Directional Distance Function Approach Research Articles

Marginal abatement cost of CO2: A convex quantile non-radial directional distance function regression method considering noise and inefficiency

By purchasing emission reduction equipment or reducing production scale, it is possible to effectively decrease CO2. Therefore, understanding the marginal abatement cost (MAC) associated with these methods is crucial for making decisions. However, previous studies using the directional distance function (DDF) approach often mis-specified production functions and neglected data noise. They also assumed decision-making units (DMUs) to be on the production frontier and used proportional changes in inputs and outputs as abatement paths. This paper addresses these limitations by developing the convex quantile non-radial directional distance function (CQR-NDDF) method, which estimates the MAC of CO2 and determines optimal abatement paths for DMUs without assuming a specific production function, employing linear programming techniques. Applying this method to 30 provinces in mainland China from 2011 to 2019, the study finds that China's CO2 MAC increased from 182 to 247 yuan/ton. The lowest-cost abatement path varies by province and time. The club convergence and ordered probit model are employed to conclude that the second industry and urbanization increase the MAC of CO2, while factors such as foreign direct investment, openness level, and human capital decrease the MAC. Moreover, the CQR-NDDF method yields significantly lower MAC estimates than the NDDF method. In conclusion, this paper provides new insights into China's CO2 MAC, emphasizing the importance of considering inefficiency and data noise in MAC estimation. We anticipate that utilizing CO2 MAC as a benchmark for carbon trading market prices could lead to an increase in prices within China's carbon trading market.

Evaluation of marginal abatement cost and potential reduction in China's industrial carbon emissions: A quadratic directional output distance function approach

As a relevant indicator for quantifying the value of carbon emissions, the marginal abatement cost (MAC) of carbon emissions has received increasing attention from academics and policymakers. This study uses a quadratic directional output distance function to analyse the technical efficiency, potential emission reduction and shadow prices of China's industrial carbon emissions. The results show that the technical efficiency of China's industry gradually decreased during the sample period. From the perspective of regions with different carbon intensity and industrial output, regions with lower carbon intensity and higher industrial output gradually closed to the optimal frontier for the technology use level and had relatively high technical efficiency. Rising technical inefficiency and carbon emissions led to a potential emission reduction that also exhibits an upwards trend. In addition, the MAC of industrial carbon emissions exhibits a U-shaped trajectory, with 2011 as the turning point. Generally, in recent years, regions with lower carbon intensity and those with higher industrial output have a relatively high MAC for industrial carbon emissions. The empirical findings reveal that a carbon emission reduction policy should be formulated and targeted to each province, and the principle of ‘easy before difficult’ can be followed to promote emission reduction.

A three-level meta-frontier directional distance function approach for carbon emission efficiency analysis in China: convexity versus non-convexity

Achieving carbon peaking and carbon neutrality goals is a fundamental requirement for advancing high-quality development in China. Carbon emission efficiency (CEE) indicates the proportion of optimal emissions to actual emissions in the production system, providing a basis for reasonable carbon emission reductions. To facilitate the realisation of China's goals, this paper analyses CEE and the carbon emission reduction potential in China from 2001 to 2020. Considering the heterogeneity of both regions and industries, this paper proposes a three-hierarchy meta-frontier directional distance function (DDF) method to measure CEE under convex and non-convex assumptions of production possibility set (PPS). The empirical results show that the assumption of convex or non-convex axiom on the innermost PPS has a great impact on efficiency distribution, and the distribution of technology gap rate (TGR) is more affected by the selection of convex or non-convex assumption compared with the distribution of CEE. Currently, China's carbon emission efficiency remains low, mostly due to management inefficiency. The primary industry has more advanced emission reduction technologies than the other two industries. The eastern region has a large potential for carbon emission reduction because of its high carbon emission base, despite its high efficiency.

