A Two‐Stage Double Bootstrap DEA: The Case of the Top 25 European Football Clubs' Efficiency Levels

This paper analyzes how European football clubs' current value and debt levels influence their performance. The Simar and Wilson (J Econometrics, 136: 31–64, 2007) procedure is used to bootstrap the data envelopment analysis scores in order to establish the effect of football clubs' current value and debt levels on their obtained efficiency scores. The results reveal that football clubs' current value levels have a negative influence on their performances, indicating that football clubs' high value does not ensure higher performance. At the same time, the empirical evidence suggests that football clubs' debt levels do not influence their efficiency levels. Copyright © 2012 John Wiley & Sons, Ltd.     

Foreign presence and efficiency in transition economies

This paper presents empirical evidence on the role of foreign presence in the performance of domestic manufacturing firms in five Central and Eastern European countries. Data Envelopment Analysis (DEA) was used to estimate a frontier for each sector with similar technology common for five transition countries in the sample − Bulgaria, Estonia, Hungary, Poland and Romania. Following Simar and Wilson (J Econom 136(1):31–64, 2007), this study applies a truncated regression and bootstrap technique in a second stage post-DEA analysis. Some evidence is found to support the hypothesis that foreign presence has an overall positive spillover effects on the performance of domestic firms.     

Explaining efficiency in municipal services providers

This paper considers the provision of some important municipal services and applies the non-parametric double bootstrap Simar and Wilson (J Econ 136(1):31–64, 2007) model based on a truncated-regression to estimate the effect of a group of relevant factors, which include the political sign of the governing party and the type of management, on robust DEA (Data Envelopment Analysis) estimates. Previous conditions, like separability, must hold for meaningful first- stage efficiency estimates and second-stage regression. After some confusion in the literature, Simar and Wilson (J Prod Anal 36(2):205–218, 2011b) clarify that their work of 2007 actually defines a statistical model where truncated (but not censored, i.e., Tobit, not Ordinary Least Square) regression yields a consistent estimation of model features. They demonstrate that conventional, likelihood-based approaches to inference are invalid, and they develop a bootstrap approach that yields valid inference in second stage regressions when these are appropriate. The results reveal a significant relation between efficiency and all the variables analysed and that municipalities governed by progressive parties are more efficient.     

Government secondary school finances in New South Wales: accounting for students’ prior achievements in a two-stage DEA at the school level

This study measures the efficiency of government secondary schools in New South Wales, Australia, using a two-stage semi-parametric production frontier approach to schooling. In contrast to previous research comparing school performance with two-stage data envelopment analysis (DEA), we control for prior academic achievement of students by using a rich data set from 2008 to 2010. We employ detailed financial data for deriving the envelope for the efficient production frontier of the schools. Using Simar and Wilson’s (J Econ 136:31-64, 2007, J Prod Anal 36:205-218, 2011a) double bootstrap procedure for two-stage DEA, the study finds that schools with lower total student numbers, a higher average of years of service of teachers, a higher ratio of special education students that attracts extra government funding, and girls only do better than other schools. On the other hand, a negative influence comes from a school’s location in provincial and outer metropolitan areas. An important result is that the socio-economic background of students attending a school has no significant effect on their academic performance, whereas higher prior academic achievements have a positive and statistically significant impact on student achievement. These results are relevant to decision makers for the school sector, in particular for funding criteria contained in the Gonski (Review of funding for schooling - Final report (December). Canberra: Commonwealth Government of Australia, 2011) review report.     

Two-stage DEA: <Emphasis Type="Italic">caveat emptor</Emphasis>

This paper examines the wide-spread practice where data envelopment analysis (DEA) efficiency estimates are regressed on some environmental variables in a second-stage analysis. In the literature, only two statistical models have been proposed in which second-stage regressions are well-defined and meaningful. In the model considered by Simar and Wilson (J Prod Anal 13:49–78, 2007), truncated regression provides consistent estimation in the second stage, where as in the model proposed by Banker and Natarajan (Oper Res 56: 48–58, 2008a), ordinary least squares (OLS) provides consistent estimation. This paper examines, compares, and contrasts the very different assumptions underlying these two models, and makes clear that second-stage OLS estimation is consistent only under very peculiar and unusual assumptions on the data-generating process that limit its applicability. In addition, we show that in either case, bootstrap methods provide the only feasible means for inference in the second stage. We also comment on ad hoc specifications of second-stage regression equations that ignore the part of the data-generating process that yields data used to obtain the initial DEA estimates.     

Incentive regulation and performance measurement of Taiwan’s incineration plants: an application of the four-stage DEA method

The aim of this paper is to provide a technical efficiency assessment of Taiwan’s incineration plants as the basis of incentive regulation schemes. We integrate the four-stage approach with Simar and Wilson’s (in J Econom 136:31–64, 2007) double bootstrapping to filter out the impacts of external variables in the efficiency measurement. Empirical results show that there is room for 15 % cost reductions and capacity, ownership, location and experience are all influential in improving the performance of these plants. We also demonstrate how the results can be applied to modify a yardstick incentive scheme.     

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.     

