Accounting for Environmental Effects and Statistical Noise in Data Envelopment Analysis

In this paper we propose a new technique for incorporating environmental effects and statistical noise into a producer performance evaluation based on data envelopment analysis (DEA). The technique involves a three-stage analysis. In the first stage, DEA is applied to outputs and inputs only, to obtain initial measures of producer performance. In the second stage, stochastic frontier analysis (SFA) is used to regress first stage performance measures against a set of environmental variables. This provides, for each input or output (depending on the orientation of the first stage DEA model), a three-way decomposition of the variation in performance into a part attributable to environmental effects, a part attributable to managerial inefficiency, and a part attributable to statistical noise. In the third stage, either inputs or outputs (again depending on the orientation of the first stage DEA model) are adjusted to account for the impact of the environmental effects and the statistical noise uncovered in the second stage, and DEA is used to re-evaluate producer performance. Throughout the analysis emphasis is placed on slacks, rather than on radial efficiency scores, as appropriate measures of producer performance. An application to nursing homes is provided to illustrate the power of the three-stage methodology.     

A PCA–DEA approach to measure the quality of life in Estonian counties

This paper investigates the application of a PCA–DEA model to assess the quality of life (QOL) scores in Estonian counties and analyses the model's results. The dataset is a balanced panel of 15 Estonian counties covering the period from 2000 to 2011. We consider a PCA–DEA model as an alternative method to estimate and predict QOL scores and rankings of Estonian counties. The method consists of a two-stage analysis that begins with a principal component analysis. In the second stage, the standard DEA is used. The results from the conventional DEA model and the PCA–DEA model are compared and discussed. A comparison of the methodologies demonstrates that a PCA–DEA model provides a powerful tool for performance ranking. The rankings of Estonian counties using QOL scores for different model specifications are presented. Finally, the QOL ranking of Estonian counties is revised using PCA–DEA.     

Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints

The field of productive efficiency analysis is currently divided between two main paradigms: the deterministic, nonparametric Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). This paper examines an encompassing semiparametric frontier model that combines the DEA-type nonparametric frontier, which satisfies monotonicity and concavity, with the SFA-style stochastic homoskedastic composite error term. To estimate this model, a new two-stage method is proposed, referred to as Stochastic Non-smooth Envelopment of Data (StoNED). The first stage of the StoNED method applies convex nonparametric least squares (CNLS) to estimate the shape of the frontier without any assumptions about its functional form or smoothness. In the second stage, the conditional expectations of inefficiency are estimated based on the CNLS residuals, using the method of moments or pseudolikelihood techniques. Although in a cross-sectional setting distinguishing inefficiency from noise in general requires distributional assumptions, we also show how these can be relaxed in our approach if panel data are available. Performance of the StoNED method is examined using Monte Carlo simulations.     

Measuring efficiency in the presence of head-to-head competition

We develop a new DEA model that measures organizational efficiency in the presence of head-to-head competition. Our model differs from existing DEA models that ignore competition (or any other form of interaction) among the organizations under analysis. The model assumes that organizations deploy inputs for the explicit purpose of increasing its own outputs while reducing the outputs of its competitors. We apply this model to the 2002, 2004, and 2006 political campaigns in New York State for the US. House of Representatives in which candidates spent money to increase the number of votes that they received and decrease the number of votes that their opponents received. We show that campaign inefficiency can alter the outcome of an election. Specifically, a loser would have won in six of the 57 races had he or she been efficient. We also show that incumbents are more likely to spend inefficiently than are challengers. Overall, inefficiency accounts for less than 5% of campaign funding but a loss of about 9% in votes received. We find evidence that campaign efficiency has increased since the passage of the Bipartisan Campaign Reform Act of 2002, known widely as the McCain-Feingold Act.     

Research performance evaluation of Chinese university: A non-homogeneous network DEA approach

Performance evaluation for universities or research institutions has become a hot topic in recent years. However, the previous works rarely investigate the multiple departments’ performance of a university, and especially, none of them consider the non-homogeneity among the universities’ departments. In this paper, we develop data envelopment analysis (DEA) models to evaluate the performance of general non-homogeneous decision making units (DMUs) with two-stage network structures and then apply them to a university in China. Specifically, the first stage is faculty research process, and the second stage is student research process. We first spit each DMU (i.e. department) into a combination of several mutually exclusive maximal input subgroups and output subgroups in terms of their homogeneity in both stages. Then an additive DEA model is proposed to evaluate the performance of the overall efficiency of the non-homogeneous DMUs with two-stage network structure. By analyzing the empirical results, some implications are provided to support the university to promote the research performance of each department as well as the whole university.     