Investigating the relationship between digital trade, natural resources, energy transition, and green productivity: Moderating role of R&D investment

This study investigates the influence of the green energy transition, natural resources dependency, digital trade, and environmental regulations on green productivity in selected OECD countries from 1990 to 2019. Considering the directional distance function (DDF) approach, it constructed the green productivity index and applied the heterogeneous linear panel estimations such as D-OLS “dynamic ordinary least square” and FE-OLS “fixed effects ordinary least square” to investigate the long-run relationship between variables. Further, it determines the magnitude of the variable association by addressing the quantile-based influence of the independent variables on the dependent variable using “Method of Moments Quantile Regression” (MMQR). The study also investigates the moderating effect of domestic R&D intensity and human capital to support the nexus between digital trade and green productivity. The outcomes of the MMQR suggested that digital trade is negatively associated with green productivity at low to medium quantiles, while at the highest quantiles, the relationship became positive. In contrast, green energy transition, environmental regulation, domestic R&D intensity, and human capital are significantly and positively associated with green productivity at all quantiles. Manifestly, natural resource dependency impedes green productivity at lower, medium, and higher quantiles. The marginal effects of the above variables are substantially heterogeneous at different levels of productivity growth. It suggests the transformation of industries from resource-dependent to high-tech and R&D to facilitate higher productivity growth.

Fuzzy cost, revenue efficiency assessment and target setting in fuzzy DEA: a fuzzy directional distance function approach

PurposeThis study aims to present the cost and revenue efficiency evaluation models in data envelopment analysis in the presence of fuzzy inputs, outputs and their prices that the prices are also fuzzy. This study applies the proposed approach in the energy sector of the oil industry.Design/methodology/approachThis study proposes a value-based technology according to fuzzy input-cost and revenue-output data, and based on this technology, the authors propose an approach to calculate fuzzy cost and revenue efficiency based on a directional distance function approach. These papers incorporated a decision-maker’s (DM) a priori knowledge into the fuzzy cost (revenue) efficiency analysis.FindingsThis study shows that the proposed approach obtains the components of fuzzy numbers corresponding to fuzzy cost efficiency scores in the interval [0, 1] corresponding to each of the decision-making units (DMUs). The models presented in this paper satisfies the most important properties: translation invariance, translation invariance, handle with negative data. The proposed approach obtains the fuzzy efficient targets corresponding to each DMU.Originality/valueIn the proposed approach, by selecting the appropriate direction vector in the model, we can incorporate preference information of the DM in the process of evaluating fuzzy cost or revenue efficiency and this shows the efficiency of the method and the advantages of the proposed model in a fully fuzzy environment.

Can green transformation finance contribute to urban carbon emission performance? An empirical analysis based on a spatiotemporal bi-fixed SPDM model.

"Carbon peaking" and "carbon neutrality" are serious challenges at this stage, and the function of the green transformation finance (GTF) in the operation of carbon dioxide emission reduction is an urgent issue to be explored. However, empirical studies on GTF and carbon emission performance (CEP) are lacking. Given that, this research employs a panel dataset of 278 cities in China spanning the years 2006 to 2020 to measure the CEP of Chinese cities using the non-radial directional distance function (NDDF) approach and applies the SPDM and the intermediary effect model to practically analyze the spatial effects and mechanisms of GTF in promoting CEP. The findings derived from the empirical analysis indicate that (1) the level of GTF and CEP shows a trend of year-on-year increase, and there is a significant spatial correlation, but the absolute difference in CEP between cities increases. (2) GTF promotes the improvement of CEP in local cities. It reveals a favorable spillover impact on enhancing the neighboring cities' CEP. Furthermore, the research findings remain pertinent even after conducting rigorous tests to ensure their robustness. (3) Regional heterogeneity has been observed in the impact of GTF on CEP, with the development of GTF significantly contributing to the amelioration of CEP of neighboring cities in the east, significantly contributing to the improvement of local CEP of central cities and simultaneously contributing to the improvement of local and neighboring cities' CEP in the west. (4) The findings of the intermediary examination show that GTF mainly promotes CEP through the positive incentive effect of promoting green innovation in technology and the reverse push-back effect of optimizing the structure of industries. (5) The spatial spillover effect of GTF on CEP is more sensitive under the geographic distance matrix, showing a "three-stage" decay characteristic from near to far, and its influence range is roughly 300km. Therefore, China should strengthen the development of GTF, cross-city communication and cooperation to boost the accomplishment of the carbon neutrality objective.

