Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> Abstract A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs. <s> BIB001 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> It is common practice to decompose measures of efficiency into component measures of technical and allocative efficiency. In this paper we show how, and why, to decompose a general measure of technical efficiency into component measures of purely technical efficiency, congestion, and scale efficiency, and we investigate the properties of each measure. We do so for a multiple-output technology which satisfies a weak axiom system that does not include either constant returns to scale or strong input disposability. <s> BIB002 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories." <s> BIB003 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> In this chapter, we described a Bayesian approach to efficiency analysis using stochastic frontier models. With cross-sectional data and a log-linear frontier, a simple Gibbs sampler can be used to carry out Bayesian inference. In the case of a nonlinear frontier, more complicated posterior simulation methods are necessary. Bayesian efficiency measurement with panel data is then discussed. We show how a Bayesian analogue of the classical fixed effects panel data model can be used to calculate the efficiency of each firm relative to the most efficient firm. However, absolute efficiency calculations are precluded in this model and inference on efficiencies can be quite sensitive to prior assumptions. Accordingly, we describe a Bayesian analogue of the classical random effects panel data model which can be used for robust inference on absolute efficiencies. Throughout, we emphasize the computational methods necessary to carry out Bayesian inference. We show how random number generation from well-known distributions is sufficient to develop posterior simulators for a wide variety of models. <s> BIB004 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> This chapter begins with a brief discussion of variations in productive efficiency using airlines as an example. It then presents the main purpose of the book, which is to study inefficiency in production and its impact on economic and financial performance. The chapter then provides background material and focuses on hypotheses that have been proposed in literature that would explain variation in producer performance; lays the theoretical foundation for the measurement of productive efficiency; offers a brief introduction to alternative techniques that have been developed to quantify inefficiency empirically; introduces various econometric approaches to efficiency estimation; introduces variants of the mathematical programming approach to efficiency estimation; introduces the Malmquist productivity index and shows how to decompose it into various sources of productivity change, including variation in productive efficiency; and describes three ways of approximating a Malmquist productivity index: the use of superlative index numbers, the use of econometric techniques, and the use of mathematical programming techniques. An overview of the succeeding chapters is also presented <s> BIB005 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> The banking industry has been the object of DEA analyses by a significant number of researchers and probably is the most heavily studied of all business sectors. Various DEA models have been applied in performance assessing problems, and the banks' complex production processes have further motivated the extension and improvement of DEA techniques. This paper surveys 80 published DEA applications in 24 countries/areas that specifically focus on bank branches. Key issues related to the design of DEA models in these studies are discussed. Much advice is included on how to design future experiments and studies in this domain. A number of areas where further research could be fruitful are suggested. <s> BIB006 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> type="main" xml:id="insr12056-abs-0001"> A rich theory of production and analysis of productive efficiency has developed since the pioneering work by Tjalling C. Koopmans and Gerard Debreu. Michael J. Farrell published the first empirical study, and it appeared in a statistical journal (Journal of the Royal Statistical Society), even though the article provided no statistical theory. The literature in econometrics, management sciences, operations research and mathematical statistics has since been enriched by hundreds of papers trying to develop or implement new tools for analysing productivity and efficiency of firms. Both parametric and non-parametric approaches have been proposed. The mathematical challenge is to derive estimators of production, cost, revenue or profit frontiers, which represent, in the case of production frontiers, the optimal loci of combinations of inputs (like labour, energy and capital) and outputs (the products or services produced by the firms). Optimality is defined in terms of various economic considerations. Then the efficiency of a particular unit is measured by its distance to the estimated frontier. The statistical problem can be viewed as the problem of estimating the support of a multivariate random variable, subject to some shape constraints, in multiple dimensions. These techniques are applied in thousands of papers in the economic and business literature. This ‘guided tour’ reviews the development of various non-parametric approaches since the early work of Farrell. Remaining challenges and open issues in this challenging arena are also described. