An overview of data envelopment analysis application in studies on the socio-economic performance of OECD countries

Abstract Due to large and deepening development disparities among countries, comparisons across them have gained utmost importance, both in theoretical and empirical sense. At the same time, overuse of natural resources and climate change are among the most difficult issues today’s world is facing. Consequently, there is a growing research interest in investigating the performance of countries, especially in terms of environmental and energy efficiency. This paper brings a literature overview on the application of data envelopment analysis (DEA) to studies that empirically explore socio-economic efficiency of OECD (Organisation for Economic Co-operation and Development) member countries. The listed papers are categorised with regard to the relevance given to economic, environmental or energy indicators. Their basic content is summarised, along with the major findings. In this way, both measurement of countries’ performance and the non-parametric approach of DEA have been given deserved attention.


Introduction
During the past several decades, the global economic environment has been dramatically transformed. The challenges of reducing high unemployment and public sector debt levels, reducing socio-economic inequalities and generating sustainable balanced growth of the world economy have to be reconciled and addressed in a satisfactory manner. Consequently, a sizeable body of economic research literature has argued as to whether reducing inequality affects economic growth positively, negatively or at all. Accordingly, theoretical and empirical economic studies on the relationship between the extent of inequality and economic growth rates have yielded to conflicting results. Most of them have suggested that greater equality is beneficial to growth, while a few have claimed the opposite. Through a brief review of the theoretical and empirical literature, Cingano (2014) summarises the conditions under which greater inequality might either reduce or increase growth, highlighting that there is no consensus on the sign and strength of this relationship. However, in the literature on economic policy-making, for some time there has been a concept of the trade-off between KEYWORDS Data envelopment analysis; efficiency; performance measurement; oEcD countries; growth equality and economic efficiency (or economic growth as one of its measures). Thus, Okun (1975) stated that a society will keep searching for better ways of drawing the boundary lines between the domain of rights and the domain of money, making progress, but never solving the problem. Claiming that the conflict between equality and economic efficiency is inescapable, he further presented an important but controversial proposition that social decisions which permit economic inequality must be justified as promoting economic efficiency. The aforementioned shows the importance of the notion of economic efficiency. It can be measured through targeted performance assessment, which is crucial in identifying the priority areas for implementation of effective measures and areas for possible improvements. Furthermore, cross-country evaluations enable us to draw an accurate picture of the situation and, thus, to identify problems and the way in which other countries deal with them and to find which countries perform better, how and why. Therefore, cross-country comparisons are of major importance for understanding the effectiveness and impact of policies and programmes adopted by individual countries, thus allowing policy-makers to learn from other countries about good practices.
With a growing number of studies using DEA as the central technique in the measurement of socio-economic efficiency of OECD countries, an overview of this field would be informative and beneficial for researchers and analysts working in or interested in this area, as well as for policy-makers. The aim of this paper is to fulfil the lack of surveys of such comprehensive literature. The paper is organised as follows. The second section gives a brief history of modern efficiency measurement and describes in short the DEA method and its basic models, together with their main extensions. An overview of DEA application in studies on the socio-economic performance of OECD countries is presented in the third and substantial section. In the fourth and final section, the main conclusions of this study are derived.

Data envelopment analysis: concept, history and basic models
Analysis of the socio-economic efficiency of countries, in the sense of questioning whether a particular country performs better than others in gaining more output while using the same or less amount of inputs, makes understandable the importance of evaluating socioeconomic relationships. The questions of convergence, frequently posed in economics, are at the focus of a respectable range of studies on socio-economic performance of nations, with diverse objectives and methodology. The method that simultaneously fulfils the need to involve a number of various socio-economic aspects into the process of efficiency evaluation, and to obtain a single performance measure, is data envelopment analysis. The following paragraphs provide a brief history of modern efficiency measurement and a basic concept of the DEA method (Rabar, 2013, pp. 17-18).
Modern efficiency measurement has its beginnings in the middle of the twentieth century. The concept of technical efficiency, according to which a producer is technically efficient if, and only if, it is impossible to produce more of any output without producing less of some other output or using more of some input, was firstly introduced in 1951 by Koopmans. This definition is accurate, but theoretical and unsuitable for application. It is, therefore, further refined by Debreu (1951) and Shephard (1953). These two authors, respectively, introduced output-and input-oriented distance functions which, in the same manner, measure technical inefficiency as the radial distance of a producer from a frontier, the first one in an output-expanding and the second one in an input-conserving direction. Extending their work, Farrell (1957) was the first to empirically introduce how to measure cost efficiency and how to decompose it into two components -technical efficiency and allocative (price) efficiency. The first one signifies the ability to gain maximum output from given inputs and the second one the ability to employ inputs in optimal proportions, given their respective prices. These components were then aggregated to form a measure of overall economic efficiency, which was later incorporated into the linear programming (LP) framework by Charnes, Cooper and Rhodes(1978), who developed a non-parametric technique of data envelopment analysis.