Effect of adoption of organic farming on technical efficiency of olive-growing farms: empirical evidence from West Bank of Palestine

Organic farming is one of the methods that increases the value added of agricultural products in a sustainable way. This paper examines how the adoption of organic farming has impacted the technical efficiency of Palestinian olive-growing farms in the West Bank. Using cross-sectional data of olive farms in the Jenin governorate, we employ an input-oriented data envelopment analysis framework to compute radial and input use efficiencies. Considering heterogeneity in technology between organic and conventional farming, a metafrontier with a directional distance function approach was applied. As self-selection bias may exist due to the decision to adopt organic farming, we apply the endogenous switching regression method to reduce bias caused by unobserved heterogeneity. Results suggest that organic farms in Jenin are not less efficient than conventional farms. Their organic farming method improves input use efficiency with respect to labor and cost relative to conventional farming. While organic farming is commonly considered to be less efficient and more costly, our findings from Jenin imply that it is, in fact, a more efficient method. We suggest that promoting organic olive farming could offer an effective strategy for small farms to add value, despite the severe geopolitical constraints of farming in the West Bank.

Evaluation of innovation efficiency in China's cultural industry: A meta‐frontier with non‐radial directional distance function approach

AbstractIn recent years, the proportion of added value of China's cultural industry to GDP has been increasing year by year. However, due to different levels of economic development and cultural resources, there are significant differences in the development of cultural industries in different regions. This study considers a sustainable positive externality by setting the patent as a new output and employs the non‐radial directional distance function in the framework of meta‐frontier to investigate the innovative performance of China's cultural industry because of regional disparities. Our main findings are that there is a major technological gap among the eastern region, the central region and the western region, in which the technical and management capabilities of the eastern region are far greater than those of the central and western regions; Cultural industries have greater room for improvement in the eastern, central and western regions, especially the western region; The efficiency level of the cultural industry is likely to be related to the local economic strength. This article explores the factors that constrain the competitiveness of cultural industries in different regions of China. Then based on its influencing factors, corresponding development measures are proposed.

Does Price Distortion Affect Energy Efficiency? Evidence from Dynamic Spatial Analytics of China

Despite market-oriented reforms, China’s energy sector is subject to energy price distortions, which are believed to be a crucial determinants of energy efficiency in China. This paper investigates the impact of energy price distortions on energy efficiency in China from the perspective of spatial correlation. Using the nonradial directional distance function approach, we first estimate the provincial-level energy efficiency in China. Paying attention to spatial correlation among the provinces of China, in stage two, we identify the determinants of energy efficiency. Our empirical results suggest that price distortions have a significant impact on energy efficiency in China. This impact holds when the cross-region effect is considered, i.e., besides its own energy price distortion, a region’s energy efficiency is also correlated to the adjacent provinces’ energy price distortions. Furthermore, we found that the levels of energy efficiencies in adjacent provinces are highly correlated. This spatial relationship can be decomposed into the ‘spillover effect’ and ‘warning effect’. These two effects work together, determining the spatial relationship among the province-level energy efficiencies.

Malmquist-Luenberger productivity indexes for dynamic network DEA with undesirable outputs and negative data

The data envelopment analysis (DEA) technique is well known for computing the Malmquist-Luenberger productivity index (MLPI) in measuring productivity change in the decision-making units (DMUs) over two consecutive periods. In this research, we detect infeasibility of the directional distance function (DDF) based DEA model of MLPI under the variable returns to scale technology when data takes on negative values. We address this problem by developing a novel DDF-based DEA model that computes an improved MLPI. We extend the DDF approach to the dynamic network structure and introduce the dynamic MLPI for analyzing the performance of DMUs over time. We also develop the dynamic sequential MLPI to detect shifts in the efficient frontiers due to random shocks or technological advancements over time. The dynamic network structure in the two indexes comprises multiple divisions in DMUs connected vertically by intermediate productivity links and horizontally over time by carryovers. The proposed models are feasible and bounded with undesirable features and negative and non-negative data values. Real data of 39 Indian commercial public and private banks from 2008 to 2019 used to illustrate the two indexes.

