Directional Distance Function Research Articles

Carbon emission reduction potential and reduction strategy of China's manufacturing industry

China's carbon reduction targets have been hampered primarily by excessive CO2 emissions from manufacturing. Considering technology heterogeneity, this study first employs the directional distance function (DDF) meta-frontier approach to evaluate the manufacturing carbon emission efficiency and carbon reduction potential in 29 Chinese provinces from 2011 to 2019. We also discuss the influencing factors affecting carbon emission efficiency using the spatial econometric model. The results indicate that: (1) China's manufacturing industry is not very efficient in terms of carbon emissions. The Eastern region exhibits a significantly higher level of performance than the Central and Western regions in carbon emission efficiency and production technology, although the gap is gradually narrowing. (2) The potential for reducing carbon emissions in China's manufacturing sector is considerable, with the greatest potential found in the Western region. Specifically, in the Eastern region, the carbon reduction potential is largely associated with management inefficiency. However, in the Central and Western regions, excessive carbon emissions are mainly due to technology gap inefficiency. (3) Through spatial econometric analysis, we find that carbon emission efficiency can be derived by adjusting the industrial structure, scaling up enterprises, accelerating urbanization, and reducing coal use. But it will be hindered by increased marketization and strict environmental regulations. Besides, China is not enough to improve carbon emission efficiency through technology introduction and technological innovation at present. Some manufacturing carbon emission reduction strategies are proposed based on the results of this study.

Spatial Effect of Green Economic Efficiency in China From the Perspective of Informatization

Green economy has been paid more and more attention in the information age. Informatization plays an important role in the development of green economy by the transmission of industrial structure rationalization and upgrading. Because of the spatial mobility of information, it is necessary to study the spatial spillover effect of information on the efficiency of green economy. In this article, the non-radial directional distance function and the comprehensive index method are used to evaluate the efficiency of green economy and informatization respectively. On this basis, the spatial characteristics of the two are analyzed. Finally, the spatial econometric model is used to analyze the spatial impact of informatization on the efficiency of green economy. The authors find that: (i)The spatial distribution of the green economy efficiency and informatization are unbalanced; (ii) There is a significant spatial spillover effect in the efficiency of green economy; and (iii) The development of informatization plays an important impact on the efficiency of green economy.

Regional Differences, Distribution Dynamics, and Convergence of the Green Total Factor Productivity of China’s Cities under the Dual Carbon Targets

Economic development in China has been severely restricted by environmental problems such as carbon emissions. Improving green total factor productivity (GTFP) is an extremely important pathway to realizing carbon peak and carbon neutrality. Nevertheless, existing studies on China’s urban GTFP under the carbon emissions constraint are still insufficient. In this context, this study adopts the directional distance function (DDF), includes carbon emissions in the undesirable output, combines the global Malmquist–Luenberger (GML) productivity index, and calculates the GTFP of China’s cities. On this basis, the Dagum Gini coefficient, kernel density estimation, and convergence model are employed to explore the regional differences, distribution dynamics, and convergence in China and in three subdivision regions of east, center, and west. The core conclusions are as follows: (1) the average annual growth rate of GTFP in China’s cities is about 0.7064%, which is relatively low, but there is great room for improvement. The growth trend of GTFP in the three subdivision regions of east, center and west is obvious, presenting a spatial distribution characteristic of “high in the east and low in the west”; (2) the regional differences in GTFP of these cities are enlarging, with the largest gap in the eastern region and the smallest in the western region. Intraregional difference is the primary source of regional differences; (3) the imbalance in urban GTFP in China is prominent, with noticeable gradient differences, making it difficult to achieve hierarchical crossing. The central and western regions even have multilevel differentiation problems; (4) there is an absolute β convergence and conditional β convergence of China’s GTFP, but no σ convergence. As a result, it is necessary to comprehensively consider and actively implement the concept of shared development, enhance technological progress, focus on narrowing the differences in GTFP, and facilitate coordinated green development within the regions.

The heterogeneous impacts of government on health system efficiency in China's new health reform, 2010-2019.

