-level global health programs: An empirical study

Motivated by the cost reductions and outcome improvements generated by benchmarking in many industries, we focus on in-country global health programs to identify and quantify opportunities for process improvement. We empirically study the major efficiency drivers of reproductive health (RH) country programs in Sub-Saharan Africa sponsored by international funding organizations. To ensure a level playing field for comparison across countries, we quantify the impact of cross-country heterogeneity and random shocks on the efficiency of RH programs. To analyze these relationships and isolate the effects attributable to managerial inefficiency, we use a three-stage Data Envelopment Analysis (DEA)/Stochastic Frontier Analysis (SFA) model. We show the impact of environmental factors on program efficiency, linking policy making decisions with operational and health outcome performance. We also show that donor fragmentation negatively impacts managerial efficiency, and we suggest actions to mitigate this effect. We then provide a way to improve performance through benchmarking efforts within groups of countries and present an initial prototype of such efforts.     

Estimating DEA technical and allocative inefficiency using aggregate cost or revenue data

In this paper, we address the question of Data Envelopment Analysis (DEA) evaluation of efficiency when aggregate cost or revenue data must be used. We show that the DEA technical inefficiency measure using total revenues as the single output variable or total costs as the single input variable equals the aggregate technical and allocative inefficiency. We employ this result to estimate allocative inefficiency and construct statistical tests of the null hypothesis of no allocative inefficiency analogous to those of the null hypothesis of no scale inefficiency. We illustrate our method using revenue and personnel data for the top U.S. public accounting firms over 1995–1998. Our empirical results indicate the existence of statistically significant allocative inefficiency in the public accounting industry.

Nonparametric estimation of the determinants of inefficiency

We consider the benchmark stochastic frontier model where inefficiency is directly influenced by observable determinants. In this setting, we estimate the stochastic frontier and the conditional mean of inefficiency without imposing any distributional assumptions. To do so we cast this model in the partly linear regression framework for the conditional mean. We provide a test of correct parametric specification of the scaling function. An empirical example is also provided to illustrate the practical value of the methods described here.     

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.