Measuring sustainability and competitiveness of tourism destinations with data envelopment analysis

This study analyses sustainability and competitiveness through measurements of efficiency, using data envelopment analysis. It constructs a meta-frontier non-radial directional distance function (meta-frontier NDDF) approach, which is then used to define a tourism development index and a tourism sustainability index. Using these indexes, the paper evaluates the efficiency of the tourism sector and its dynamic evolution for 27 cities in the Yangtze River Delta, China, (YRD) from 2010 to 2019. Considering regional heterogeneity, this paper analyzes the meta-frontier, group-frontier efficiency and technology gap ratio of urban tourism in the YRD, and explores the competitiveness of the cities. The results show that the more traditional measure of tourism efficiency, namely the tourism development index, which does not take account of the sector’s undesirable output (i.e., the negative impacts of carbon emissions from travel), produces overestimates. This study highlights the following practical implications: The increasing competition among tourism destinations requires tourism industry managers to determine the appropriate allocation of resources to promote the sustainable development of urban tourism. In the context of the need for global ‘carbon neutrality’, more consideration should be given to the negative impact of tourism on the natural environment to enhance the competitiveness of tourist destinations.

Dynamic changes and convergence of China's regional green productivity: A dynamic spatial econometric analysis

Low-carbon economic development is at the heart of the post-pandemic green recovery scheme worldwide. It requires economic recovery without compromising on the environment, implying a critical role that green productivity plays in achieving the carbon neutrality goal. Green productivity measures the quality of economic growth with consideration for energy consumption and environmental pollution. This study employs the slacks-based measure directional distance function (SBM-DDF) approach and the Malmquist-Luenberger (ML) index to calculate green productivity and its components of 30 provinces in China between 2001 and 2018. Using a spatial panel data model, we empirically analyzed the conditional β-convergence of China's green productivity. We found that overall, since 2001, China's green productivity has demonstrated a continuous upward trend. When taking into account spatial factors, China's green productivity demonstrates a significant conditional β-convergence. In terms of regional effects, the results indicate that the green productivity of the eastern and western regions demonstrates club convergence, implying a more balanced green economic development. Moreover, the convergence rate of China's green productivity increases with the addition of environmental regulation variable, and so the corresponding convergence time decreases. It indicates that environmental regulations help to facilitate the convergence of China's green productivity, narrowing the gap between the regional green economic development. The findings provide guideline for achieving a low-carbon development and carbon neutrality from a regional green productivity perspective.

Holistic Impact and Environmental Efficiency of Retrofitting Interventions on Buildings in the Mediterranean Area: A Directional Distance Function Approach

The study focuses on the application of a nonparametric methodology for evaluating the sustainability of retrofitting interventions to be applied on different typologies of buildings and different climate zones of the Mediterranean area. The paper starts from the analysis of data collected through the HAPPEN project, that is a H2020 European project which proposes a holistic approach for a deep and sustainable renovation of the Mediterranean residential Building stock. Even if the European Commission allocated considerable funds for retrofitting interventions, the choice of the optimal solution is not always that easy because several variables have to be considered. The present manuscript proposes a methodology to compare different retrofitting solutions combining Life-Cycle Cost (i.e., LCC) estimations with the nonparametric Directional Distance Function approach (i.e., DDF). In detail, the literature suggests that the DDF can be effectively used for comparing different observations through efficiency scores. The main result of the paper is the definition of a hybrid methodology that, starting from estimates of LCC and applying a DDF technique, represents a simple method for evaluating the best retrofitting intervention. Results are represented by two scores where the former represents a holistic efficiency measure, while the latter shows an environmental efficiency score.