中国高技术产业技术创新三阶段特征及其演变

基于投入产出分析的逻辑思路建立技术创新三阶段模型,运用链式网络DEA方法测量我国高技术产业技术创新三阶段效率,通过技术创新效率的动态变化观察高技术产业技术创新演变规律。研究发现,1996~2011年我国高技术产业技术开发阶段经历了整体上类似“U”形的变化,源于技术开发阶段的投入增多、企业重视力度加大;技术转化阶段滞后于技术开发阶段近两年的变化时期,主要起因于纯技术无效率、技术开发阶段和产业化阶段的脱节;产业化阶段滞后于技术开发阶段近5年的变化时期和技术转化阶段近3年的变化时期,主要由于产业化阶段作为技术开发和技术转化的下游阶段,偏低的技术转化率必然导致最终的产业化率极低,但改进的空间很大。     

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.

DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea—Ratio Analysis. Our model, called DEA-R, treats all possible ratios “output/input” as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts’ opinions via flexible restrictive conditions on individual “output/input” pairs.     

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.     

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 financial and green effects of cultural values on mission drifts in European social enterprises

The sustainable social enterprises (SEs) literature shows that SEs have to simultaneously pursue economic, social, and environmental aims. However, tensions between these objectives can make this a challenging task and lead towards mission drift. This work investigates if the cultural dimension can forecast the mission drift. We empirically analyze this relationship in three stages. In the first stage, we identify a homogeneous dataset of 287 sustainable SEs from seven EU countries from 2011 to 2020. Then, in the second stage, we apply the data envelopment analysis (DEA) methodology to calculate the efficiency of the SEs. An efficient SE has to simultaneously achieve social, environmental, and economic aims. We calculate a proxy of the mission drift and generate a dichotomous category variable that assigns value 1 to the SE not affected by mission drift, 0 otherwise. In the last stage, we implement the 2SLS logistic regression between the variable that identifies the SEs affected by mission drift and three cultural dimensions: avoidance of uncertainty, masculinity, and short-term orientation.     

DEA target setting using lexicographic and endogenous directional distance function approaches

Directional Distance Function (DDF) is an approach often used in data envelopment analysis (DEA) due to its clear interpretation and to the flexibility provided by the possibility of choosing the projection direction towards the efficient frontier. In this paper two new DDF approaches are considered. The first one uses an exogenous directional vector and a multi-stage methodology that at each step uses the projection along the input and output dimensions of the directional vector that can be improved. This lexicographic DDF approach also computes a directional efficiency score and a directional inefficiency indicator for each input and output variable. The second approach is a non-linear optimization model that endogenously determines the directional vector so that the smallest improvement required to reach the efficient frontier is computed.     

A close look at second stage data envelopment analysis using compound error models and the Tobit model

In 2014 the Brazilian Electricity Regulator (ANEEL) evaluated the efficiency of power distribution utilities using Data Envelopment Analysis (DEA). Estimated efficiencies range from 22.46% to 100%. Although environmental information is available in the data set, corrected efficiencies were not investigated. Different second stage models can be applied to adjust for environmental heterogeneity. Although statistical correlation among efficiencies and environmental variables can be easily estimated, corrected efficiencies are subject to the underlying structure of the second stage model. Therefore, different second stage models may achieve different corrected efficiencies. We provide a detailed statistical analysis of the Tobit model and compound error models for second stage analysis. Limitations are described and the corrected efficiencies using these models are evaluated. Potentially, Brazilian power distribution utilities may achieve substantial changes in estimated efficiencies if second stage analysis is used.     

Another Approach to Data Envelopment Analysis in Noisy Environments: DEA+

In this paper a DEA+ labeled approach for efficiency measurement in the stochastic case is presented along with a consistency proof and some preliminary evidence illustrating the small sample performance. DEA+ can basically handle multi-output technologies like standard DEA but allows to filter noise, that might have disturbed production and unlike a related approach does not require panel data. Consistency of DEA+ relies on the assumption of i.i.d. distributed and bounded noise and requires radial efficiency measurement. First Monte Carlo experiments show that a DEA+ based average inefficiency estimator performs well for samples of size n=100 in one-output, two-input settings compared to the corresponding Stochastic Frontier Estimator. Sensitivity of DEA+ performance with respect to parametrization of noise is weak, but higher noise contribution requires much larger sample size for satisfactory results.     