Contextualizing in China's recent health reform, we empirically explore the heterogeneous effects of two distinct government roles, accommodating private hospitals vs investing in public hospitals, on health system efficiency. We use panel data covering 31 provinces during 2010-2019 to assess health system efficiency. We incorporate health service volumes and population health outcomes to ascertain health system outputs, employing the non-radial directional distance function to estimate efficiency. We employ Bayesian Tobit quantile regression to explore the heterogeneous effects of the share of private hospitals and government subsidy to public providers on efficiency. China's health system inefficiency scores range from 0 to 0.45. The association between the share of private hospitals and inefficiency score are only significant in higher-inefficiency quantiles (coefficients -0.0258, -0.0315 and -0.0327 for quantiles 0.7, 0.8 and 0.9), meaning a heterogeneously positive impact for low-efficiency provinces. The association between government subsidy and inefficiency score are positive for all quantiles (from 0.0339 to 0.0567), meaning persistent negative impacts on efficiency. The heterogeneous impacts of the share of private hospitals suggest that the government should accommodate more private hospitals in provinces with low efficiency. The persistent negative impacts of government subsidy suggest that the government investment seems not be subjected to economic objectives.

Evaluating the resource recovery efficiency of garbage removal and disposal in Taiwan.

All countries recognize the importance of enhancing circular resource utilization and promoting zero waste in order to achieve a circular economy. This study focuses on 22 counties (cities) in Taiwan and analyses the relationship between changes in resource recovery efficiency and productivity over an 8-year period (2011-2018) using the super efficiency directional distance function and total factor productivity. The results indicate that the average total efficiency of resource recovery in the 22 counties (cities) is 1.3951, with 17 counties (cities) exceeding 1. The average gross productivity of resource recovery is 1.0417, and only four counties have a gross productivity of less than 1. Despite having more administrative resources, municipalities directly under the central government have a slightly lower average total efficiency of resource recovery (1.1464) than non-municipalities (1.4885). To improve efficiency, the government should allocate resources rationally and upgrade technology. The study's findings can serve as a reference for the 22 counties (cities) in Taiwan and provide guidance for municipal governments worldwide in developing policies related to resource recovery.

Sustainable development in China? A nonparametric decomposition of economic growth

China has undergone significant deviations from the command economy established in 1949, achieving unprecedented success in sustaining high growth. Consequently, numerous scholars have devoted their attention to studying China's economic development. In this study, we contribute to this literature using a new technique to examine China's economic development. This technique utilizes nonparametric directional distance function in the framework of neoclassical growth theory. It avoids the assumptions imposed on parametric production functions that are often short of practical justifications. Our analysis shows that capital and energy inputs account for 75.7% and 20.8% of China's GDP growth during 1985–2020. These figures characterize a capital-driven growth model that is unlikely to be sustainable by conventional wisdom. However, our empirical evidence, obtained through an interactive-fixed effects model, indicates that it is not unreasonable to say that growth in China is government-led rather than capital-driven; the former could be sustained by desirable reforms under strong national leadership while the latter is not.

Coordination of public-private transport and sustainability measurement: A futuristic perspective in transport

Coordination in providing sustainable and effective transport services can be beneficial for both the public and private sectors. Although there is considerable research in each of public and private transport, the literature shows that research on public-private coordination is rare. Furthermore, performance measurement of public-private transport has been another less explored topic in transport systems. Based on these knowledge gaps, we make contributions to the transportation field by performance measurement and coordination of public-private transport within multimodal transport networks. In this paper, we model public-private transport networks by developing a novel network data envelopment analysis (NDEA) with some distinctive features. The model is built based on the directional distance function (DDF) and provides detailed insights into the sustainability and coordination of public-private transport networks operating in a supply chain. It also provides resource allocation among decision making units (DMUs).

