Nonparametric Frontier Models Research Articles

Accuracy of Deterministic Nonparametric Frontier Models with Undesirable Outputs

The accuracy of deterministic nonparametric frontier models with desirable outputs has been extensively investigated. However, research on the models’ accuracy in the presence of undesirable outputs is almost nonexistent, though applications in this regard are abundant. This paper evaluates the accuracy of seven representative deterministic nonparametric frontier models in dealing with undesirable outputs. The experimental design employs Monte Carlo simulation and translog production functions across a wide range of settings. We find that the integration of undesirable outputs lowers model accuracy. All seven models display robust performance under different returns-to-scale assumptions. Outputs correlation has a positive effect on model performance. Using a large sample can improve the models’ accuracy except for the range-adjusted measure model. The models’ accuracy is most sensitive to noise at low noise levels. Endogeneity has a negative effect on the models’ accuracy, but depreciation of accuracy is minor at low to medium endogeneity levels. Heteroskedasticity leads to improved performance. Overall, the experimental results support the usage of the by-production approach and strongly disfavor the range-adjusted measure approach and the hyperbolic approach. The directional distance function method has an edge for large samples, if the objective is to identify top and bottom units. Another approach, treating undesirable outputs as inputs, is dominated by other methods. The ranking of the methods is generally robust to the variations of returns-to-scale, sample size, noise, outputs correlation, endogeneity, and heteroskedasticity. We also show that the slacks-based measure under the by-production framework has better performance than the Färe–Grosskopf–Lovell index proposed in literature.

The origins and development of statistical approaches in non-parametric frontier models: a survey of the first two decades of scholarly literature (1998–2020)

This paper surveys the increasing use of statistical approaches in non-parametric efficiency studies. Data Envelopment Analysis (DEA) and Free Disposable Hull (FDH) are recognized as standard non-parametric methods developed in the field of operations research. Kneip et al. (Econom Theory, 14:783–793, 1998) and Park et al. (Econom Theory, 16:855–877, 2000) develop statistical properties of the variable returns-to-scale (VRS) version of DEA estimators and FDH estimators, respectively. Simar & Wilson (Manag Sci 44, 49–61, 1998) show that conventional bootstrap methods cannot provide valid inference in the context of DEA or FDH estimators and introduce a smoothed bootstrap for use with DEA or FDH efficiency estimators. By doing so, they address the main drawback of non-parametric models as being deterministic and without a statistical interpretation. Since then, many articles have applied this innovative approach to examine efficiency and productivity in various fields while providing confidence interval estimates to gauge uncertainty. Despite this increasing research attention and significant theoretical and methodological developments in its first two decades, a specific and comprehensive bibliometric analysis of bootstrap DEA/FDH literature and subsequent statistical approaches is still missing. This paper thus, aims to provide an extensive overview of the key articles and their impact in the field. Specifically, in addition to some summary statistics such as citations, the most influential academic journals and authorship network analysis, we review the methodological developments as well as the pertinent software applications.

Latent heterogeneity to evaluate the effect of human capital on world technology frontier

Although human capital has been recognized as playing important role in spurring productivity growth, its empirical effect remains ambiguous due to the possibility of latent heterogeneity. To reveal the impact of this important driver of economic growth, we propose an alternative empirical methodology, robust frontier in non parametric location-scale models for accommodating simultaneously the problem of model specification uncertainty, latent heterogeneity and cross-section dependence in modelling technical efficiency. We estimate a nonparametric frontier model to define the world technology frontier of 40 countries over the period 1970–2007. Conditional versions of the frontier enables us to investigate the effect of external factors on the production process. One of these factors will allow to measure the openness of the economy of the country and the second will be this latent factor of heterogeneity linked to the absorptive capability and hence to human capital of the country. We have to adjust the methodology to take into account the panel structure of our data set, i.e., handling the time dimension and the cross-sectional dependence affecting the process. Our findings prove that human capital plays an important role in accelerating the technological catch-up (increase in the efficiency) but not on the technological changes (shifts in the frontier). This result seems to confirm the theoretical hypothesis that countries benefit from new technology (technological catch-up) only when they have the ability to exploit it, hence only when they have high level of absorptive capability.

