Data Envelopment Analysis Estimates Research Articles

A bootstrapping dynamic two-stage SBM model: An application to assess industrial water use and health risk systems

Despite the great number of applications of bootstrapping data envelopment analysis (DEA) with a one-stage structure, there are limited attempts for approximating the distribution of the DEA estimator considering the two-stage structure across multiple periods. This research develops the dynamic two-stage non-radial DEA model based on smoothed bootstrap and subsampling bootstrap. Then, we run the proposed models on assessing the efficiency of China's industrial water use and health risk (IWUHR) systems and compare them with the bootstrapping results on standard radial network DEA. The results are as follows. (1) The proposed non-radial DEA model based on smoothed bootstrap can adjust original over-estimated and under-estimated values. (2) China's IWUHR system has good performance, and its HR stage performs better than the IWU stage for 30 provinces from 2011 to 2019. The poor performance of the IWU stage in Jiangxi and Gansu needs to be noticed. The provincial differences of the detailed bias-corrected efficiencies expand in the later period. (3) The rankings of IWU efficiency in the three regions are in agreement with that of HR efficiency: eastern, western, and central regions in this order. Particular attention should be paid to the downward trend of the bias-corrected IWUHR efficiency in the central region.

Analyzing the accuracy of variable returns to scale data envelopment analysis models

The data envelopment analysis (DEA) model is extensively used to estimate efficiency, but no study has determined the DEA model that delivers the most precise estimates. To address this issue, we advance the Monte Carlo simulation-based data generation process proposed by Kohl and Brunner (2020). The developed process generates an artificial dataset using the Translog production function (instead of the commonly used Cobb Douglas) to construct well-behaved scenarios under variable returns to scale (VRS). Using different VRS DEA models, we compute DEA efficiency scores with artificially generated decision-making units (DMUs). We employ five performance indicators followed by a benchmark value and ranking as well as statistical hypothesis tests to evaluate the quality of the efficiency estimates. The procedure allows us to determine which parameters negatively or positively influence the quality of the DEA estimates. It also enables us to identify which DEA model performs the most efficiently over a wide range of scenarios. In contrast to the widely applied BCC (Banker-Charnes-Cooper) model, we find that the Assurance Region (AR) and Slacks-Based Measurement (SBM) DEA models perform better. Thus, we endorse the use of AR and SBM models for DEA applications under the VRS regime.

Financing energy transition in COVID-19 for energy efficiency: Does mitigation of energy price risk that essential?

The aim of the study is to test the nexus between energy prices risk and energy efficiency for energy transition to recommend the implication for the period of COVID-19 crises. This study uses short-term daily data of G-20 countries for COVID-19 crises was taken to better estimate the study findings. To estimate the results Data Envelopment Analysis estimation method was applied for empirical inference. The findings revealed that the COVID-19 crises have the biggest negative influence with 47.1% on oil prices which raised energy prices risk at large. The aforementioned results hold even after substituting the magnitude of extreme list of variables, re-estimating the equations with energy efficiency. Such risk has further halted energy efficiency with 33.69% in G-20 countries during COVID-19 which is one of the largest dent of the mankind history. Our results also inferred that the relationship of energy prices risk with energy efficiency remained significant but negative with energy transition. Extending to it, the post-COVID-19, the danger of energy stock price crashes is expected to diminish dramatically. The study suggest that the corporations must participate in greater corporate social responsibility activities have lower post-COVID-19 energy price collapse risk. Finally, we demonstrate that post-COVID-19, the impact of COVID-19 on energy price collapse risk.

Dynamics of total factor productivity growth: An empirical analysis of Indian commercial banks

This paper investigates the total factor productivity (TFP) change scenario among Indian commercial banks during 1998–2017. We measure the change in the Malmquist TFP index and decompose this into technological, efficiency, and scale change components using data envelopment analysis (DEA). Further, the bootstrap-based Simar and Wilson (2007) procedure is applied to correct the bias from the conventional DEA estimates. We also explain the variations in TFP estimates using a set of bank-specific and macroeconomic variables with a system-generalised method of moments and bias-corrected fixed-effects models. Our results show an improvement in TFP among Indian commercial banks– with growth relatively higher during the pre-crisis than in the post-crisis period. The productivity gains are driven mainly by technological progress rather than efficiency improvements. Amongst different ownership categories, foreign-owned banks achieve the highest overall productivity gains, followed by the domestic privately owned and state-owned banks. Finally, our TFP regression results show that return on assets, diversification, GDP per capita, Herfindahl–Hirschman Index, and inflation are the main variables responsible for driving these total factor productivity differences.