Africa Countries’ Energy Efficiency: Evidence from a Directional Distance Function Approach

Energy is recognized as the backbone of economic development while at the same time it is the most contributor to global warming. This paper aims to assess energy-efficiency of a sample of African countries over the period from 1971 to 2014. Through a directional distance function approach, we estimated both the energy efficiency and the environmental energy efficiency scores in the sample. The results showed that ignoring the undesirable output, i.e. dioxide carbon emissions associated with environmental degradation, overestimates countries’ energy inefficiency. Besides, from a non-parametric approach, we shed light on the sensitivity of countries environmental energy efficiency to the income level. Our findings confirmed the sensitivity of environmental-energy efficiency to the Kuznets curve hypothesis. In particular, countries with high-level income are the most environmental-energy efficient in the sample over the period of study. The paper ends with some policy implications and some research perspectives.

Weak Disposability of Input and Output in a Nonparametric Production Analysis

In some production processes, unlike traditional data envelopment analysis (DEA), decision making units (DMUs) consume widely used inputs since increasing them is more favorable for improving the efficiency. Plastic wastes and rotten fruits are two instances of widely used inputs for recycling factories. In this paper, weak disposability of inputs will be presented with non-uniform profit factors for inputs, and then the model will be extended to cases which consume normal and widely used inputs, and produce desirable and undesirable outputs, simultaneously. Due to a nonlinear form of the final model, a linearization method is presented to provide a linear structure of the technology. Actually, a directional distance function approach, including weakly disposable inputs and outputs is introduced to deal with widely used inputs and undesirable outputs. Finally, the approach will be tested by applying it on some domestic sewage treatment plants in China. Results show the proposed approach can discriminate between DMUs in a rational way and less computational efforts and also it can be used for the efficiency analysis when widely used inputs and undesirable outputs are presented.

Assessing the impact of global financial crisis on the intermediation efficiency of Indian banks in the presence of non-performing loans

PurposeBy incorporating the role of nonperforming loans (NPLs), the study aims to assess the impact of global financial crisis (GFC) on the intermediation efficiency of Indian banks for the period of 1998/99 to 2016/17.Design/methodology/approachTo obtain efficiency level of Indian banks, this study applied sequential data envelopment analysis (DEA) based directional distance function (DDF) approach, which performed simultaneous expansion of desirable output and reduction of undesirable output in the bank's loan production structure. Additionally, using fixed effect regression approach in the panel data framework, this study assesses both the phenomenon of σ- and unconditional β-efficiency convergence in public sector banks (PSBs), private banks (PBs), foreign banks (FBs) and overall scheduled commercial banks (SCBs) during the pre-crisis, crisis and post-crisis years in India.FindingsIrrespective of the bank's production model, the evidence suggests that the accounting NPLs as an undesirable output significantly deteriorating the intermediation technical efficiency levels of Indian banks, especially after the crisis years until the last year of the study period. This reflects that Indian banks failed more to achieve their financial intermediation objective in the post-crisis years as compared to the crisis and pre-crisis years. In-depth, statistical evidence of commercial bank ownership groups reveals that public sector banks exhibit a higher level of efficiency in pursuance of traditional loan-based activity followed by private and foreign banks. The study also found the existence of sigma convergence in technical efficiency levels of Indian banks and ownership groups as well.Originality/valueThis study is perhaps the first one, which present the robust evolution of Indian banks intermediation efficiency by taking into account both endogenous (i.e. NPLs as an undesirable output and equity as a quasi-fixed input in the bank production process) crisis and exogenous (i.e. global financial and economic stress) crises. Moreover, none of the existing studies have conducted sub-period wise analysis to show the apparent occurrence of both convergence properties in technical efficiency, adding novelty in the literature.

Improving electricity supply reliability in China: Cost and incentive regulation

Electricity regulators pay attention to electricity supply reliability in many countries, considering that power interruption can cause damage and destruction as modern societies increasingly rely on electricity. Since 2020, China's regulators have designed incentive schemes to encourage power grid firms to improve electricity supply reliability in some regions. An effective incentive scheme requires that regulators identify the cost of reliability improvement and match it to the incentive scheme. Using provincial panel data for 2012–2018, this paper employs the directional output distance function approach to estimate the shadow price of power interruptions in China's grid system—that is, the marginal cost of electricity supply reliability improvements. Results indicate that the shadow price of 1 min of interruption per customer ranged from 59.66 to 74.65 RMB in 2012–2018. This estimation also shows that the shadow price of 1 min of interruption varies substantially among provincial grid utilities. The marginal cost of improving electricity supply reliability in China's grid system is lower than in developed countries. Since the incentives far from cover the cost of improvement, the schemes implemented in some Chinese regions cannot provide incentives for quality improvements.