The DEA approach is used for empirically determining the relative efficiency of operating entities, called decision-making units (DMUs), that are mutually comparable -consuming the same inputs and creating the same outputs. The major limitations of traditional benchmarking techniques are overcome by the following features. DEA does not assume any specific functional form linking inputs and outputs, thus avoiding problems of model misspecification. The production possibility frontier is determined empirically -by the observed values of the DMUs that are efficient (with respect to the rest of DMUs in the sample) and are all assigned an efficiency score of one (or 100%). The term 'envelopment' derives from the fact that the frontier envelops the set of observations. If a DMU does not belong to this piecewise linear or log-linear envelopment surface and, therefore, lies in its interior, then that DMU is not operating efficiently and, according to the distance from the point representing its input and output values to the corresponding reference point on the efficient frontier, receives an efficiency score of less than one (best performance), but greater than zero. The inefficiency is ascribed to input surpluses and/or output shortages and can be overcome by reaching an efficient projection point of operation on the 'best practice' frontier. This point is usually returned by DEA models for each inefficient entity, thus identifying the entities that can be used as performance benchmarks for inefficiently operating entities. Furthermore, DEA requires no a priori designation of input and output weights, which are instead determined by the LP model itself. This is achieved in a way that each evaluated entity receives the highest possible efficiency rating, thus circumventing the subjectivity associated with the estimation of their importance. Moreover, DEA can simultaneously handle multiple variables, each of which can be expressed in different and usually incongruous units of measurement, while still providing a single real number as a relative performance efficiency index. This index is obtained by solving the chosen DEA linear programming model that uses empirical data on inputs and outputs of all observed entities.
A number of basic and advanced DEA models that have been constructed significantly contributed to practitioners' general acceptance of this method. The models differ primarily in the assumption about returns-to-scale (constant or variable) exhibited by the production function, and in the orientation type of efficiency measurement (to input minimisation or to output maximisation). Their further distinctions are reflected in miscellaneous extensions to the basic DEA methods. Regardless of the model type, they all produce a large set of concrete, relevant and useful results. In addition to the efficiency score for each observed entity, a potential performance target is assigned for each inefficient entity, in terms of inefficiency sources and amounts, proposed improvements in each of the inputs and outputs (resulting in efficient projection onto the frontier) or reference set (defined by the closest efficient units). These results provide policy-makers with information crucial for operating more efficiently in today's dynamic business environment, where competitive rivalry is increasing exponentially.
The two most commonly applied basic DEA models are generally distinguished -CCR model, named after Charnes et al. (1978) and BCC model, named after Banker, Charnes, and Cooper (1984). These two models obtain efficiency measures under constant returnsto-scale (CRS) and variable returns-to-scale (VRS) assumptions, respectively, thus yielding two types of envelopment surfaces. The first model's efficiency score represents overall technical efficiency, which measures inefficiencies due to the input-output configuration and the size of operations. The second model results in a pure technical efficiency score which purely reflects managerial under-performance. To avoid the choice of model orientation, numerous DEA models that simultaneously estimate potential input reductions and output expansions have been developed. Thus, based on the BCC model, Charnes, Cooper, Golany, Seiford, and Stutz (1985) constructed the (input and output) translation-invariant additive model. This model was then extended by Tone (2001) into the slacks-based measure (SBM) model with unit invariant and monotone efficiency measure. Another non-oriented model that transforms data using a logarithmic structure is the multiplicative model, developed by Charnes, Cooper, Seiford, and Stutz (1982). Although these non-oriented models are more realistic in numerous real-world cases than oriented ones, they have been under-valued in the efficiency measurement literature.
In basic DEA models, DMUs are usually classified as efficient and inefficient. Thereby, the inefficient entities can be easily ranked according to their efficiency scores, while, for the efficient ones, the ranking within the DEA context can be considered post-analysis. Adler, Friedman, and Sinuany-Stern (2002) described ranking methods developed in the literature and grouped them into six basic areas, according to various criteria.