Innovation and export activities in the German mechanical engineering sector: an application of testing restrictions in production analysis

Since Solow (Q J Econ 70:65–94, 1956) the economic literature has widely accepted innovation and technological progress as the central drivers of long-term economic growth. From the microeconomic perspective, this has led to the idea that the growth effects on the macroeconomic level should be reflected in greater competitiveness of the firms. Although innovation effort does not always translate into greater competitiveness, it is recognized that innovation is, in an appropriate sense, unique and differs from other inputs like labor or capital. Nonetheless, often this uniqueness is left unspecified. We analyze two arguments rendering innovation special, the first related to partly non-discretionary innovation input levels and the second to the induced increase in the firm’s competitiveness on the global market. Methodologically the analysis is based on restriction tests in non-parametric frontier models, where we use and extend tests proposed by Simar and Wilson (Commun Stat Simul Comput 30(1):159–184, 2001; J Prod Anal, forthcoming, 2010). The empirical data is taken from the German Community Innovation Survey 2007 (CIS 2007), where we focus on mechanical engineering firms. Our results are consistent with the explanation of the firms’ inability to freely choose the level of innovation inputs. However, we do not find significant evidence that increased innovation activities correspond to an increase in the ability to serve the global market.     

Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In the literature two main approaches have been developed: one-stage approaches and two-stage approaches. Daraio and Simar (2005, J Prod Anal 24(1):93–121) propose a fully nonparametric methodology based on conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. However, convexity has always been assumed in mainstream production theory and general equilibrium. In addition, in many empirical applications, the convexity assumption can be reasonable and sometimes natural. Lead by these considerations, in this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models for convex and nonconvex technologies. Extending earlier contributions by Daraio and Simar (2005, J Prod Anal 24(1):93–121) as well as Cazals et al. (2002, J Econometrics 106:1–25), we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is proposed too. These various measures of efficiency provide also indicators of convexity which we illustrate using simulated and real data. Cinzia Daraio received Research support from the Italian Ministry of Education Research on Innovation Systems Project (iRis) “The reorganization of the public system of research for the technological transfer: governance, tools and interventions” and from the Italian Ministry of Educational Research Project (MIUR 40% 2004) “System spillovers on the competitiveness of Italian economy: quantitative analysis for sectoral policies” which are acknowledged. Léopold Simar received Research support from the “Interuniversity Attraction Pole”, Phase V (No. P5/24) from the Belgian Government (Belgian Science Policy) is acknowledged.     

Measurement of the efficiency of football teams in the Champions League

In the case of football it could be argued that the purpose of clubs is to win the competitions in which they participate. However, the assessment of football clubs from the efficiency would be relevant in judging whether the results have been obtained without waste. The chosen sample is football teams who played in the Champions League from 2003 to 2007 and the method of calculating the efficiency will be both the traditional version of the DEA as well as the version proposed by Andersen and Petersen (1993), which allows discrimination among efficient units. Copyright © 2010 John Wiley & Sons, Ltd.     

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.      

Flexible Term Structure Estimation: Which Method is Preferred?

We show that the recently developed non-parametric procedure for fitting the term structure of interest rates developed by Linton, Mammen, Nielsen, and Tanggaard (J Econ 105(1):185–223, 2001) overall performs notably better than the highly flexible McCulloch (J Finon 30:811–830, 1975) cubic spline and Fama and Bliss (Am Econ Rev 77:680–692, 1987) bootstrap methods. However, if interest is limited to the Treasury-bill region alone then the Fama–Bliss method demonstrates superior performance. We further show, via simulation, that using the estimated short rate from the Linton–Mammen–Nielsen–Tanggaard procedure as a proxy for the short rate has higher precision then the commonly used proxies of the one and three month Treasury-bill rates. It is demonstrated that this precision is important when using proxies to estimate the stochastic process governing the evolution of the short rate     

A response to the critiques of DEA by Dmitruk and Koshevoy, and Bol

We here critique the articles by Dmitruk & Koshevoy (1991, J Econ Theory 55:121–144) and by Bol (1986, J Econ Theory 38:380–385) by showing how to solve the examples they erected to show the non-existence of functions for evaluating performance efficiencies in DEA. We also show that functions satisfying these criteria—and other important criteria as well—were already available prior to the publications of D&K and by Bol and have since been greatly extended to increase the power and scope of DEA.

Corporate Governance and Firm’s Efficiency: The Case of a Transitional Country, Ukraine

In this study, we look for empirical support for the hypothesis that there is a positive relationship between the levels of corporate governance quality across firms and the relative efficiency levels of these firms. This hypothesis is related to Leibenstein’s idea of X-efficiency. We use the data envelopment analysis (DEA) estimator to obtain proxies for X-[in]efficiency of firms in our sample and then analyze them with respect to different ownership structures by comparing distributions and aggregate efficiencies across different groups. We also use truncated regression with bootstrap, following Simar and Wilson Estimation and influence in two stage, semi-parametric models of production process, Simar and Zelenyuk (2003) to infer on relationship of inefficiency to various indicators of quality of corporate governance, ownership variables, as well as industry and year specific dummies. The data is coming from seven industries in Ukraine. “The entrepreneurship structure itself may be critical, with the classic issue of the separation of ownership from control being regarded as one of the earliest and most important sources of X-efficiency” (Button and Weyman-Jones, 1992, American Economic Review). We would like to dedicate this paper to the memory of Christos Panzios—co-editor who handled our paper to almost the very end, whose suggestions and encouragement have helped us substantially improve our paper.     

