Meta-frontier Directional Distance Function Research Articles

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.

Game directional distance function in meta-frontier data envelopment analysis

Meta-frontier directional distance function (DDF) is an important method to evaluate the efficiency of decision-making units (DMUs) with technical heterogeneity. However, this method can only use exogenous technology to determine the direction, because the application of endogenous technique has the theoretical dilemma that DMUs have two frontiers with different data characteristics. According to this dilemma, game theory is introduced to balance the relationship between group-frontier and meta-frontier, and then their data characteristics can be unified. Sequentially, Stackelberg game and non-cooperative game are gradually applied to construct the meta-frontier DDF with endogenous technique, and their convergence, uniformity and optimality are proved; while their advantages and relationship are discussed, respectively. Compared with traditional methods, the new meta-frontier DDF methods uses an endogenous technique to determine the unified improvement direction of DMUs based on different frontiers, and then the results can be more objective and reasonable. Finally, an empirical example is used to illustrate the effectiveness of these new methods.

Measurement of Environmental Efficiency Based on Stochastic Directional Distance Function: A Metafrontier Approach

This study measures environmental efficiency (EE) based on CO₂ emissions for five groups of countries between 1998 and 2018, using the stochastic metafrontier directional distance function. The model estimates environmental efficiency scores for a panel of 163 countries using data on GDP and CO₂ emissions as economic growth and the consumption of fossil fuels lead to increased CO₂ emissions. Moreover, meta inefficiency and technical gap differences (TGD) are compared, and the findings indicate that most countries have higher mean TGDs than their group’s average inefficiency measures. Furthermore, except for the low-income group, the OECD group is closest to the meta environmental frontier, suggesting that the OECD countries have advanced technologies to govern the environment. Alternatively, the findings also showed that upper-middle-income countries have the worst meta efficiency, implying that this group of countries sustain a high pollution growth path. Finally, we compare the difference between the stochastic metafrontier method and the pooling method and show that the pooling approach underestimates the severity of environmental problems.

Directional Distance Function Technical Efficiency of Chili Production in Thailand

To overcome the challenging food safety and security problem, in 2003, the Thai government initiated ‘Good Agricultural Practices’ (GAP) technology. This paper used a sample of 107 small chili farms from the Chiyaphoom province for the 2012 crop year, and data envelopment analysis (DEA) meta-frontier directional distance function technique to answer two questions: (1) Are GAP-adopting farms, on average, more efficient than conventional farms? (2) Does access to GAP technology affect farmers’ decisions to adopt GAP technology? We also developed an ‘indirect’ approach to reduce the potential sample selection bias for small samples. For the dry-season subsample, GAP farms were more technically efficient when compared with non-GAP farms. These dry-season non-GAP farms may not adopt the GAP method because they have limited access to GAP technology. For the rainy-season subsample, on average, GAP farms were more efficient than non-GAP farms at the 5% level. Access to the GAP technology is not a possible reason for non-GAP rainy season farms to not adopt the GAP technology. To enable sustainable development, government agencies and nongovernmental organizations (NGOs) must develop and implement appropriate educational and training workshops to promote and assist GAP technology adoption for chili farms in Thailand.

Technical efficiency of Islamic and conventional banks with undesirable output: Evidence from a stochastic meta-frontier directional distance function

We examine technical efficiency of Islamic and conventional banks. We contribute to the literature by applying a stochastic meta-frontier directional distance function model with undesirable output, which helps to overcome misestimating technical efficiency. For a sample of banks from 28 countries, we find that a typical Islamic bank is less technically efficient compared to its conventional counterpart. This is due to Islamic banks using less advanced technology compared to conventional banks rather than group-specific technical inefficiency. The findings are robust across six geographical regions of the world.