Regional environmental efficiency in China: An empirical analysis based on entropy weight method and non-parametric models

While vigorously developing its economy, China is attaching more and more importance to environmental protection and pollution control. In different regions of China, however, there are great differences in economic development and the degree of environmental pollution. In this study, we use the entropy weight method to calculate the pollution indexes of different regions from 2015 to 2017. Then we evaluate the Chinese regional environmental efficiency based on a new non-parametric frontier model. Moreover, a new set of ranking interval models that treat the undesirable outputs as inputs is proposed to further describe the regional disparities of the environmental efficiency between different regions with robustness. Finally, we conduct an empirical analysis by combining the stepwise regression and principal component analysis to identify the most influential variables that may affect regional environmental efficiency. According to the results, the southeast region of China performs best in environmental efficiency, followed by the northeast region, then the southwest region, and the worst is the northwest region. For managerial implications, we find that the investment of high education and the development of the IT industry can significantly increase regional environmental efficiency. More importantly, the results of the principal component analysis provide the government with a set of variables to strategically select the most appropriate strategy.

Estimation of additive frontier functions with shape constraints

ABSTRACTProduction frontier is an important concept in modern economics and has been widely used to measure production efficiency. Existing nonparametric frontier models often only allow one or low-dimensional input variables due to ‘curse-of-dimensionality’. In this paper we propose a flexible additive frontier model which quantifies the effects of multiple input variables on the maximum output. In addition, we consider the estimation of the nonparametric frontier functions with shape restrictions. Economic theory often imposes shape constraints on production frontier, such as, monotonicity and concavity. A two-step constrained polynomial spline method is proposed to give smooth estimates that automatically satisfy such shape constraints. The proposed method is not only easy to compute, but also more robust to outliers. In theory, we established uniform consistency of the proposed method. We illustrate the proposed method by both simulation studies and an application to the Norwegian farm data. The numerical studies suggest that the proposed method has superior performance by incorporating shape constraints.

Technical Efficiency of Construction Companies: A Stochastic Frontier Model with Dependent Error

There are several problems with using the Standard Stochastic Frontier (SF) model to produce a company’s technical efficiencies. One of the problem is the hypothesis of independence between the error components, known as, statistical noise and inefficiency term. Recent studies have used the SFA-copula model where the copula element captures the joint distribution of the two error components thus assuming that the errors are dependent. This research seeks to use the Cobb-Douglas Stochastic Frontier production model (standard model), SFA-copula models and DEA models (DEA-CCR and DEA-BCC) to compare the technical efficiencies of 12 publicly listed construction companies in Malaysia. The latter models are non-parametric frontier models which will be used as a base to determine the best SF model. The four copulas considered in this study are Clayton, Gumbel, A12 and Product copulas. The main findings of this study are the SFA-copula models showed consistency in terms efficiency scores and rankings of companies as compared to DEA models. The results further raise the question of the reliability of standard SF model especially when SFA-product copula was chosen as the best model for measuring efficiency performance. Therefore, it is obvious that it is not possible to ignore the reliance between the noise and inefficiency term

A comparison of different full and partial non-parametric frontier models for measuring technical efficiency: With an application to Iran’s cotton producing provinces

A comparison of different full and partial non-parametric frontier models for measuring technical efficiency: With an application to Iran’s cotton producing provinces

Sustainability performance of countries matters: A non-parametric index

Tracking consumers' expectation, researchers' concentration, practitioners' competition, and governments’ legislation, we observe increasing interests in incorporating sustainability initiatives into managerial decision-making. Sustainability development centers on how to achieve balance among economic, environmental, and social objectives of involved stakeholders in the process of value creation. This paper focuses on the macro-level performance measurement of countries through a sustainability-conscious lens. Our methodological objective is to develop a non-parametric frontier model in the presence of undesirable integer-valued indicators which constructs a nationwide sustainability composite index. Particularly, a super-efficiency formulation is investigated which enables us to differentiate between equally efficient entities. From an empirical perspective, we apply the proposed model to a case study assessing the sustainability productivity of 133 countries. Our computational results demonstrate that conventional metrics commonly used globally to reflect the sustainability performance of governments may mislead decision makers. We, however, design a more comprehensive platform to benchmark the country-level productivity against all triple aspect of sustainability development. Accordingly, the proposed index permits valid inference by accounting for environmental measures and social aspects.

Модели непараметрических границ производственных возможностей: опыт применения в сельском хозяйстве

Модели непараметрических границ производственных возможностей: опыт применения в сельском хозяйстве

An evaluation of the impact of environmental regulation on the efficiency of technology innovation using the combined DEA model: A case study of Xi’an, China

The objective of this paper is to explore the impact of environmental regulation on the efficiency of technological innovation and its temporal and spatial evolution in an innovative city with a combined Data Envelopment Analysis (DEA) model. DEA is a common non-parametric frontier model for studying multi-input and multi-output systems. The DEA method uses an input-output index data to mine information such as technology frontier and efficiency evaluation relative to reference technology. Using environmental factors, the efficiency of technological innovation in Xi’an from 2006 to 2015 is measured. The research results show that low scale efficiency is the main factor that restricts the efficiency of technological innovation in innovative city Xi’an. Environmental regulations have no influence on the measurement of technological innovation efficiency in Xi’an. The “Porter hypothesis” is not tenable. There are some differences in the pure technical and scale efficiencies of the two subsystems (R&D and technology transformation) of the network DEA model. The technology transformation process has a more important objective position in the innovation system of Xi'an. The results provide a valuable reference for the measurement of technological innovation efficiency and the formulation and implementation of environmental regulation policies in the innovative cities of developing counties.