Subsampling bootstrap in network DEA

Data Envelopment Analysis (DEA), provides an empirical estimation of the production frontier, based on an observed sample of decision making units (DMUs). Except for the single input-single output case, the asymptotic distribution of the DEA estimator can only be approximated through bootstrapping approaches. Therefore, bootstrapping techniques have been widely applied in the DEA literature to make statistical inference for the cases when the production process has a single-stage structure. However, in many cases, the transformation of inputs into outputs has an inner structure that needs to be considered. This paper examines the applicability of the subsampling bootstrap procedure in the approximation of the asymptotic distribution of the DEA estimator when the production process has a network structure, and in the presence of undesirable factors. Evidence on the performance of subsampling bootstrap is obtained through Monte Carlo experiments for the case of two-stage series structures, where overall and stage efficiency estimates are calculated using the additive decomposition approach. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process. Subsampling methodology is then applied to construct confidence interval estimates for the overall and stage efficiency scores of railways in 22 European countries, where the railway transport process is decomposed into two stages and the railway noise pollution problem is considered as an undesirable output.

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.

Assessment of the Economic Security of Russia in the Foreign Economic Sphere on the Basis of the Non-parametric Method

Purpose: is to assess the security of Russia's economic security in the foreign economic sphere.Methods: the article is based on the analysis of the theoretical foundations of the formation of target values of economic security indicators, the study of the methodology for applying the non-parametric method for assessing data envelopment analysis and the use of the statistical method of information processing. The method of comparative analysis of the economic development of foreign countries was also used. To form a holistic view of the results of the assessment, the data visualization method was used.Results: based on the result of considering the methodology of the non-parametric data envelopment analysis estimation method, the advantages of its application are described, as well as the key features that need to be paid attention to when assessing by this method. The content of two main assessment models used in the framework of the data envelopment analysis (DEA) method is disclosed, the use of one of them in the context of assessing the country's economic security is justified. By using specialized software (Deap version 1.2), the economic security of Russia in the foreign economic sphere was assessed, as a result of which the target value of the economic security indicator for the long term was obtained.Conclusions and Relevance: the method for assessing economic security considered in the article makes it possible to deepen the existing assessment tools, supplement the existing methods for calculating the target indicators of economic security and, if necessary, adjust the current target indicators. The information obtained on the basis of the DEA method can be used in the formation of plans and forecasts in the field of economic security, as well as in the development of methodological support for the Economic Security Strategy of the Russian Federation for the period up to 2030.

An alternative Bayesian data envelopment analysis approach for correcting bias of efficiency estimators

In this study, we introduce an alternative Bayesian data envelopment analysis (DEA) approach yielding consistent efficiency estimators for convex sets. This approach draws on two distributional assumptions, a uniform likelihood and a beta prior. It is known from the literature that the combination of those two distributions leads to a reasonable estimator of the parameter. The prior of our approach is “non-informative” in a relative sense and does not depend on sample size. The consistency of the estimates is proven by formal statistical analysis, empirical analysis using real-world data, and computational analysis using simulated data. Our findings justify the appropriateness of our distributional assumptions and the validity of the presented bias-correction procedure. Our estimates are strongly correlated with the DEA-smoothed bootstrap estimates while presenting lower mean square error (MSE) and mean absolute error (MAE). Specifically, the correlation coefficients range between 0.898 and 0.952. The MSE of the alternative Bayesian DEA estimates gradually decreases while sample size increases. For samples of 500, 1,000 and 1,500 units, the MSE is as low as 6.410−4, 1.410−4 and 610−5, respectively. Also, an inverse relationship between the sample size and the length of the confidence intervals of the alternative Bayesian DEA estimates is present.

