Adjusting for the environment in DEA: A comparison of alternative models based on empirical data

Due to the existence of free software and pedagogical guides, the use of Data Envelopment Analysis (DEA) has been further democratized in recent years. Nowadays, it is quite usual for practitioners and decision makers with no or little knowledge in operational research to run their own efficiency analysis. Within DEA, several alternative models allow for an environmental adjustment. Four alternative models, each user-friendly and easily accessible to practitioners and decision makers, are performed using empirical data of 90 primary schools in the State of Geneva, Switzerland. Results show that the majority of alternative models deliver divergent results. From a political and a managerial standpoint, these diverging results could lead to potentially ineffective decisions. As no consensus emerges on the best model to use, practitioners and decision makers may be tempted to select the model that is right for them, in other words, the model that best reflects their own preferences. Further studies should investigate how an appropriate multi-criteria decision analysis method could help decision makers to select the right model.     

Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates

Many studies devoted to efficiency performance evaluation in the education sector are based on measures of central tendency at school level as, for example, the average values of students belonging to the same school. Although this is a common and accepted way of summarizing data from the original observations (students), it is not less true that this approach neglects the existing dispersion of data, which may become a serious problem if variability across schools is high. Additionally, imprecision may arise when experts on each evaluated subject select the battery of questions, with different levels of difficulty, which will be the base for the final questionnaires completed by students. This paper uses data from US students and schools participating in PISA (Programme for International Student Assessment) 2015 to illustrate that schools' efficiency measures based on aggregate data and imprecision may reflect an inaccurate picture of their performance if they are compared to measures estimated accounting for broader information provided by all students of the same school. In order to operationalize our approach, we resort to Fuzzy Data Envelopment Analysis. This methodology allows us to deal with the notion of fuzziness in some variables such as the socio-economic status of students or test scores. Our results indicate that the estimated measures of performance obtained with the fuzzy DEA approach are highly correlated with those calculated with traditional DEA models. However, we find some relevant divergences in the identification of efficient units when we account for data dispersion and vagueness.     

Efficiency analysis of emergency departments in metropolitan areas

The demand in the healthcare industry is increasing exponentially due to aging population of the world and this is leading to a rapid increase in the cost of healthcare. The emergency departments of the hospitals are the frontline of health care systems and play an additional critical role in providing an efficient and high-quality response for patients. The overcrowding at the emergency departments due to growing demand results in a situation where the demand for ED services exceeds the ability to provide care in a reasonable amount of time. This has led countries to reconsider their health policies in a way to increase their efficiency in their healthcare systems in general and in emergency departments, in particular. As in many countries, there has been a steady and significant increase in the number of patients that seek health services at the emergency departments of state hospitals of Turkey, due to the significant structural reforms in health services since 2003. While meeting this increasing demand, it is ever more important to provide these critical health services efficiently. Therefore, the efficiency of the emergency departments of seven general hospitals run by Istanbul's Beyoglu State Hospitals Association have been analyzed using categorical Data Envelopment Analysis (DEA) models. The analysis of DEA results is supported by a set of statistical methods to make it easier for the hospital administrators to interpret the analysis and draw conclusions. The analysis shows that less-equipped EDs are supported by better equipped, larger EDs, resulting in a hub-and-spoke type of structure among the EDs where “satellite” EDs serve an important referral function and thus evaluating their efficiency without taking the interoperability among these units into account would not be an accurate assessment of their performance.     

Economic interpretations of DEA

Research on productive efficiency at the firm level has developed as an important and active strand of research the last decades, both within operations research, management science and economics. Two apparently different definitions of efficiency are examined, but it is shown that when both estimation methods are based on solving linear programming problems the definitions of efficiency are identical. The purpose of the paper is to give the basic ideas of efficiency analyses using DEA as a tool for researchers not so familiar with efficiency analysis and DEA. The concept of shadow prices is given special attention.     

Changes in hospital efficiency and size: An integrated propensity score matching with data envelopment analysis

Turkey has made huge investments in city hospitals. The distinguishing feature of these hospitals is that they are physically large. Although many studies have investigated the efficiency of public hospitals, there are a few studies on the effect of hospital size on efficiency. This study examines the effect of hospital size on changes in public hospital efficiencies. The analysis is made up of three steps. First, using a bootstrap data envelopment analysis (DEA), the pure efficiency scores of each hospital were calculated. Second, propensity score matching (PSM) was used to ensure that any differences could be attributed to a particular class of hospital size, and not be due to differences in sample characteristics between the intervention and control groups. To highlight a potential time difference between small and large hospitals, the efficiencies of hospitals were examined from 2014 to 2017. Third, the Mann–Whitney U test was used to conduct a robustness check of the DEA and PSM results. Fourth, logistic regression was used on balanced data to examine the determinants of the efficiency of public hospitals. There are remarkable differences in the results obtained before and after matching the groups based on the bed-occupancy rate. Additionally, urban location is a key predictor of efficient and inefficient hospitals. This study also highlights that integrating DEA and PSM is a useful strategy in accurately identifying predictors of efficiencies of hospitals by creating balanced groups. Health policymakers should consider the efficiency advantages of high workload and service burden in the planning of public hospitals.     