How to Choose a Nonparametric Frontier Model? Technical Efficiency of Turkish Banks Assessing Global

This article aims to address current gaps in the literature on banking efficiency using the data envelopment analysis (DEA) model. The study assesses the technical efficiency of the Turkish banking sector in the period spanning from 1990 to 2010 in-line with DEA model. In comparison with the DEA model, the CCR model (developed by Charnes, Cooper & Rhodes, European Journal of Operational Research, 1978, 2(6): 429–444) does not need model assumptions on input/output orientation. It also avoids the dilemma about the choice of input/output indicators. The comparison analysis of this study reveals that the CCR model yields more significant efficiency results than the BCC model (developed by Banker, Charnes & Cooper, Management Science, 1984, 30(9): 1078–1092). This study provides important contribution to the current empirical research on banking efficiency. The empirical results of the study reveal a steady increase in global efficiency of the Turkish banking sector over the past two decades. The future research could focus on the behavioural aspects of bank efficiency (e.g., managerial practices). The study also offers managerial implications.

A systematic methodology for the robust quantification of energy efficiency at wastewater treatment plants featuring Data Envelopment Analysis

This article examines the potential benefits of using Data Envelopment Analysis (DEA) for conducting energy-efficiency assessment of wastewater treatment plants (WWTPs). WWTPs are characteristically heterogeneous (in size, technology, climate, function …) which limits the correct application of DEA. This paper proposes and describes the Robust Energy Efficiency DEA (REED) in its various stages, a systematic state-of-the-art methodology aimed at including exogenous variables in nonparametric frontier models and especially designed for WWTP operation. In particular, the methodology systematizes the modelling process by presenting an integrated framework for selecting the correct variables and appropriate models, possibly tackling the effect of exogenous factors. As a result, the application of REED improves the quality of the efficiency estimates and hence the significance of benchmarking. For the reader's convenience, this article is presented as a step-by-step guideline to guide the user in the determination of WWTPs energy efficiency from beginning to end. The application and benefits of the developed methodology are demonstrated by a case study related to the comparison of the energy efficiency of a set of 399 WWTPs operating in different countries and under heterogeneous environmental conditions.

Nonparametric Frontier Analysis Using Stata

In this article, we describe five new Stata commands that fit and provide statistical inference in nonparametric frontier models. The tenonradial and teradial commands fit data envelopment models where nonradial and radial technical efficiency measures are computed (Färe, 1998, Fundamentals of Production Theory; Färe and Lovell, 1978, Journal of Economic Theory 19: 150–162; Färe, Grosskopf, and Lovell, 1994a, Production Frontiers). Technical efficiency measures are obtained by solving linear programming problems. The teradialbc, nptestind, and nptestrts commands provide tools for making statistical inference regarding radial technical efficiency measures (Simar and Wilson, 1998, Management Science 44: 49–61; 2000, Journal of Applied Statistics 27: 779–802; 2002, European Journal of Operational Research 139: 115–132). We provide a brief overview of the nonparametric efficiency measurement, and we describe the syntax and options of the new commands. Additionally, we provide an example showing the capabilities of the new commands. Finally, we perform a small empirical study of productivity growth.

Technical efficiency of Kansas arable crop farms: a local maximum likelihood approach

AbstractThis study uses local maximum likelihood (LML) methods recently proposed by Kumbhakar et al. (2007) to assess the technical efficiency of arable crop Kansas farms. LML techniques overcome the most relevant limitations associated to mainstream parametric stochastic and nonparametric frontier models. LML allows deriving farm‐level frontier parameter estimates. The relevance of using localized estimates is evidenced by the observed heterogeneity in production technologies. Technical efficiency scores derived from the LML approach [0.905] are higher than those of the DEA model under CRS [0.808] and SFA [0.804] and close to DEA‐VRS [0.917] ratings. Deriving reliable information about farm efficiency performance is relevant to identify inefficient farms and define adequate policy and management strategies. The use of refined methods has thus important implications.