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute <s> BIB007 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> Given the importance the concept of productive efficiency has on analyzing the human development process, which is complex and multidimensional, this study conducts a literature review on the research works that have used the data envelopment analysis (DEA) to measure and analyze the development process. Therefore, we researched the databases of Scopus and Web of Science, and considered the following analysis dimensions: bibliometrics, scope, DEA models and extensions used, interfaces with other techniques, units analyzed and depth of analysis. In addition to a brief summary, the main gaps in each analysis dimension were assessed, which may serve to guide future researches. <s> BIB008 </s> Empirical Surveys of Frontier Applications: A Meta-Review <s> Introduction <s> This article reports the evolution of the literature on Dynamic Data Envelopment Analysis (DDEA) models from 1996 to 2016. Systematic searches in the databases Scopus and Web of Science were performed to outline the state of the art. The results enabled the establishment of DDEA studies as the scope of this article, analyzing the transition elements to represent temporal interdependence. The categorization of these studies enabled the mapping of the evolution of the DDEA literature and identification of the relationships between models. The three most widely adopted studies to conduct DDEA research were classified as structuring models. Mapping elucidated the literature behavior through three phases and showed an increase in publications with applications in recent years. The analysis of applications indicated that most studies address evaluations in the agriculture and farming, banking and energy sectors and consider the facilities as transition elements between analysis periods. <s> BIB009
The field of efficiency and productivity analysis using frontier estimation methodologies has been developing very rapidly in the last four decades. Since the seminal articles of BIB001 , BIB003 and BIB002 the literature developing both methodological and empirical contributions to the nonparametric frontier literature (often identified via the moniker Data Envelopment Analysis (DEA)) have been literally booming. Equally so, since the seminal articles of  and Meeusen and van den Broeck (1977) stochastic frontier analysis (moniker SFA) has almost equally flourished along both methodological and empirical lines. Further methodological developments have led to new and somewhat separate streams of literature (see BIB005 for an overview). Common to this broad efficiency and productivity literature using some form of frontier estimation is the enormous and booming empirical literature that has emerged. A wide diversity of sectors has been studied using cross-section, time series or panel data covering a wide variety of geographical areas (from municipalities and counties to regions, and from countries to continents). On the one hand, this efficiency and productivity literature has led to an abundance of surveys aimed at summarising general or specialised methodological advancements (examples include BIB009 , BIB004 or BIB007 ). On the other hand, this flood of empirical frontier applications has also lead to a multitude of empirical surveys. The latter empirical surveys are the main topic of this contribution. As a matter of fact, there are a lot of empirical surveys available in the literature focusing on specific sectors of application (see, e.g., BIB008 , or BIB006 , among others). But, to the best of our knowledge, none of the existing studies have looked at what are the most surveyed fields of empirical applications and what are instead those in which there are no or few surveys, and how this situation evolved over time. To the best of our knowledge, there is no survey on surveys in the field of frontier methods (SFA, FDH, DEA and their extensions) proposed to evaluate the many facets of the efficiency literature in the different areas of the economic activities. The main real difference from our proposal to other surveys is to use a bibliometric methodology to assess the size and importance of the applications in those areas: in addition to the number of surveys, the co-occurrence of the concepts, methods and areas is used to define a degree of generality that allows the visualisation of gaps and overlaps in the field. The topic of this paper is exactly to fill up this gap. The basic objective of this contribution is to provide a state of the art survey of empirical surveys of frontier estimation applications as applied to different economic sectors. By lack of a better concept, we label this a meta-survey. This amounts to asking the basic question: in which sectors and fields do empirical surveys exist? And if such empirical survey exists for a sector, we want to determine how many such surveys exists for this field and how recent these surveys are? Furthermore, we look at the connections among different sectors and fields of application through co-citation analysis. This should allow us to identify the gaps in the existing sectors and fields and offer some interpretations of the currently available literatures. To develop such a meta-survey of empirical surveys of frontier estimation applications, we encounter the following series of methodological problems. We obviously need to have a full description of all the possible economic sectors and fields, so as to be able to identify existing gaps in the literature. To identify a rather universal taxonomy of economic activity, we adopt the UNESCO manual (2008) . We allocate all of the empirical surveys we encounter to one of the available taxonomic classes. This is done manually here, but our work could also provide useful suggestions on how one could standardize this activity in the future (see also the concluding section). Finally, we attribute all empirical surveys also to the Journal of Economic Literature (JEL) classification, which is often used to classify research papers mainly in the economics literature. We discuss in the concluding section about the importance of these classifications to standardize, improve and facilitate further analysis and updates of this study. The main methodological tool applied in our meta-survey is the systematic review. In addition, we employ advanced clustering and mapping techniques. Finally, a co-citation analysis is performed to investigate the evolution of the interconnections among economic sectors and fields of application. This contribution is structured as follows. We first put the notion of research review in context to clearly delineate what we do different from other existing reviews. In the next section of methodological notes, we introduce the notion of a systematic review in some detail. In the following sections, we specify in detail the methodology used and in particular, the queries that have been run in the systematic search (Section 3), the main outcomes of the survey (Section 4), and the bibliometric and mapping exercises done on the keywords (Section 5). A concluding section offers some final comments and outlines future research.