The benefits of non-radial vs. radial super-efficiency DEA: an application to burden-sharing amongst NATO member nations

Using radial super-efficiency data envelopment analysis (DEA) has improved the discriminating performance across efficient decision-making units (DMUs). This paper extends the super-efficiency approach to a non-radial super-efficiency DEA (NRSE-DEA) index. NRSE-DEA is shown to be invariant to units of input (output) measurement. NRSE-DEA is illustrated here via an application to NATO burden-sharing assessment in which the DMUs are the member nations of NATO. The NRSE-DEA provides additional insights into the ranking of efficient countries, suggesting which are absorbing a particularly large share of NATO responsibilities. The NRSE-DEA generates a smaller set of efficient DMUs. This, in turn, provides more discriminatory power, a more accurate measure of super-efficiency, a more meaningful ranking of the efficient burden sharing countries, and a more reliable assessment of contributions by NATO members, amongst other policy issues.     

Causes of inefficiency in Japanese railways: Application of DEA for managers and policymakers

Although railway services have been suffering financially due to modal shifts and aging populations, they have been, and will continue to be, an essential component of nations' basic social infrastructures. Since railway firms generate positive externalities, and are required to operate in pre-determined licensed areas, governmental intervention/support may, in some cases, be justified. Indeed, many types of subsidies are created and offered for railway operations in Japan; while some are meant to cover large investments, others are used as compensation for regional disparities. However, thus far, no attempt has been made to analyze the reasons for the underperformance of Japanese railway services. In other words, it is unclear whether this underperformance can be attributed to exogenous and uncontrollable causes, or endogenous phenomena and, hence, capable of being handled by managers. The optimal degree of intervention is thus not sufficiently known. In the current paper, we propose a method based on data envelopment analysis (DEA) to analyze the causes of inefficiency in Japanese railway operations, and, further, to calculate optimal subsidy levels. The latter are designed to compensate for railways' lack of complete discretion in changing location of their operations and/or increasing/decreasing these operations since they are a regulated service. Our proposed method was applied to 53 Japanese railway operators. In so doing, we identified several key characteristics related to their inefficiencies, and developed optimal subsidies designed to improve performance.     

Measuring efficiency in Australian Schools: A preliminary analysis

In this paper, we apply a public sector Data Envelopment Analysis model to estimate the efficiency of Australian primary and secondary schools. Standard microeconomic production theory showing the transformation of inputs into outputs is extended to allow nondiscretionary environmental variables characteristic of educational production. Failure to properly control for the socioeconomic environment leads to inappropriate comparisons and biased efficiency estimates. We employ a conditional estimator that does not allow a school with a better environment to serve as a benchmark for a school with a worse environment. The results suggest that Australian schools are moderately inefficient and that efficiency increases for the quintile of schools with the most favorable environment. Further, efficiency gains are realized with increasing enrollment.     

Environmental taxes,reforms and economic growth: an empirical analysis of panel data

This paper explores the relationship between environmentally related taxes and the economic growth rate. The analysis also investigates whether this relationship differs between countries that have implemented environmental tax reforms (ETRs) and those that have not. Using panel data from 31 OECD countries over the period 1994–2013, the paper finds that when we allow environmentally related tax revenues to interact with an initial level of real GDP per capita, the overall revenues of these taxes are negatively associated with the economic growth rate in the short and long term. Furthermore, we show that the higher the initial level of GDP per capita, the more environmentally related tax revenues can promote the economic growth rate. The analysis also reveals that the relationship between environmentally related tax revenues and economic growth varies between countries that have a mechanism to redistribute environmentally related tax revenues and those that do not.     