A new Malmquist productivity index with an application to commercial banks

Abstract Accepted by: Aris Syntetos Management-led productivity improvements are crucial for achieving sustainable development, and the Malmquist productivity index is known to be useful in relevant contexts. This study aims to extend such index by using non-parametric mathematical modelling of production processes. Specifically, and in the spirit of the existing index, we introduce the directional distance function to develop a new one applicable to the joint production of desirable and undesirable outputs. Furthermore, we decompose the new index into two constituent components to provide more intuitive explanations when revealing the root sources of productivity changes over time. Under the cost minimization assumption, the new index is applicable when producers implement resource allocation management, and the input–output quantities and the micro-level input prices are known. The index emphasizes that the allocative efficiency should be regarded as an important aspect of productivity assessment like the technical efficiency. As a practical benchmarking tool, it can offer valuable information and provide appropriate strategies for managerial decision-making. The index’s application and usefulness is demonstrated in the commercial bank sector in China.

Efficiency decomposition for multi-level multi-components production technologies

This paper addresses the efficiency measurement of firms composed by multiple components, and assessed at different decision levels. In particular it develops models for three levels of decision/production: the subunit (production division/process), the DMU (firm) and the industry (system). For each level, inefficiency is measured using a directional distance function and the developed measures are contrasted with existing radial models. The paper also investigates how the efficiency scores computed at different levels are related to each other by proposing a decomposition into exhaustive and mutually exclusive components. The proposed method is illustrated using data on Portuguese hospitals. Since most of the topics addressed in this paper are related to more general network structures, avenues for future research are proposed and discussed.

A step toward inclusive green growth: can digital finance be the main engine?

Inclusive green growth (IGG) has become a worldwide consensus to achieve the target of sustainable development goals. Although the prominent role of digital finance (DF) against the pandemic has drawn considerable attention from policymakers, its plausible effect on IGG and underlying mechanisms have not been distinctly explored in academia. The aim of the study is to explore the causal effect of DF on IGG based on prefecture city-level data from 2011 to 2019 in China. To this end, we employed the non-radial direction distance function approach within the global production technology to evaluate the aggregate IGG performance and its three sub-dimensions. The empirical results demonstrate that DF exerts a significant promotional effect on urban IGG. This finding continues to survive in an extensive set of robustness checks using an alternative dependent variable, model specifications, instrumental variable, and difference-in-difference approaches to address the endogeneity concerns. Meanwhile, sub-dimensional regressions show that this positive effect is driven predominantly by the scale economy of DF, while the depth of usage and digitalization playing a minor role. Moreover, we uncover that DF enhances IGG by leveraging greater marginal product of labor rather than capital, improving environmental externalities, increasing fuller employment, and reducing rural-urban income inequality. However, we also reveal the dark side of DF on imbalanced regional development. The promotional effect of DF on IGG is only prominent for cities with better inherent comparative advantages, and we are thus likely to see a widening digital divide resulting from the "Matthew effect" on regional disparity without timely policy interventions.

Assessing performance of directional output distance function: Simulation-based Analysis

Assessing performance of directional output distance function: Simulation-based Analysis

What Is the State of Development of Eco-Wellbeing Performance in China? An Analysis from a Three-Stage Network Perspective

After rapid development in recent decades, China has laid a strong economic foundation and established material conditions. Despite this, the country still confronts a range of challenges that impede higher-quality economic and social development. To measure high-quality regional development, eco-wellbeing performance (EWP) has become an important tool that seeks to strike a balance between economic development, human wellbeing, and environmental protection. This paper proposes a three-stage network efficiency evaluation model to decompose EWP into three stages, namely ecological economic efficiency (EEE), economic innovation efficiency (EIE), and innovation wellbeing efficiency (IWE). A directional distance function (DDF) model was utilized to assess the overall EWP efficiency and phase-in efficiency for 248 cities over the period from 2016 to 2020. The study results indicate that EWP in China is generally low. In terms of the three sub-stages of EWP, the first stage performs optimally, the third stage performs the second best, and the second stage is the worst. The research suggests that the principal reason for the generally low EWP may be linked to the efficiency of the transformation of economic investments into innovative outcomes in the second stage. From a regional viewpoint, EWP generally shows a gradually decreasing trend from the east, central, and west to the northeast, but the stage performance varies among regions. The eastern region has lower EEE, but both EIE and IWE perform better than the national average; the central region is well-balanced between the three stages; the western region leads the country in EEE, but lags in both EIE and IWE; and the northeast region has inferior performance in all stages. This study’s findings provide vital reference values for policy-makers to determine key points for enhancing EWP in different regions of China.