Spatio-temporal evolution characteristics and influencing factors of carbon emission reduction potential in China

This study first attempts to use the parameterized quadratic directional distance function (DDF) approach to calculate China’s provincial carbon abatement cost and carbon reduction potential (CRP) under different scenarios from 2000 to 2017. Afterward, considering three different scenarios, we analyze the spatio-temporal characteristics and the dynamic evolution pattern of CRP. We also employ spatial Durbin model (SDM) to investigate the influencing factors of CRP. The results are obtained as follows: (1) CRP across the three scenarios varies considerably across provinces and different-located groups. CRP higher areas are mainly located in the economically developed eastern coastal regions, while most provinces with low CRP are concentrated in the western region. (2) Provinces with a similar CRP showed a significant geographic agglomeration, and the agglomeration effect was strengthened first and then weakened. Simultaneously, the local spatial distribution of moderation carbon reduction potential (MCRP), fairness carbon reduction potential (FCRP), and efficiency carbon reduction potential (ECRP) shows a slight spatial polarization feature. (3) Through the SDM analysis and spillover effect decomposition, we find that improvement of regional CRP not only depends on economic development, industrial structure adjustment, and energy efficiency elevation, but also involves energy structure optimization, low-carbon innovation, and population. The low-carbon innovation provides critical support for local CRP under the efficiency scenario but restrains the local CRP under the fairness scenario. Therefore, the central government should emphasize local conditions and the ex-ante scenario assessment, strengthen regional interactive governance, optimize energy efficiency, and promote the application of clean energy to enhance CRP.

Cost-benefit analysis and technical efficiency evaluation of full-scale membrane bioreactors for wastewater treatment using economic approaches

While the membrane bioreactor (MBR) technology has been broadly applied to treat wastewater, a rational assessment of its techno-economy is required for its sustainable development. In this study, we performed cost-benefit analysis (CBA) and data envelopment analysis (DEA) of 35 large-scale MBRs (each with a treatment capacity of ≥10,000 m3/d). Based on the investment and operation data, we evaluated the marginal cost and environmental benefit (as a function of the shadow prices of pollutants) and hence obtained the net profit (averagely ∼35 CNY/m3 or ∼4.9 USD/m3). According to the non-radial directional distance function (NDDF) approach in the DEA framework, the average cost efficiency and energy efficiency of the MBRs were 0.77 and 0.66, respectively. The distributions of the net profit and cost/energy efficiencies significantly varied according to the geographical location, effluent standard, and operating year of the MBRs as indicated by the results of nonparametric tests. Economic panel modeling showed that the cost/energy efficiencies were also affected by external factors such as regional economic level and population density. The techno-economy of MBRs is prominent on occasions of strict effluent standards and underground locations, and could be improved by further technological advancements and policy incentives.

Examining the Relationship between Social Inefficiency and Financial Performance. Evidence from Wisconsin Dairy Farms

Although social sustainability is an important component of sustainable agricultural production, little research has been conducted to assess social sustainability performance at the farm level. This study measures farmers’ social sustainability performance using (in)efficiency measures derived from a non-parametric dynamic directional distance function approach. It further examines the relationship between social (in)efficiency and financial performance measured by profitability, which is crucial to understand the financial impact of engaging in socially responsible activities. The empirical application focuses on a sample of Wisconsin dairy farms over the period 2007–2017. Results show that sample farms could have (decreased/)increased their social (in)efficiency by an average of 14%. Social (in)efficiency was found to be (negatively/)positively related to farm profitability, implying that social objectives can be achieved in tandem with economic goals.