Directional Distance Function Model Research Articles

The roles of innovation and internationalisation in explaining dynamic business performance

This study examines the effects of innovation (patent-related proxies), internationalisation (proxies measuring overseas business), and the interaction terms of the two variables on dynamic business performance (technical efficiency). A dynamic production model has been developed and assessed using a directional distance function (DDF) model under the Luenberger benefit function to measure technical efficiency of 467 firm-year observations of Taiwanese listed semiconductor companies during the sample period 2009-2015. The DDF efficiency analysis shows that technical efficiency fluctuated but remained relatively stable, with an overall mean value of 0.828. Regression results indicate that innovation and internationalisation contribute positively to dynamic business performance; although, the interaction between the two variables is not related to dynamic business performance. While innovation and internationalisation are important factors driving the dynamic business performance of the semiconductor companies in Taiwan, the vital economic assets of the industry have to be continuously protected.

The role of different paths of technological progress in improving China's energy efficiency

Improving energy efficiency is one of the most effective ways to address environmental constraints and achieve high-quality economic development. The existing literature suggests that technological progress has an important impact on energy efficiency, but ignores the role of different paths of technological progress. Herein, the impact of different technological progress paths on energy efficiency was analyzed using the dynamic panel data model and the threshold model based on the energy efficiency measurement using the Meta-frontier and Nonradial Directional Distance Function model. The findings of this study were as follows: (1) During the study sample period, a fluctuating upward trend was observed in China's energy efficiency, and there were significant differences in energy efficiency in different regions of China. (2) The energy efficiency in China could be significantly improved by domestic innovation and regional technology diffusion. Even though the imported technologies do not play a significant role in promoting energy efficiency and have no positive effect on the improvement of energy efficiency from the perspective of domestic technology absorption or foreign technology absorption. (3) The eastern and central regions of China improve their energy efficiency through domestic innovation. However, none of the technological progress paths in the western and low-energy-efficiency regions have played a positive role in promoting energy efficiency. (4) The effect of promoting domestic innovation and regional technology diffusion on energy efficiency is gradually increasing with human capital improvement, and the restriction of foreign technology import on energy efficiency has obviously decreased. In a nutshell, different paths of technological progress have differential effects on energy efficiency improvements. Based on the above results, this paper makes some targeted policy recommendations on the choice of technological progress paths to improve energy efficiency in different regions of China.

Green technological innovation, green finance, and financial development and their role in green total factor productivity: Empirical insights from China

Considering the environmental deterioration challenges and a sharp decline in the quality and quantity of natural resources, the need for capitalizing on renewable energy sources and environment-friendly practices has increased a lot. The United Nations also has urged firms to shift their reliance on fossil fuels to renewable and eco-friendly practices. Several nations have begun shifting from economic growth to green productivity practices, such as green finance, green innovation, etc., which signifies collaboration between the economy, resources, and ecological development to achieve sustainable development goals (SDGs). This study is based on a comprehensive index of green finance development. Using the nonparametric data envelopment analysis and directional distance function (DEA-DFF) model, it examines the impact of green finance, financial development and green technology innovation (GTI) on green total factor productivity (GTFP) in 28 Chinese provinces from 2011 to 2021. The findings indicate that green finance raises the degree of green productivity significantly. Other elements, such as financial development and technological innovation, contribute significantly to green production. It is also found that establishing green finance legislation can help accelerate the growth of green finance. The empirical findings in this study have policy implications for China's environmental and green finance planning. This study is among the pioneer investigations integrating green finance, financial development, and green technology innovation into a unified research framework.

Measurement of Green Total Factor Productivity and Its Spatial Convergence Test on the Pig-Breeding Industry in China

The pig-breeding industry is one of the pillar industries of China’s agriculture. Improving the green total factor productivity of pig breeding is the basis for ensuring the stable supply of pork, and is also the key to the green transformation of the pig industry. The existing studies about the green total factor productivity of pig breeding lack an analysis of regional coordination and the spillover of spatial technology efficiency at the macro level, and most studies focus on the impact of agricultural production’s environment pollution and other undesirable outputs. Based on the input–output index system of the pig-breeding industry’s green production, the DDF directional distance function model and the Malmquist–Luenberger (ML) productivity index were combined to measure the green total factor productivity of the pig-breeding industry. Moran’s I-Theil index model was used to measure and reveal the technical efficiency differences among the dominant regions of the pig-breeding industry in China and the σ-convergence test was adopted to reveal the convergence trend of green total factor productivity. The results showed that: (1) The growth level of green total factor productivity of pig breeding in China was generally low from 2006 to 2018, and there were obvious regional and scale differences. (2) The green total factor productivity of pig breeding in each province had spatial autocorrelation; that is, there was technology spillover. From 2006 to 2018, with the advance of time, a pattern of gradual evolution from low-level equilibrium to high-level imbalance was formed. (3) Through the convergence test, the convergence trend of large and medium-scale development between different regions fluctuated, while the convergence trend of small-scale development between different regions was not obvious. Therefore, it is necessary to increase investment in technological innovation, promote the large-scale and standardized development of the pig-breeding industry, and strengthen the promotion of technology in producing areas with advantages in pig breeding.