Efficiency aggregation with enhanced Russell measures in data envelopment analysis

In aggregation for data envelopment analysis (DEA), a jointly determined aggregate measure of output and input efficiency is desired that is consistent with the individual decision making unit measures. An impasse has been reached in the current state of the literature, however, where only separate measures of input and output efficiency have resulted from attempts to aggregate technical efficiency with the radial measure models commonly employed in DEA. The latter measures are “incomplete” in that they omit the non-zero input and output slacks, and thus fail to account for all inefficiencies that the model can identify. The Russell measure eliminates the latter deficiency but is difficult to solve in standard formulations. A new approach has become available, however, which utilizes a ratio measure in place of the standard formulations. Referred to as an enhanced Russell graph measure (ERM), the resulting model is in the form of a fractional program. Hence, it can be transformed into an ordinary linear programming structure that can generate an optimal solution for the corresponding ERM model. As shown in this paper, an aggregate ERM can then be formed with all the properties considered to be desirable in an aggregate measure—including jointly determined input and output efficiency measures that represent separate estimates of input and output efficiency. Much of this paper is concerned with technical efficiency in both individual and system-wide efficiency measures. Weighting systems are introduced that extend to efficiency-based measures of cost, revenue, and profit, as well as derivatives such as rates of return over cost. The penultimate section shows how the solution to one model also generates optimal solutions to models with other objectives that include rates of return over cost and total profit. This is accomplished in the form of efficiency-adjusted versions of these commonly used measures of performance.     

Using DEA to improve the management of congestion in Chinese industries (1981–1997)

Congestion is said to be present when increases in inputs result in output reductions. An “iron rice bowl” policy instituted in China shortly after the revolution led by Mao Tze Tung resulted in congestion that ultimately led to bankruptcy in the textile industry, and near bankruptcy in other industries. A major policy shift away from the “iron rice bowl policy” in 1990 led to massive layoffs and increasing social tensions. Were these massive layoffs necessary? Extensions of data envelopment analysis models effected in the present paper identified inefficiencies in the management of congestion. Using textiles and automobiles for illustration, it is shown how elimination of such managerial inefficiencies could have led to output augmentation without reducing employment. Thus, even in the presence of congestion, it proved to be possible to identify additional (managerial) inefficiencies that provided opportunities for improvement. In the heavily congested textile industry, these output augmentations could have been accompanied by reductions in the amounts of capital used (as an added bonus). In any case, we show how to identify and evaluate new types of efficiency—viz., the efficiency with which needed (or desired) inefficiencies are managed.     

Investment and dynamic DEA

A dynamic version of data envelopment analysis (DEA) is developed in the present paper. Our model introduces investment in traditional DEA and imposes intertemporal cost minimization. Adding an intertemporal adjustment constraint into the cost minimization problem, we derive the relation between the DEA variables of the variable cost function and those of the primary production frontiers’ coefficients. The augmented DEA model can be solved using standard linear programming. This dynamic framework enables computing the production frontiers, measuring the productive efficiencies and evaluating the potential economies all in the presence of adjustment costs.

Classification in automobile insurance using a DEA and discriminant analysis hybrid

In this article, we adopt an efficiency approach to the two-group linear programming method of discriminant analysis (DA), using principles taken from data envelopment analysis (DEA), to predict group membership in an insurance underwriting scheme. Using an empirical insurance data base we illustrate the effectiveness of our model as a decision-making tool to distinguish among automobile insurance applicants by contrasting our hybrid model with both statistical and LP methods of discriminant analysis. We find for this insurance application that our hybrid model significantly outperforms the more traditional methods in separation and misclassification outcomes.     

Environmental performance evaluation: A state-level DEA analysis

In recent years, the continuous development of every country's economic activities has generated undesirable impacts on the environment. Common problems are high water and energy consumption rates, jointly with harmful pollution levels. This situation has gained the research community's interest in exploring and analyzing the extent to which initiatives to reduce such environmental problems have succeeded. Therefore, it is relevant to have measures that encompass information on the results obtained by such initiatives. Using the data envelopment analysis (DEA) methodology, it is possible to measure the efficiency of an entity under evaluation, such as an industry, state, or country. DEA also allows one to compare the performance measures of entities operating in similar circumstances and identify which entities are performing best, given the inputs they use and the outputs they produce. This study evaluates different states in Mexico in terms of their environmental performance and provides a perspective on how environmental initiatives can contribute to protecting and preserving the environment. By addressing this problem, best-performers and practices are identified, and valuable insights are gained regarding how each state carries out such initiatives.     

An application of data envelopment analysis to evaluate the efficiency level of the operational cost of Brazilian electricity distribution utilities

This paper shows efficiency indices for 60 Brazilian electricity distribution utilities. The efficiency scores are gauged by three DEA models. For both models, these quantities are evaluated under different contexts. One treats with respect to the regulator perspective. The others examine an alternative approach based on cluster analysis and restrictions on factor weights. It is worth pointing out that these developments can reduce the information asymmetry and improve the regulator's skill to compare the performance of the utilities, a fundamental in incentive regulation schemes.     