The effect of innovation pilot on carbon total factor productivity: Quasi-experimental evidence from China

Since the policy design for carbon emission reduction must consider both the efficiency and the cost of emission reduction, improvement in carbon total factor productivity (CTFP) is widely regarded as an important economic path in reducing carbon emissions. With prefecture-level data in China from 2003 to 2016, this paper explores the role of innovation pilot on the CTFP using China's Innovative City Pilot (ICP) policy as a quasi-experiment. First, we construct a novel CTFP framework, that combines the non-parametric Luenberger productivity indicator with the biennial non-radial directional distance function, to take the slack issues and infeasibility problem into consideration. Next, with the staggered difference-in-differences model, we examine whether innovation can stimulate CTFP improvement. The results show that the ICP policy exerts a significant positive effect on CTFP, increasing cities' CTFP by 0.015 on average. Moreover, we identify five potential channels from both economic analysis and comprehensive factor decomposition: technological and low-carbon innovation, industrial upgrading, energy efficiency, carbon emission intensity, and efficiency change. These positive impacts are heterogeneous across different kinds of cities. Specifically, the effects of innovation are stronger in the eastern and central cities, large cities, and cities with tighter environmental regulations. Meanwhile, the political incentives analysis shows that in cities with higher political incentives, officials perform better in energy intensity reduction and CTFP improvement. This paper explores direct evidence for the innovation's effect on carbon productivity, which provides a novel perspective for improving carbon productivity and the future direction of innovation in China.

Carbon abatement in the European chemical industry: assessing the feasibility of abatement technologies by estimating firm-level marginal abatement costs

As many other industries, the chemical industry has to strongly reduce its' carbon emissions, for which various abatement technologies exist. We study the economic feasibility of these abatement technologies by estimating the Marginal Abatement Cost (MAC) of CO2 emissions for 24 firms in the European chemical sector over the period 2015–2020. We estimate the firm-level MAC by using a quadratic directional output distance function (DDF) model. We find a median MAC of 429 €/t CO2, which is significantly above current carbon prices, indicating that most firms in this industry prefer to use carbon allowances instead of reducing their own emissions. We conclude that carbon abatement in the chemical industry is only likely when the carbon price is significantly higher or when financial support is provided for certain abatement technologies, such as renewable hydrogen and bio-based ammonia.

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.

Measuring efficiency of safe work environment from the perspective of the decent work Agenda

Decent Work Agenda consists of a comprehensive initiative for promoting safety at work and social protection. Over 20 years since its conceptual release, measuring the progress of its elements is still challenging even after the publication of the decent work indicators guideline by the International Labour Organization in 2012. To close this gap, we use a Directional Distance Function (DDF) to measure the efficiency of safe work environment, and propose a combined measure taking into consideration also the efficacy. To illustrate the application of DDF in a reality-based case, we conducted a longitudinal study in a multinational organization. Data were collected from 21 branches of the company over 4 years (2018–2021). In the period of analysis, 60% of the branches were efficient in average, composing an overall efficiency score of 0.91. Our results also indicated low dispersion between the efficiency scores year on year due to a small-scale interquartile range. Finally, the use of efficiency combined with efficacy resulted in a promising approach for managerial applications. This research presents some contributions. One is the novelty approach of measuring the efficiency of safe work environment using a DDF model in a real-world application. Another is the managerial benefits of identifying benchmarks, as well as revealing potential improvements as a mechanism to reduce decent work deficits. From a modeling perspective, our conclusions suggest caution in considering only efficiency to measure safe work environment due to its relative nature. Thus, further studies are recommended to explore the use of combined measures in the analysis of decent work.

