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.

     

The Application of Mathematical Programming Approaches to Estimating Container Port Production Efficiency

Container terminal production is both an important and complicated element in the contemporary global economy. This paper aims to evaluate the efficiency of the world’s most important container ports and terminals using the two alternative techniques of Data Envelopment Analysis (DEA) and the Free Disposal Hull (FDH) model. The results give an insight into the current efficiency ranking of the world’s major container ports and terminals. They also confirm expectations that the available mathematical programming methodologies lead to different results and that appropriate variable definition of input and output factors is a crucial element in meaningful applications of DEA and FDH. It is also concluded that the availability of panel data, rather than cross-sectional data would greatly improve the validity of the efficiency estimates derived from all the mathematical programming techniques applied.JEL Classification:C61, D24, E23, L23, L25, L92     

Some Remarks on Modified FDH

One of the tools in theoretical and empirical work on the measurement of productive efficiency is the socalled Free Disposal Hull (FDH) method. As a result of its very generous character, many of the observations belonging to an evaluated dataset are labeled efficient by this method. Modified FDH, similar in spirit as Andersen and Petersen's modified Data Envelopment Analysis, may thus be used to discriminate between FDH-efficient units. We aim to show why particularly for FDH this method seems quite apt and may be called for as a valuable complementary tool to standard FDH analysis.     

Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies

This paper draws attention for the fact that traditional Data Envelopment Analysis (DEA) models do not provide the closest possible targets (or peers) to inefficient units, and presents a procedure to obtain such targets.It focuses on non-oriented efficiency measures (which assume that production units are able to control, and thus change, inputs and outputs simultaneously) both measured in relation to a Free Disposal Hull (FDH) technology and in relation to a convex technology. The approaches developed for finding close targets are applied to a sample of Portuguese bank branches.     

The effect of foreign ownership on SMEs performance: An efficiency analysis perspective

This paper uses both Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH) models in order to determine different performance levels in a sample of 353 foreign equities operating in the Greek manufacturing sector. Particularly, convex and non-convex models are used alongside with bootstrap techniques in order to determine the effect of foreign ownership on SMEs’ performance. The study illustrates how the recent developments in efficiency analysis and statistical inference can be applied when evaluating performance issues. The analysis among the foreign equities indicates that the levels of foreign ownership have a positive effect on SMEs’ performance.     

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.     

Radial and nonradial measures of technical efficiency: An empirical illustration for Belgian local governments using an FDH reference technology

This paper serves two purposes. First, we argue that radial efficiency measures are inappropriate for the Free Disposal Hull (FDH) technology, and we provide a comparative analysis of alternative nonradial measures. In particular, using information on Belgian local government expenditures and output indicators we implement various radial and nonradial measures on the FDH reference technology, and we investigate to which extent these efficiency measures imply different distributions and rankings. Second, we analyze the patterns of measured technical efficiency implied by the various indices. Specifically, we investigate whether different measures make any substantial difference for the explanation of the calculated inefficiencies. The empirical results suggest that more important differences in rankings exist between radial and nonradial measures than between different nonradial alternatives; moreover, the radial and the nonradial efficiency measures do yield a somewhat different pattern of explanation.This is a revision of a paper presented at the 38th Conference of the Applied Econometrics Association in Athens (April 12–13, 1993). Comments of R. Goudriaan, Henry Tulkens, and two anonymous referees are gratefully acknowledged.     

EXPLAINING DIFFERENCES IN EFFICIENCY: A META‐STUDY ON LOCAL GOVERNMENT LITERATURE

This paper reviews the literature on local government efficiency by meta‐reviewing 360 observations retrieved from 54 papers published from 1993 to 2016. The meta‐regression is based on a random‐effects model estimated with the two‐step random‐effects maximum likelihood (REML) technique proposed by Gallet and Doucouliagos. Results indicate that the study design matters when estimating a frontier in local government. We find that studies focusing on technical efficiency provide higher efficiency scores than works evaluating cost efficiency. The same applies when using panel data instead of cross‐section data. Interestingly, studies that use the Free Disposal Hull (FDH) approach yield, on average, higher efficiency scores than papers employing the data envelopment analysis (DEA) method, thereby suggesting that in this literature the convexity hypothesis of the production set is a matter. Finally, the efficiency of local government increases with the level of development of the analysed countries and is positively related to the national integrity of the legal system. The opposite holds when considering the corruption.     

Technical Efficiency of the Brazilian Municipalities: Correcting Nonparametric Frontier Measurements for Outliers

In this paper we estimate the DEA technical efficiency for 4796 Brazilian municipalities, by applying a recently proposed “Jackstrap” method, which combines Bootstrap and Jackknife resampling techniques, to reduce the effect of outliers and possible errors in the data set. We perform calculations to identify and eliminate high leverage municipalities, using different variants of Data Envelopment Analysis (DEA), as well as Free Disposal Hull (FDH). Corroborating previous results, efficiency results for the Brazilian municipalities show a clear relationship between the size of the municipality and its efficiency scores. Indeed, under both DEA variants, smaller cities tend to be less efficient than larger ones hence indicating that the quality of the frontier adjustment improves significantly as the size of the municipality increases. We present arguments that may explain to some extent these findings, such as economies of scale and the excess spending due to revenue from royalties. However, such effects require further, more careful examination.     