Aside from the above-mentioned, there have been a number of research thrusts, resulting in an impressive growth in the development of the advanced models and in the number of their applications to practical situations. By focusing primarily on methodological developments, Cook and Seiford (2009) reviewed a large number of models. They particularly discussed CRS, VRS and additive models, slacks-based measures, the Russell measure, alternative views such as the free disposal hull model and cross efficiency, least distance projections and invariance to data alterations. Multi-level models, such as multi-stage/serial models, including network DEA and supply chains, multi-component/parallel models and hierarchical/nested models, and multiplier restrictions, such as absolute multiplier and cone ratio restrictions, assurance regions, facet models and generating unobserved DMUs were also reviewed. The authors gave special consideration to different types of variables such as non-discretionary, non-controllable, categorical and ordinal, also including undesirable factors and flexible measures. In the same paper, data variation was also envisaged, including sensitivity analysis for problem size issues, direct and indirect data perturbations and super-efficiency, data uncertainty and probability-based models, window analysis and Malmquist models 1 as DEA approaches for investigating efficiency and productivity changes over time and stochastic data-statistical inference. Some of the models from the above partial review went somewhat beyond the usual definition of DEA. However, the usefulness and appropriateness of all these DEA-based approaches in the measurement of socio-economic performance of countries is unquestionable and proven by their increasing popularity. The main reasons behind this lie in the possibility of handling variables that are not under the direct control of policy-makers and/or their values have to remain fixed, capturing qualitative and modelling undesirable variables, incorporating flexible variables that are allowed to be on both the input and output sides of the model, providing a fair evaluation of countries that fall into natural categories, etc. Furthermore, there are acceptable solutions regarding the sensitivity of a country's efficiency to the addition of countries to or extraction of countries from the analysis, the question of a given country's maximum allowable increase in outputs or decrease in inputs that will maintain its efficiency status, the problem of modelling technical efficiency when the data for the inputs and outputs are random variables, the treatment to efficiency and productivity changes in a time series sense, etc.
Many of the above-mentioned advantageous features became prominent reasons for choosing DEA over traditional efficiency-measuring methods. However, two major obvious limitations associated with DEA method should also not be left out of consideration. First, there are the rules of thumb that provide guidance for the minimum number of entities (in relation to the total number of input and output variables) required for some discriminatory power to exist in the model, and hence for a reliable analysis. The existing considerable differences in opinions of various authors on the size of this number are summarised in Sarkis (2007). Second, the multi-criteria decision-making methodologies are generally applied to ex ante problems where data are not available, while DEA provides an ex post analysis of the past from which to draw conclusions, and on which to build (Adler et al., 2002).
Due to its aforementioned unique, desirable and powerful features, data envelopment analysis has been widely applied in many different areas such as education, healthcare, banking, service industries, engineering and science, as well as in evaluations of regional and country performances. Since 1978, when the seminal work of Charnes et al. introduced the DEA concept, up through the year 2009, around 4500 DEA-related papers, both theoretically and practically oriented, have been published in ISI Web of Science database (Liu, Lu, Lu, & Lin, 2013). In addition to this collection, around 2000 papers have been published in the same database during the period 2010 to 2014, as reported by Liu, Lu, and Lu (2016). All these papers have covered a series of decision analysis applications involving schools, hospitals, banks, hotels, airports and even countries and regions. Due to the robust characteristics and diverse practical uses in microeconomics as well as in macroeconomics, the DEA approach has been receiving deserved thorough consideration and has progressively evolved into a superior and academically accepted discipline.

Main findings of the empirical studies
Although the literature related to economic growth across OECD countries, based on the use of DEA method, is substantial and growing, there is a lack of a literature review in this field. Table 1 presents a brief chronological survey of the main findings on this topic. The various potential socio-economic determinants that have been used in these studies are selected based on the research scope, thus classifying this literature into three main categories (Skare & Rabar, 2016), labelled 1, 2 and 3 in Table 1. The focus of the studies in the first category is mostly on economic indicators. The most frequently used are gross domestic product (GDP), employment and capital stock. The studies in the second category underline the significance of environmental issues, combining economic indicators with ecological, usually the undesirable ones. Most commonly, these are greenhouse gas emissions to the environment, such as carbon dioxide, nitrous oxide, etc. In the studies from the third category, the emphasis is placed on the impact of energy supply and consumption. Therefore, alongside economic hyperbolic and radial efficiency measures are used to represent efficient production processes and environmentally inefficient processes, respectively. the results show that the cost of co 2 weak disposability congestion accounts for 5.26% and 7.57% of the oEcD's total manufacturing production in 1990 and 1995, respectively. on the other hand, the cost associated with the 5% reduction regulation represents 1.96% and 0.03% of their manufacturing production. the first one attempts to proportionally reduce the energy inputs to the frontier of the best practice. the other two, based on non-radial and slack-based models, account for the energy mix effects. the results indicate that, without increasing the amounts of non-energy inputs and co 2 emissions or decreasing GDP, canada and japan have the greatest potential to reduce their energy consumption.