Learning from input–output mixes in DEA: a proportional measure for slack‐based efficient projections

Several Data Envelopment Analysis (DEA) models use a radial distance measure that is based on the Debreu–Farrell notion of (in)efficiency. While this measure has an attractive interpretation, its use may be problematic if slacks or zeros are present in the data. The additive DEA model can perfectly deal with these problems, but the meaning of its associated scores is less intuitive than the one attached to the radial measures. We introduce an alternative efficiency measure, based on the results of the additive model, that can be decomposed in a Debreu–Farrell component and a factor that captures differences in input–output mixes with respect to those of the best practice reference observation. On an aggregate level, this second component can be considered as an indicator of the dispersion between radial efficiency measurement and results based on the Pareto–Koopmans efficiency notion. On the individual level, the measure allows us to regard relative inefficiency as resulting from (i) a divergence of implicit cost price vectors, and (ii) a cost level that is too high, even after adjustment for the implicit cost prices. Copyright © 1999 John Wiley & Sons, Ltd.     

Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China

A balance between environmental regulation and economic prosperity has become a major issue of concern to attain a sustainable society in China. This study proposes the application of Data Envelopment Analysis (DEA) for measuring the efficiencies of the ecological systems in various regions of that country. The proposed approach differs from most of the previous ecological systems models in that we view it in a two stage setting; the first stage models the ecological system itself, and from an economic perspective, while the second stage (decontamination system) models water recycling as a feedback process, and the treatment of other undesirable outputs coming from the first stage. There, we separate polluting gases and water into two parts; one part is treated, while the other is discharged. The model considers two major desirable outputs from the first stage, namely Population and Gross Region Product by expenditure (GRP), as well as undesirable variables in the form of consumed water, and certain pollutants, namely nitrogen oxide, sulfur dioxide and soot. At the same time, these undesirable outputs from the first stage are inputs to the second decontamination stage. As well, recycled water is fed back into stage 1. Thus, intermediate variables such as consumed water and waste gas emission simultaneously play dual roles of both outputs and inputs in the ecological system.     

Productivity drivers and market dynamics in the Spanish first division football league

This paper analyses efficiency drivers of a representative sample of Spanish football clubs by means of the two-stage data envelopment analysis (DEA) procedure proposed by Simar and Wilson (J Econ, 136:31–64, 2007). In the first stage, the technical efficiency of football clubs is estimated using a bootstrapped DEA model in order to establish which of them are the most efficient; the ranking is based on total productivity in the period 1996–2004. In the second stage, the Simar and Wilson (J Econ, 136:31–64, 2007) procedure is used to bootstrap the DEA scores with a truncated bootstrapped regression. Policy implications of the main findings are also considered.     

Ownership structure and cost efficiency: A study of publicly owned passenger-bus transportation companies in India

This paper estimates the determinants of cost inefficiency of several publicly operated passenger-bus transportation companies in India in terms of their ownership structure as well as other firm-specific characteristics. A panel data on publicly operated passenger-bus transportation companies is used to estimate a translog cost system with inefficiency. Inefficiency is specified in such a way that both its mean and variance are firm- and time-specific. For the estimation of production technology and cost inefficiency we have used a multi-step estimation procedure instead of the single-step maximum likelihood (ML) method. In the first step we estimate the translog cost system with heteroskedastic cost function without using any distributional assumptions on the error terms. The second stage uses the ML method to estimate the parameters associated with inefficiency, conditional on the parameter estimates obtained from the first stage. Finally, the residual of the cost function is decomposed to obtain firm-and time-specific measures of cost inefficiency, with ownership type and other firm-specific characteristics as explanatory variables.Financial support of the Nevada Agricultural Experiment Station is gratefully acknowledged.     

A model of stochastic choice from lists

We study stochastic choice from lists. All lists present the same set of alternatives albeit in different orders. Faced with a list, the decision maker makes her choice in two stages. In the first stage she searches through the list till she sees $k$ alternatives. In the second stage she chooses from the alternatives she has seen. Both $k$ and the choice rule governing her second stage behavior are random. We show that the underlying primitives of our model are revealed by the decision maker’s choice frequencies from lists. We characterize the model and two of its special cases. In the first special case the decision maker deterministically chooses the best observed alternative according to a given preference. In the second, the decision maker maximizes random preferences.