基于扫描算法的启发式构造方法比较

针对车辆路径问题,基于扫描算法第一阶段的解,应用启发式算法中的最近插入算法、凸包算法和最远插入算法求解第二阶段。通过仿真实验,从总里程和算法运行时间两个方面对各算法性能给出评价。结果显示,在应用扫描算法进行聚类后,求解路径排程阶段,凸包算法虽然用时多于其它两种算法,但在里程上有明显优势,最远插入算法与最近插入算法在运行时间上没有显著差别,但在总里程上,前者较好。     

Axiomatic foundations of efficiency measurement on data-generated technologies

We assess the ability of three well-known technical efficiency indexes, the Debreu-Farrell index, the Färe–Lovell index, and the Zieschang index, to satisfy the Färe–Lovell axioms and continuity axioms (for technologies as well as input quantities) on the class of technologies generated by standard mathematical-programming methods of measuring efficiency: data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Färe–Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu–Farrell index), but (b) none of the indexes satisfies all Färe–Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.     

A note on “A directional slacks-based measure of technical inefficiency”

In this note we show, by means of several examples, that a directional distance function model cannot be matched with an additive model. Specifically, we show the difference between the directional slacks-based measure and the corresponding directional distance function.     

A directional slacks-based measure of technical inefficiency

Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.     

Efficiency analysis of East European electricity distribution in transition: legacy of the past?

This paper provides a cross-country efficiency analysis of electricity distribution companies in the East European transition countries of Poland, the Czech Republic, Slovakia and Hungary. We use common nonparametric efficiency measurement such as Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH) under different assumptions and apply recent developments of statistical inference in nonparametric frontier models to test our hypotheses. We discuss the empirical problems of cross-country benchmarking approaches, in particular the comparability of different structures of electricity distribution companies. Our results suggest that Poland’s distribution companies are still inefficiently small; the Czech Republic features the highest efficiency; and Slovakia and Hungary occupy the middle range. We also note that privatization has had a positive effect on technical efficiency in the four countries. We use the phrase “legacy of the past” to describe the four countries in comparison to the efficiency of electricity distribution companies we studied in Germany.

Statistical Inference in Nonparametric Frontier Models: The State of the Art

Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-statistical, as opposed to econometric approaches where particular parametric expressions are posited to model the frontier. We can now define a statistical model allowing determination of the statistical properties of the nonparametric estimators in the multi-output and multi-input case. New results provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator in the bivariate case. Sampling distributions may also be approximated by bootstrap distributions in very general situations. Consequently, statistical inference based on DEA/FDH-type estimators is now possible. These techniques allow correction for the bias of the efficiency estimators and estimation of confidence intervals for the efficiency measures. This paper summarizes the results which are now available, and provides a brief guide to the existing literature. Emphasizing the role of hypotheses and inference, we show how the results can be used or adapted for practical purposes.     

The Relationship Between Stock Market Returns and Technical Efficiency Innovations: Evidence from the US Airline Industry

This paper analyzes the association between two firm performance measures: stock market returns and relative technical efficiency. Using linear programming techniques (Data Envelopment Analysis and Free Disposal Hull), technical efficiencies are calculated for a panel of eleven US airlines observed quarterly from 1970–1990. A relationship, between efficiency news in a quarter and stock market performance in the following two months, is found. A risky arbitrage portfolio strategy, of buying firms with the most positive efficiency news and short-selling those with the worst news during this time frame, results in zero beta risk yet yields annual returns of 17% and 18% for the two methodologies.     

车辆数不确定的软时间窗车辆路径问题的改进遗传算法

综合考虑车辆数和行驶距离两种优化目标,提出了VRPSTW的多目标优化模型,同时提出了解决VRPSTW问题的一种改进遗传算法。在算法中,通过适应度函浸透的变化,较好地解决了多目标优化的问题;通过对交叉算子改进,增加了算法的寻优能力,同时又克服了算法对群体多样性的要求;针对遗传算法局部搜索能力弱的问题。加入了2-opt局部搜索方法,很好地弥补了遗传算法的不足。经过实验,本方法能较好地解决VRPSTW问题,从而对运榆决策提供有力支持。     

An iterative approach to the estimation of the abatement costs of harmful emissions

The ability to quantify tradeoffs involved in the process of reducing harmful emissions is essential to successful policy-making in the environmental planning area. The approach by Färe et al. (J Econom 126: 469–492, 2005) to computing point estimates of the marginal abatement costs (MACs) of reducing pollution by estimating the directional output distance function has been gaining popularity in recent years. The contribution of this study is to compute MACs as slopes of the iterated parametric production possibilities frontier (PPF) estimated on the basis of the set of efficient projections of observable output combinations obtained from the parameters of directional output distance function. Policy makers are thus provided with the general shape of the production possibilities set for a polluting technology rather than with a set of point estimates of the MACs. We apply our methodology to a balanced panel of seven Korean manufacturing sectors spanning the period between 1999 and 2009, obtaining theoretically consistent concave PPFs based on a large set of directional output distance vectors. Finally, we estimate the parameters of a directional output distance function corresponding to the iterated PPF.     

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.      

Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we find the optimal scale to be situated around 7–10 million m³.