Energy efficiency and technology gap of enterprises in Guangdong province: A meta-frontier directional distance function analysis

Our study proposes to capture the heterogeneities and estimate the energy efficiency, technology gap and carbon emission performance of enterprises in Guangdong province. We employ group-frontier and meta-frontier directional distance function to analyze the technical efficiency based on the groups categorized in terms of both geographical boundaries and industrial classification system. The estimation indicates that enterprises in Mountainous region have a lower mean efficiency and a wider range of efficiency than the others, they have the largest potential to contribute to CO2 reduction, which can be further reduced by 35%. A small part of the enterprises in Industries sector have the lowest efficiency, although the sector has the smallest technology gap ratio. Comparatively, Information Technology sector has the highest efficiency (mean value is 0.95), efficiency of Energy sector is the lowest (mean value is 0.65).

Efficiency and technology gaps in Indian banking sector: Application of meta-frontier directional distance function DEA approach

Government of India aims at making the Indian Banks internationally competitive. In the wake of intense competition and changing global and national business environment, the efficiency issues have emerged as an important pillar of success in the Indian banking sector. Therefore, it is an essential task to comprehend the efficiency levels of the overall Indian banking sector and also across different ownership structures (viz. Public, Private and Foreign). The present study endeavors to carry out an assessment of intra-sector efficiency in the Indian banking sector based on a cross-sectional data of 66 banks for the year 2015-16. The authors employ directional distance function based meta-frontier DEA approach and the results reveal that the Indian banking sector is 73.44% efficient. It also confirms the existence of different production functions across different ownership structures of the industry. Among the different ownership structures, the group frontier of foreign banks coincides with the meta-frontier. The group frontier of private sector banks is the second closest to the meta-frontier and public sector banks are found to be the laggards in the overall industry. The study gains special significance in the backdrop of the recommendations floated by the Reserve Bank of India and Ministry of Finance (Government of India) to consolidate the public sector banks in order to retain fewer but healthier banks. The finding of the study fully support these recommendations and affirms that consolidation in the industry will bring positive synergies and will lead to the enhancement of efficiency levels in the industry.

Incorporating Risk into Technical Efficiency: The Case of ASEAN Banks

The objective of this paper is to incorporate risk in technical efficiency of listed ASEAN banks in a panel data framework for the period 2000 to 2015. Many researchers apply frontier estimation techniques such as data envelopment analysis (DEA) or stochastic frontier analysis (SFA) for their efficiency analysis. However, the banks’ complex production process requires more sophisticated techniques to account for internal structures within the black box so relying only traditional DEA or SFA is not adequate to deal with a multiple-input and multiple-output production technology. To incorporate undesirable outputs such as risk into inefficiency, we rely on the directional distance function (DDF). We employ the DDF under both parametric (SFA) and semi-parametric (SEMSFA) framework to make a comparison efficiency scores with risk adjusted in two scenarios. Our results suggest that risk is an important factor that bank managers should pay more focus to achieve long-term efficiency in ASEAN banks
 Keywords
 Bank efficiency; risk; directional distance function (DDF); semiparametric estimation of stochastic frontier models (SEMSFA)
 References
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Effect of 2008's Beijing Olympic Games on environmental efficiency of 268 China's cities

This paper mainly investigates how 2008's Beijing Olympic Games affects environmental efficiency of China's cities. First, we evaluate environmental efficiency through metafrontier directional distance function (DDF), and compare environmental efficiency in different region from static and dynamic perspectives. We also analyze the different treatment of before Olympic Games, during Olympic Games, after Olympic Games on different groups. We find that TGR in the east is the highest, which indicates that environmental production technology in the east has relatively less difference than other three regions. During Olympic Games positively affected environmental efficiency in Beijing, which negatively affected on environmental efficiency under metafrontier in neighbor cities. After Olympic Games positively affected environmental efficiency in Beijing and co-host cities, however, which has insignificant effect on environmental efficiency in neighbor cities. We try to propose some policy implication. First, it is import to develop high-end industry and lengthen value chain of China's secondary industry. Furthermore, it is necessary to improve environmental threshold of FDI and attract clean FDI, which can decrease environmental pollution. Last, China will host 2022 Winter Olympic Games. It is important to use more environmental-soundly building material, and increase clean renewable energy public bus, which can promote green Olympic Games.