How Sustainable Are Tourist Destinations Worldwide? An Environmental, Economic, and Social Analysis

Sustainable tourism is the idea of managing the negative impacts or potential for serious harm to the economic, environmental, or social elements of a destination, and thus reaching the goals of sustainable development. This research benchmarks the sustainability of 111 tourist destinations throughout the world, using an advanced integration of a two-stage network DEA under the meta-frontier concept, directional distance function, and network-based ranking methods. The empirical outcomes of these analyses clarify that the sources of sustainable inefficiencies are the self-production process and the technology gap among the tourism regions, rather than the capacity of utilizing the input resources or maintaining the production outcomes. The network-based ranking emphasizes the sufficiency and deficiency of each place, and provides a map of reference among destinations. Based on these, the article reports some managerial suggestions, theoretical implications, and future research directions.

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.

Impact of China’s Low-Carbon City Pilot Policies on Enterprise Energy Efficiency

An increase in energy efficiency is an essential element and a powerful driving force for the in-depth implementation of the sustainable development strategies necessary in accelerating the promotion of green, circular, and low-carbon development, as well as to promote the comprehensive green transformation of economic and social development. An important question with regard to this paper is thus: can the low-carbon city pilot policy promote energy efficiency improvement, and if so, through what mechanisms? This paper uses the SBM–Malmquist–Luenberger index method to measure the green total factor energy efficiency and examines the impact and pathways of the pilot policy on the energy efficiency of enterprises, using a sample of listed manufacturing enterprises in 230 prefecture-level cities in China from 2007 to 2020. Additionally, the time-varying difference-in-differences (DID) method is approached in this paper. After replacing energy efficiency with slack-based measure directional distance function model (SBM-DDF) and conducting a series of robustness tests, this study found that the pilot policy can significantly improve the energy efficiency of manufacturing enterprises. A mechanism test shows that this policy can promote green innovation effect and agglomeration effect to improve enterprises’ energy efficiency. The low-carbon city pilot policy has contributed the most to energy efficiency through enterprise investment in green innovation and manufacturing agglomeration. Heterogeneity analysis found that policy effect differs among firms in terms of different sizes and properties, and the pilot policy plays different roles among different regions. This paper provides firm-level theoretical support and empirical evidence for evaluating low-carbon city pilot policy and offers policy recommendations.

Analysis on the shadow price of carbon emissions from China's forestry fruit industry-taking peaches as an example.

The shadow price of carbon emissions can measure the marginal output effect under the carbon emission regulation and is also one of the key indicators to construct a low-carbon development path for production units. Currently, international research on shadow price is focused on the industrial and energy sectors. However, in the context of carbon peaking and carbon neutrality targets in China, the use of shadow price to study the cost of reducing emissions from agricultural production, especially forestry fruit industries, is significant. In this paper, we use a parametric approach to construct the quadratic ambient directional distance function. Using the input-output data of peach, we then calculate the environmental technical efficiency and shadow price of carbon emissions from peach production in Guangxi, Jiangsu, Shandong, and Sichuan provinces, and further estimate the values of green output in each province. The results show that (i) the environmental technology efficiency of peach production in Jiangsu province, located in the coastal plain area of eastern China, is the highest among the four provinces, while that in Guangxi province, located in the hilly area of southeast China, is the lowest. (ii) Guangxi province has the smallest carbon shadow price of peach production among the four provinces, while Sichuan province, located in the mountainous area of southwest China, has the largest. (iii) The green output value of the peach production in Jiangsu province is the highest among the four provinces, and that in Guangxi province is the lowest. In order to effectively reduce carbon emissions in peach production without affecting economic benefits, the paper puts forward the following suggestions: for peach-producing areas in the southeast hills of China, it is necessary to increase the application of green environmental technology while reducing the input of production factors in peach production. For peach-producing areas in the northern plains of China, the input of production factors should be reduced. It is not easy for peach-producing areas in the southwest mountains of China to reduce the input of production factors while increasing the application of green technologies. Finally, for peach-producing areas in China's eastern coastal plain, the implementation of environmental regulations for peach production should be gradual.