A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies

Data Envelopment Analysis (DEA) is a linear programming methodology for measuring the efficiency of Decision Making Units (DMUs) to improve organizational performance in the private and public sectors. However, if a new DMU needs to be known its efficiency score, the DEA analysis would have to be re-conducted, especially nowadays, datasets from many fields have been growing rapidly in the real world, which will need a huge amount of computation. Following the previous studies, this paper aims to establish a linkage between the DEA method and machine learning (ML) algorithms, and proposes an alternative way that combines DEA with ML (ML-DEA) algorithms to measure and predict the DEA efficiency of DMUs. Four ML-DEA algorithms are discussed, namely DEA-CCR model combined with back-propagation neural network (BPNN-DEA), with genetic algorithm (GA) integrated with back-propagation neural network (GANN-DEA), with support vector machines (SVM-DEA), and with improved support vector machines (ISVM-DEA), respectively. To illustrate the applicability of above models, the performance of Chinese manufacturing listed companies in 2016 is measured, predicted and compared with the DEA efficiency scores obtained by the DEA-CCR model. The empirical results show that the average accuracy of the predicted efficiency of DMUs is about 94%, and the comprehensive performance order of four ML-DEA algorithms ranked from good to poor is GANN-DEA, BPNN-DEA, ISVM-DEA, and SVM-DEA.     

Financial development and governance: A panel data analysis incorporating cross-sectional dependence

This study investigates bidirectional causality between governance and financial development using panel data of 101 countries from 1984 to 2013. The financial development–governance nexus is explored using econometric methods robust to cross-sectional dependence, and the relationship between different levels of development and openness is analyzed. Long-run equation estimates show clear evidence that financial development positively affects governance, and this positive impact is found to be robust to three different measures of governance. Further analysis shows that improving governance quality has a positive effect on financial development, while Granger causality tests demonstrate bidirectional causality between financial development and the governance measures. Finally, the impact of financial development on governance is dependent on a country’s level of development and openness. These findings underscore the crucial role of financial development in bringing about good governance reforms and economic growth that, in turn, can further develop the financial sector. As such, a symbiotic and synergistic relationship can persist between good governance, growth, and financial development. The findings provide significant motivation for policymakers to encourage openness and financial sector development to lift the standard of living, especially in emerging economies.     

A new method for measuring congestion in data envelopment analysis

In data envelopment analysis (DEA), there are two principal methods for identifying and measuring congestion: Those of Färe et al. [Färe R, Grosskopf S. When can slacks be used to identify congestion. An answer to W. W. Cooper, L. Seiford, J. Zhu. Socio-Economic Planning Sciences 2001;35:1–10] and Cooper et al. [Cooper WW, Deng H, Huang ZM, Li SX. A one-model approach to congestion in data envelopment analysis. Socio-Economic Planning Sciences 2002;36:231–8]. In the present paper, we focus on the latter work in proposing a new method that requires considerably less computation. Then, by proving a selected theorem, we show that our proposed methodology is indeed equivalent to that of Cooper et al.     

Target and technical efficiency in DEA: controlling for environmental characteristics

In this paper we propose a target efficiency DEA model that allows for the inclusion of environmental variables in a one stage model while maintaining a high degree of discrimination power. The model estimates the impact of managerial and environmental factors on efficiency simultaneously. A decomposition of the overall technical efficiency into two components, target efficiency and environmental efficiency, is derived. Estimation of target efficiency scores requires the solution of a single large non-linear optimization problem and provides both a joint estimation of target efficiency scores from all DMUs and an estimation of a common scalar expressing the environmental impact on efficiency for each environmental factor. We argue that if the indices on environmental conditions are constructed as the percentage of output with certain attributes present, then it is reasonable to let all reference DMUs characterized by a composed fraction lower than the fraction of output possessing the attribute of the evaluated DMU enter as potential dominators. It is shown that this requirement transforms the cone-ratio constraints on intensity variables in the BM-model (Banker and Morey 1986) into endogenous handicap functions on outputs. Furthermore, a priori information or general agreements on allowable handicap values can be incorporated into the model along the same lines as specifications of assurance regions in standard DEA.

Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. This paper extends this methodology in two substantive ways. First, a method is developed that determines the least-norm projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the observable frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs (or convex combinations of such) and thus, the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical example is used to illustrate the importance of these two methodological extensions.