Evaluation of the eco-efficiency of territorial districts with seaport economic activities

The port sector has received growing attention from port authority managers and policymakers. The strategic relevance of ports has improved, but the environment is negatively affected by port operations. This study attempts to assess the performance of twenty-four European ports considering their eco-efficiency. The stochastic frontier analysis has been proposed to evaluate the port performance, and several data envelopment analysis estimations have been calculated to verify the consistency condition. Evidence suggests that recent management efforts to increase the volume of the ports’ activity do not impair their eco-efficiency, and policymakers can refer to different theoretical patterns to verify the potential impact of specific measurements targeted at improving eco-efficiency performance.

How energy insecurity leads to energy poverty? Do environmental consideration and climate change concerns matters.

The aim of the study is to estimate the nexus between energy insecurity and energy poverty with the role of climate change and other environmental concerns. We used DEA like WP methods and properties of MCDA, a most common form of data envelopment analysis (DEA) to estimate the nexus between constructs.This paper presents a measurement and analysis of G7 countries' energy, economic, social, and environmental performance associated with energy poverty indexes. The study used the multiple, comprehensive, and relevant set of indicators, including energy economics and environmental consideration of energy poverty. The net energy consumption of al G7 economies is equal to 34 percent of the entire world along with the net estimate GDP score of around 50 percent. Using DEA modelling and estimation technique, our research presented valuable insights for readers, theorists and policy makers on energy, environment, energy poverty and climate change mitigation. For this reasons, all theseindicators combined in a mathematical composite indicator to measure energy, economic, social, and environmental performance index (EPI). Results show that Canada has the highest EPII score, which shows that Canada's capacity to deal with energy self-sufficiency, economic development, and environmental performance is greater than the other G7 countries. France and Italy rank second and third. Japan comes next with 0.50 EPI scores, while the USA has the lowest average EPI score environment vulnerable even though have higher economic development among the G7 group countries. We suggest a policy framework to strengthen the subject matter of the study.

The curse of dimensionality (COD), misclassified DMUs, and Bayesian DEA

Data envelopment analysis (DEA) is used to assess the relative efficiency of a set of decision-making units (DMUs). A potential drawback to DEA is that one must include a sufficient number of observations to ensure that all input–output dimensions are adequately characterized. Employing DEA with too few DMUs for a given set of inputs/outputs generates estimates that overstate efficiency. This is known as the “curse of dimensionality (COD)”. Because production processes vary widely in technology and complexity, it is difficult to analytically characterize the effects of the COD on DEA-generated efficiency scores. This paper uses Bayesian methods to characterize and adjust for the possibility of misclassified DMUs and COD-related biases in DEA. Based on the nature of the COD bias we propose an appropriate prior distribution for the proportion of misclassified DMUs and use it to derive the concordant posterior distribution. A simulation analysis compares our model to those obtained with an ignorance prior distribution to evaluate the utility of the new model, and it is then applied to data from the Turkish electricity industry. We find that estimates of the probability of misclassification can be improved using our proposed prior distribution, especially in sample sizes of less than 40 observations. Highlights We account for the curse of dimensionality in the misclassification of DEA estimates. A left skewed (proposed) distribution is used to model prior misclassification beliefs. Simulations suggest that a left skewed prior outperforms an ignorance prior in small samples.

Adding a Social Risk Adjustment Into the Estimation of Efficiency: The Case of Chilean Hospitals.

There is much interest in adding social variables to hospital performance assessments. Many of the existing analyses, however, already include patients' diagnosis data, and it is not clear that adding a social adjustment variable would improve the quality of the results: the growing literature on this issue provides mixed results. The purpose in this study was to add evidence from a developing country into this discussion. We estimate the efficiency of hospitals controlling for casemix, with and without adjusting the hospital's casemix for the patients' sociodemographic variables. The magnitude of the adjustment is based on the observed impact of age, sex, and income on length of stay, conditional on the diagnosis related group (DRG). We use a data envelopment analysis (DEA) to assess the efficiency of 50 Chilean hospitals' discharges, including 780 DRGs and covering about 60% of total discharges in Chile from 2013 to 2015. We found that the sociodemographic adjustment introduces very small changes in the DEA estimation of efficiency. The underlying reason is the relatively low influence of sociodemographics on hospital costs, conditional on DRG, and the changing pattern of sociodemographics across DRGs for any given hospital. We conclude that the casemix-adjusted estimation of hospital efficiency is robust to the heterogeneity of patients' sociodemographic heterogeneity across hospitals. These results confirm, in a developing country, what has been observed in developed countries. For management purposes, then, the processing costs of adding social variables into hospitals' performance assessments might not be justified.