Nonparametric instrumental variables estimation for efficiency frontier

The paper investigates endogeneity issues in nonparametric frontier models. It considers a nonseparable model for a cost function C=φ(Y,U) where C and Y are the cost and the output, U is uniform in [0,1] and φ is increasing with respect to U. The cost frontier corresponds to U=0 and U can be interpreted as a normalized level of inefficiency. The endogeneity issue arises when Y is dependent of U. For identification and estimation, we use a nonparametric instrumental variables estimator of the model for fixed value U=α, and obtain an estimate of the α-quantile cost frontier φ(Y,α). This involves the solution of a non linear integral equation. If the true frontier φ(Y,0) is wanted, it is then estimated by estimating the bias correction φ(Y,0)−φ(Y,α) under additional regularity conditions. The procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices.

How to bootstrap in non-parametric frontier models? Technical efficiency of Tunisian banks

This paper presents a bootstrapped efficiency score through estimating the DEA model. We focus on an input-oriented approach using returns to scale. By using input and output data on 20 Tunisian banks over the period 1990-2010, we construct more accurate bootstrapped confidence intervals; hence, we provide more reliable and useful results for decision-makers. Moreover, we find that 4 out of 20 Tunisian banks are perfectly efficient using a data-driven estimate of the smoothing parameter.

Energy efficiency in the European Union: What can be learned from the joint application of directional distance functions and slacks-based measures?

Over the last few years concerns have increased about the energy mix in many countries. These concerns have been of greater magnitude for countries with a common energy regulation such as European Union (EU) member states. An important aspect to take into account when choosing a given energy mix is the efficiency involved in its generation. In this context, the present study analyzes the efficiency with which electricity and derived heat was produced in 25 EU member states over the last decade. This analysis considers not only the inputs and outputs involved but, more importantly, which undesirable by-products were generated during the production process, a relevant issue for EU climate policy. To this end, two nonparametric frontier models are applied: first, a Directional Distance Function (DDF), based on Briec’s (1997) [16] proposal and, second, a modified version of Tone’s (2001) [51] Slacks-Based Measure (SBM) model, both of which are especially appropriate in this particular context due to their treatment of undesirable outputs. Results are partly innovative since, with few exceptions, applications on this issue are relatively scarce. From a policy implications’ point of view, our achievements are also interesting because they reveal remarkable efficiency differences among EU countries: those countries from the latest EU enlargements account for the lowest efficiencies, with large opportunities for improvement in CO2 abatement and primary energy saving. Results also show stable efficiencies along the evaluated period and, therefore, highlighting the need to further intensify the initiatives designed to harmonize environmental policies and identifying drivers for efficiency improvement turn out to be still key objectives.

Book Reviews

Carlos Martins-Filho of University of Colorado and IFPRI reviews, “Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives” by Leopold Simar and Paul W. Wilson. The Econlit abstract of this book begins: “Presents recent developments in, and perspectives on, estimation and inference in nonparametric frontier models. Discusses nonparametric statistical models of production—combining economics and statistics; the nonparametric envelopment estimators; bootstrap inference using data envelopment analysis and free disposal hull estimators; robust order-m estimators; robust order-α estimators; outlier detection; explaining inefficiency; and unanswered questions, promising ideas. Simar is at the Catholic University of Louvain. Wilson is at Clemson University.”

Local Exponential Frontier Estimation

In this paper we propose a local exponential estimator for a multiplicative nonparametric frontiermodel rst introduced by Martins-Filho & Yao (2007). We improve their estimation procedure by adoptinga variant of the local exponential smoothing introduced in Ziegelmann (2002). Our estimator is shown to beconsistent and asymptotically normal under mild regularity conditions. In addition, due to local exponentialsmoothing, potential negativity of conditional variance functions that may hinder the use of Martins-Filhoand Yao's estimator is avoided. A Monte Carlo study is performed to shed light on the nite sample proper-ties of the estimator and to contrast its performance with that of the estimator proposed in Martins-Filho &Yao (2007). We also conduct an empirical exercise in which a production function and associated ecienciesfor branches of nancial institutions in the United States are estimated.

The Market Structure of Urban Solid Waste Services: How Different Models Lead to Different Results

Urban waste services in Portugal have historically been provided together with other services, such as the water services. Despite the lack of discussion on this subject in the literature, some questions have been raised about the gains, in terms of efficiency, of this policy. Following a recent and robust partial nonparametric frontier model, based on order-α, we intend to evaluate the presence of economies of scope in the Portuguese waste sector. Furthermore, we also estimate the economies of scale using the traditional data envelopment analysis. The results show the absence of economies of scope between waste and water (and wastewater) services. In addition, we identify the presence of economies of scale in smaller municipalities. These outcomes might be useful for policy and decision makers in further reforms.