Assessing bankruptcy prediction models via information content of technical inefficiency

We use a stochastic frontier model with firm-specific technical inefficiency effects in a panel framework (Battese and Coelli in Empir Econ 20:325–332, 1995) to assess two popular probability of bankruptcy (PB) measures based on Merton model (Merton in J Financ 29:449–470, 1974) and discrete-time hazard model (DHM; Shumway in J Bus 74:101–124, 2001). Three important results based on our empirical studies are obtained. First, a firm with a higher PB generally has less technical efficiency. Second, for an ex-post bankrupt firm, its PB tends to increase and its technical efficiency of production tends to decrease, as the time to its bankruptcy draws near. Finally, the information content about firm’s technical inefficiency provided by PB based on DHM is significantly more than that based on Merton model. By the last result and the fact that economic-based efficiency measures are reasonable indicators of the long-term health and prospects of firms (Baek and Pagán in Q J Bus Econ 41:27–41, 2002), we conclude that PB based on DHM is a better credit risk proxy of firms.     

A two-stage double-bootstrap data envelopment analysis of efficiency differences of New Zealand secondary schools

We conduct a two-stage (DEA and regression) analysis of the efficiency of New Zealand secondary schools. Unlike previous applications of two-stage semi-parametric modelling of the school “production process”, we use Simar and Wilson’s double bootstrap procedure, which permits valid inference in the presence of unknown serial correlation in the efficiency scores. We are therefore able to draw robust conclusions about a system that has undergone extensive reforms with respect to ideas high on the educational agenda such as decentralised school management and parental choice. Most importantly, we find that school type affects school efficiency and so too does teacher quality.     

Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations

This paper examines the technical efficiency of US Federal Reserve check processing offices over 1980–2003. We extend results from Park et al. [Park, B., Simar, L., Weiner, C., 2000. FDH efficiency scores from a stochastic point of view. Econometric Theory 16, 855–877] and Daouia and Simar [Daouia, A., Simar, L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics 140, 375–400] to develop an unconditional, hyperbolic, α-quantile estimator of efficiency. Our new estimator is fully non-parametric and robust with respect to outliers; when used to estimate distance to quantiles lying close to the full frontier, it is strongly consistent and converges at rate root-n, thus avoiding the curse of dimensionality that plagues data envelopment analysis (DEA) estimators. Our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices.     

Measuring the effect of Kyoto protocol agreement on countries’ environmental efficiency in CO2 emissions: an application of conditional full frontiers

This paper applies the probabilistic approach developed by Daraio and Simar (J Prod Anal 24:93–121, 2005, Advanced robust and nonparametric methods in efficiency analysis. Springer Science, New York, 2007a, J Prod Anal 28:13–32, 2007b) in order to develop conditional and unconditional data envelopment analysis (DEA) models for the measurement of countries’ environmental efficiency levels for a sample of 110 countries in 2007. In order to capture the effect of countries compliance with the Kyoto protocol agreement (KPA) policies, we condition first the years since a country has signed the KPA until 2007 and secondly the obliged percentage level of countries’ emission reductions. Particularly, various DEA models have been applied alongside with bootstrap techniques in order to determine the effect of KPA on countries’ environmental efficiencies. The study illustrates how the recent developments in efficiency analysis and statistical inference can be applied when evaluating environmental performance issues. The results indicate a nonlinear relationship between countries’ obliged percentage levels of emission reductions and their environmental efficiency levels. Finally, a similar nonlinear relationship is also recorded between the duration which a country has signed the KPA and its environmental efficiency levels.     

Measuring residential energy efficiency improvements with DEA

This paper measures energy efficiency improvements of US single-family homes between 1997 and 2001 using a two-stage procedure. In the first stage, an indicator of energy efficiency is derived by means of Data Envelopment Analysis (DEA), and the analogy between the DEA estimator and traditional measures of energy efficiency is demonstrated. The second stage employs a bootstrapped truncated regression technique to decompose the variation in the obtained efficiency estimates into a climatic component and factors attributed to efficiency improvements. Results indicate a small but significant improvement of energy efficiency over the studied time interval, mainly accounted for by fuel oil and natural gas users.     

Capacity shortfall and efficiency determinants in Brazilian airports: Evidence from bootstrapped DEA estimates

This paper reports on the use of different approaches for assessing efficiency related-issues in 63 major Brazilian airports. Starting out with the bootstrapping technique presented in Simar and Wilson (1998, 2004), several DEA estimates were generated, allowing the use of confidence intervals and bias correction in central estimates to test for significant differences in efficiency levels, returns-to-scale, and input-decreasing/output-increasing potentials. The findings corroborate anecdotal and empirical evidence regarding a capacity shortfall within Brazilian airports, where infrastructure slack is virtually inexistent, regardless of the airport type and location.