INFERENCE IN DYNAMIC, NONPARAMETRIC MODELS OF PRODUCTION: CENTRAL LIMIT THEOREMS FOR MALMQUIST INDICES

The Malmquist index gives a measure of productivity in dynamic settings and has been widely applied in empirical work. The index is typically estimated using envelopment estimators, particularly data envelopment analysis (DEA) estimators. Until now, inference about productivity change measured by Malmquist indices has been problematic, including both inference regarding productivity change experienced by particular firms as well as mean productivity change. This paper establishes properties of a DEA-type estimator of distance to the conical hull of a variable returns to scale production frontier. In addition, properties of DEA estimators of Malmquist indices for individual producers are derived as well as properties of geometric means of these estimators. The latter requires new central limit theorem results, extending the work of Kneip, Simar, and Wilson (2015, Econometric Theory 31, 394–422). Simulation results are provided to give applied researchers an idea of how well inference may work in practice in finite samples. Our results extend easily to other productivity indices, including the Luenberger and Hicks–Moorsteen indices.

Measuring the financial efficiency of agricultural cooperatives in South Africa: an application of the Simar–Wilson methodology

ABSTRACT Post-1994, the South African government has favoured cooperatives over other types of corporate entities in its rural development programmes. An improved understanding of the key drivers underpinning the performance of cooperatives is important for informing government programmes and policies that target cooperatives. This study examined the financial efficiency, and its determinants, of 387 agricultural cooperatives in South Africa, using the Simar–Wilson methodology. Bias-corrected Data Envelopment Analysis estimates for financial efficiency were obtained in the first stage. The results indicated that many agricultural cooperatives are relatively inefficient, compared to the three best-performing cooperatives on the efficient boundary. In the second stage, a double bootstrap truncated regression model was used to obtain bias-corrected scores that excluded the best-performing cooperatives. The statistically significant efficiency determinants identified from the analysis were the age and size of the cooperative, the gender of the principal manager of the cooperative, its governance and the training indicators. The observed relationship between governance and efficiency may be attributed to institutions that prioritise non-financial goals by being relatively more willing to compromise on governance quality. Furthermore, deviations from sound institutional control mechanisms are more likely to emerge in cooperatives that have weak institutional and organisational arrangements.

A comparative approach of stochastic frontier analysis and data envelopment analysis estimators: evidence from banking system

PurposeThe consistency of stochastic frontier analysis (SFA) and data envelopment analysis (DEA) cost efficiency measures using a sample of 650 commercial and domestic banks in the United States is investigated based on cluster analysis while accounting for the yearly variation in banks.Design/methodology/approachDue to the importance of efficiency measures for policy and managerial decision-making, the cost efficiency measures of SFA and DEA estimators are examined according to four criteria: levels, rankings, stability over time and stability over clustering groups. In this paper, we present two clustering methods, Gap Statistic and Dindex, that involve SFA and DEA cost efficiency measures. The clustering approach creates homogeneous groups of banks offering a similar mix of efficiency levels. Hence, each evaluated bank knows the cluster to which it belongs. Furthermore, this paper provides nonparametric statistical tests of SFA and DEA cost efficiency measures estimated with and without a clustering approach.FindingsThe results suggest that the clustering approach plays a considerable role in the rankings of US banks. Furthermore, the average SFA and DEA cost efficiency measures over time of the homogeneous US banks are substantially higher than those of the heterogeneous US banks.Originality/valueThis research is the first to provide comparative efficiency measures needed for desirable policy conclusions of heterogeneous and homogeneous US banks.