Carbon productivity growth, technological innovation, and technology gap change of coal-fired power plants in China

This paper proposes a sequential meta-frontier Luenberger productivity index (SMLPI) that incorporates undesirable outputs to measure carbon productivity growth over time. This new index combines the concepts of sequential production technology, meta-frontier directional distance function, and the Luenberger productivity Index to produce a composite indicator, so that it can take group heterogeneities and the progressive nature of technology into consideration for productivity measurement. The SMLPI is then applied to a unique dataset of China's coal-fired power plants, including 5048 observations covering the period 1999–2008. The results show an increasing trend of carbon productivity growth during the sample period for both state- and non-state-owned power plants. Further decomposition analyses show that the production technology also exhibits an increasing trend for both groups, but the efficiency change exhibits a decreasing trend. For the state-owned group, the technology gap decreased before 2003, but increased thereafter. On the contrary, for the non-state-owned power plants, the technology gap increased before 2003, but decreased thereafter.

Applying the New Metafrontier Directional Distance Function to Compare Banking Efficiencies in Central and Eastern European Countries

This paper establishes a new metafrontier directional technology distance function (MDDF) under a stochastic framework, rather than a deterministic setting like the one proposed by Battese et al. (2004). The new MDDF allows for calculating comparable technical efficiencies for banks under different technologies relative to the potential technology available to the industry across nations. The inefficiency term of the new MDDF is further associated with relevant environmental variables of the form proposed by Battese and Coelli (1995). The new MDDF is then applied to examine and compare bank efficiencies of 17 Central and Eastern European countries. Non-performing loans (NPLs) are regarded as an undesirable, jointly produced with various loans, and the omission of them tends to underestimate technical inefficiency scores. Evidence is found that the estimated technology gap dominates technical efficiencies. Bank managers are suggested to swiftly adopt new financial innovations with an eye to shift the group frontier closer to the metafrontier.

Measuring Environmental Performance Under Regional Heterogeneity in China: A Metafrontier Efficiency Analysis

This paper examines total-factor environmental performance for various regions in China based on the metafrontier directional distance function. This approach can measure the environmental performance of undesirable outputs (pollutants). Technological heterogeneity can be taken into account simultaneously by taking a metafrontier approach. First, the concept of a generalized metafrontier directional distance function is proposed for the model. Second, several standardized composite indicators of environmental performance are developed. Third, the metafrontier directional distance function is estimated by solving a series of data envelopment analysis models. Finally, various regions in China are empirically examined, and the results and their implications are discussed. The results indicate substantial heterogeneity in environmental performance across regions, and some policy suggestions are proposed based on these results.

Strategic corporate sustainability performance of Chinese state-owned listed firms: A meta-frontier generalized directional distance function approach

Although sustainability recently became a key factor in social science, little progress has been made toward improving the measurement of sustainability performance. This paper proposes composite corporate sustainability performance indicators using a meta-frontier generalized directional distance function. This advanced approach can measure the efficiency of corporate social responsibility activities by benchmarking, while simultaneously considering industrial heterogeneities, using the meta-frontier approach. First, we propose the concept of a meta-frontier generalized directional distance function. Second, several standardized composite indicators related to corporate sustainability performance are developed. The meta-frontier directional distance function is estimated by solving a series of data envelopment analysis models. Chinese state-owned listed enterprises are then empirically examined using the proposed model. We find significant group heterogeneities in terms of corporate sustainability performance. We also derive some policy implications using the empirical results.

A metafrontier directional distance function approach to assessing eco-efficiency

This paper uses directional distance functions to extend the non-parametric metafrontier approach to efficiency measurement proposed by O’Donnell et al. (Empir Econ 34:231–255, 2008) to the assessment of technological differences in eco-efficiency between groups of producers. Furthermore, eco-efficiency is assessed at the level of specific environmental pressure management. This methodology is applied to a sample of Spanish olive producers that belong to both traditional mountain and traditional plain growing systems. We find great potential for both olive growing systems to reduce environmental pressures. In terms of pressures on natural resources, the most eco-efficient technology is the traditional plain system, while the traditional mountain system is the most eco-efficient when considering pressures on biodiversity. These results might help policymakers design strategies to improve the performance of olive growing and meet the demands of society regarding the economic and ecological functions of this farming activity.