Emrouznejad
halkos and tzeremes ( • GDP in PPs per worker • Governance effectiveness Based on semi-parametric analysis, computing DEa-based malmquist productivity indices and on stochastic frontier analysis, the findings point out that private capital is important for growth. Public and human capital also contribute positively, but less significantly. the government effectiveness indicator explains inefficiency suggesting, as expected, that better governance helps countries to achieve a better performance.
camarero, castillo, Picazo-tadeo, and tamarit • co 2 emissions Using an output-oriented window analysis model under vRs, the relative efficiency of the countries is measured in two steps -first employing four economic indicators and then adding four new indicators that cover social, institutional and environmental dimensions. it is found that performance rankings change, in some cases very significantly and that the overall relative performance of the countries increases when the set of economic indicators is extended.
notes: ch4 -methane; co -carbon monoxide; co2 -carbon Dioxide; G7 -Group of seven; GLmm -Generalized Linear mixed model; mcmc -markov chain monte carlo; n2o -nitrous oxide; naFta -north american Free trade agreement; nox -nitrogen oxide; PPP -Purchasing Power Parity; PPs -Purchasing Power standard; Ram -Range adjusted measure; R&D -Research and Development; so2 -sulphur Dioxide; sox -sulphur oxide source: authors' survey and environmental ones, energy indicators, such as gas, power, coal and oil consumption, are usually employed. Although researchers' interest and engagement in formulating and applying analytical and modelling techniques in energy and environmental studies goes much further back in time, it has rapidly intensified over the past 15-20 years. Consequently, a significant portion of the studies listed in Table 1, particularly of more recent ones, tackle environmental and energy issues in performance measurement. Comprehensive reviews of the empirical applications of DEA techniques in this type of studies are given by Zhou et al. (2008a), and more recently by Song, An, Zhang, Wang, and Wu (2012). Another two studies by Zhou, Ang, and Poh (2008b) and Zhou, Poh, and Ang (2016) focused on the theoretical foundation and several models for DEA-based measurement of environmental efficiency and productivity (i.e., environmental DEA technology). The last paper also presents a case study on measuring the environmental performance of OECD countries. The number of countries being the subject of the analyses reviewed in this paper varies for several reasons, depending not only on the authors' preferences and research efforts, but on the availability of data and on the number of OECD members in the observed period. Although the OECD countries have been the subject of numerous studies in which they were compared both mutually and to non-member countries, this survey is narrowed down to their mutual comparisons.
For the purpose of macroeconomic examination, data envelopment analysis was first used by Färe, Grosskopf, Norris, and Zhang (1994). An interesting feature of this study, which makes it extremely important for our research, is that it addressed precisely the OECD countries. Although all the studies from Table 1 use DEA-inspired approaches to evaluate the efficiency and productivity of OECD countries, range of employed models, their extensions and combinations is quite extensive. Moreover, the relative performance measurement was supported and enriched using a wide range of ideas like using differently based strategies for designing various performance indices and tests to validate those indices and to assess the degree of convergence, decomposing productivity growth into changes in efficiency and changes in technology, dividing the set of countries into sub-groups (e.g., European and non-European countries, countries with below and above median performance), comparing socio-economic efficiency estimated with and without the inclusion of environmental factors, combining DEA with other statistical and non-statistical methods, dividing the observed period into sub-periods, summarising performance by merging separate dimensions into a single synthetic measure, determining lower and upper bounds for inputs and outputs, dividing inputs into both energy and non-energy and outputs into both desirable (good) and undesirable (bad) outputs, constructing environmental efficiency as a ratio of good efficiency performance (using a good output) to a bad efficiency measure (using a bad output), etc. A progressive shift of researchers' focus from economic efficiency in the 1990s to environmental efficiency in the 2000s, and consequently to energy efficiency in the 2010s is evident. Hence, the theme of environmental and energy issues took precedence in the new millennium and became dominant in the papers dealing with efficiency measurement using DEA.

Concluding remarks
The empirical application of data envelopment analysis in the macroeconomic performance evaluation of OECD countries is here certainly not completely covered. Certain pertinent articles may have been omitted because they are of mostly theoretical character, are out of reach, have a narrow scope (focusing on single aspects of socio-economic development, such as healthcare, education, agriculture, public spending, etc.) or analyse similar but older datasets as already selected articles and/or are less often cited.
A multitude of studies using different DEA-based approaches have been presented in this paper, all with the common goal to assist researchers and practitioners, interested in using DEA, in choosing the most suitable tools for cross-country comparisons of socio-economic inequalities. Although each approach may be useful for specific issues of interest, none of them can be prescribed as the best solution. Nevertheless, they all provide a stimulus for further research that might result in an advancement of this field. Note 1. Although the Malmquist productivity index is defined based on the concept of distance function, it can also be directly represented by DEA efficiency measures (Zhou, Ang, & Poh, 2008a).