Impact of financial liquidity and solvency on cost efficiency: evidence from US banking system

PurposeThe purpose of this paper is to evaluate the importance of financial liquidity and solvency on US commercial and domestic banks’ cost efficiency while accounting for internal and external factors.Design/methodology/approachThe Stochastic Frontier Analysis and Data Envelopment Analysis estimators are used to estimate the cost efficiency of 11,044 US commercial and domestic banks from 2005 to 2017. Using Tobit regression model, the importance of financial liquidity and solvency on cost efficiency is examined.FindingsThe results provide evidence that the financial liquidity and solvency negatively impact the cost efficiency of US commercial and domestic banks. Overall, US commercial and domestic banks were inefficient during the financial crisis in comparison to the tranquil period. The importance of financial solvency on the cost efficiency was not statistically significant, while the financial liquidity negatively collapsed because of contagion. Finally, the results provide evidence that the amount of total assets matters in the improvement of the cost efficiency.Originality/valueThis paper estimates and identifies the 2007-2009 financial crisis with liquidity, solvency or both financial factors.

Benchmarking the benchmarks – Comparing the accuracy of Data Envelopment Analysis models in constant returns to scale settings

Despite the massive use of Data Envelopment Analysis (DEA) models for efficiency estimations in scientific applications, no paper cared about identifying the DEA model, which is able to provide the most accurate efficiency estimates, so far. We develop an established method based on a Monte Carlo data generation process to create artificial data. As we use a Translog production function instead of the commonly utilized Cobb Douglas production function, we are able to construct meaningful scenarios for constant returns to scale. The decision-making units resulting from the generated data are then used to calculate DEA estimators using different DEA models. Finally, the quality of the resulting efficiency estimates is evaluated by five performance indicators and summarized in benchmark scores. With this procedure, we can postulate general statements on parameters that influence the quality of DEA studies in a positive/negative way and determine which DEA model operates in the most accurate way for a range of scenarios. Here, we can show that the Assurance Region and Slacks-Based-Measurement models outperform the CCR (Charnes–Cooper–Rhodes) model in constant returns to scale scenarios. We therefore recommend a reduced utilization of the CCR model in DEA applications.

Statistical inference for the Russell measure of technical efficiency

Data envelopment analysis (DEA) has become a popular approach to nonparametric efficiency measurement. The statistical inference using bootstrap methods is readily available for the radial DEA estimator; however it is missing for the Russell measure, the nonradial DEA estimator. We propose a bootstrap based procedure for making statistical inference about the individual Russell measures of technical efficiency. We perform simulations to examine finite sample properties of the proposed estimator. Finally, we present an empirical study using proposed bootstrap procedure.

A comparison of parametric and nonparametric estimation methods for cost frontiers and economic measures

ABSTRACTThis article examines the empirical performance of alternative frontier estimators’ ability to replicate a known underlying technology and economic measures such as multi-product and product-specific economies of scale, and economies of scope. A cross sectional Monte Carlo procedure to simulate data is used to evaluate a two-sided error system, an OLS system restricting errors to be above the cost frontier, the stochastic frontier method, and data envelopment analysis (DEA). The data are generated assuming a half-normal distribution, and a uniform distribution. Data were also simulated with single and two output firms. The DEA estimator was most robust in estimating the “true” cost frontier and associated economic measures including data sets without single output firms and less effected by distributional assumptions.

Bias in Transport Efficiency Estimates Caused by Misspecified DEA Models

This paper examines transport modes that have employed Data Envelopment Analysis (DEA). It ascertains whether key DEA specifications necessary for estimating valid efficiency scores are present, the impact on the scores when they are not, and methods for correcting the errors. One critical specification is that for the sample data being used, each output must have been produced by various proportions of the inputs, with the substitutions between each pair of inputs shown on an isoquant. And, for the sample data, each input must have produced various proportions of the outputs, with the transformations between each pair of outputs shown on a production frontier. It is essential that these specifications are met by the data sample being used. DEA estimates input weights based solely on the Marginal Rate of Substitutions (MRS) between inputs on the sample data’s efficient frontier (isoquant). And DEA estimates output weights based solely on the Marginal Rate of Transformations (MRT) between outputs on the sample data’s production frontier. If there are no substitutions or transformations for the sample at hand, then there are no valid MRSs and MRTs, so DEA will utilize false weights and thereby produce false efficiency scores. In this paper, we analyze inputs and outputs that have often been used in DEA articles involving airline, urban transit, and freight rail data. Our data samples show that input substitution and output transformation are often not present. And, for our sample data, these misspecifications result in badly biased estimates of both technical efficiencies and second-stage regression parameters. We suggest methods for identifying and correcting for these specification errors, so future transportation DEA articles can avoid these problems.