Comparative analysis of port efficiency in Yangtze River Delta and Pearl River Delta: a meta Dynamic D.D.F. approach

The Yangtze River Delta and Pearl River Delta are two regions with the highest level of economic development in China, and their port development is at the forefront of the country. This study measures the efficiency of 23 major ports in the two deltas from 2010 to 2018 using the meta Dynamic Directional Distance Function (D.D.F.) model and discusses the technology gap and the reasons for inefficiency of the ports. The research results show that 80% of the ports in these two deltas are inefficient. The Yangtze River Delta’s port efficiency is higher than that of the Pearl River Delta, but the internal efficiency difference of the Yangtze River Delta port cluster is more significant. The efficiency ranking of most ports is inconsistent under the meta-frontier (M.F.) and group frontier (G.F.), and the average technology gap ratio (T.G.R.) of ports in the Pearl River Delta gradually exceeds that in the Yangtze River Delta. The inefficiency of ports in the Pearl River Delta is caused by input factors, and the inefficiency of ports in the Yangtze River Delta is also related to the containerisation level.

The Impact of Digital Economy on Industrial Carbon Emission Efficiency: Evidence from Chinese Provincial Data

Digital economy has become an important driving force for green economic growth in China. Based on the province-level data of China from 2003 to 2018, this paper constructed the Total-factor Nonradial Directional Distance Function (TNDDF) model to measure the carbon emission efficiency of industrial sector and discussed the impact of digital economy on carbon emission efficiency. Empirical analysis shows that the carbon emission efficiency of China’s industrial sector is low, and there is obvious regional heterogeneity where the carbon emission efficiency of eastern China is higher than that of central and western China. Areas with high level of digital economy development have higher carbon emission efficiency, and digital economy is conducive to promoting energy conservation and pollution reduction in China’s industrial sector. The optimal threshold interval of digital economy for promoting carbon emission efficiency is explored by means of threshold model. In view of this, the Chinese government should vigorously develop the digital economy, promote industrial enterprises to networking and digital evolution, and improve the efficiency of carbon emission as well.

Technological innovation, resource endowment, and green total factor energy efficiency.

Technological advancements and resources availability are the main components of green total factor energy efficiency (GTFEE). This study measured GTFEE using the Meta-frontier and Non-radial Directional Distance Function (MNDDF) models and empirically evaluated the effect of technological innovation and resource endowment on GTFEE using dynamic panel and panel threshold models. The following are the primary findings: (1) Throughout the study sample period, the average change trend of China's GTFEE was generally in the shape of a "W," with regional variations. (2) Independent innovation can significantly improve GTFEE, whereas technology introduction has little effect on GTFEE advancement. Similarly, it confirmed the existence of the "Resource Curse." (3) While independent innovation has reduced the severity of the resource curse to a certain extent, the introduction of this technology has no positive effect on the resource curse problem. (4) Heterogeneity research indicates that only large cities' independent innovation has significantly increased GTFEE. There is a particular resource curse phenomenon regardless of the city size, but it is more prominent in small and medium-sized cities. (5) At various phases of economic development, a significant difference was noticed in the impact of independent innovation, technology introduction, and resource endowment on GTFEE.

Efficiency of Carbon Dioxide (CO2) Emission Control Target Allocations in China

Effectively allocating emission control targets is critical for China to achieve its emission reduction goals. This study researched the efficiency of total carbon dioxide (CO2) emission control target allocations during the 13th Five-Year Plan period (2015–2020). The efficiency of carbon intensity reduction targets, allocated by the National Development and Reform Commission in 30 regions, was assessed using a Directional Distance Function (DDF) model. Then, a Zero-Sum Gains (ZSG)-DDF model was constructed to determine how to optimally allocate total CO2 emission, under the premise of maximizing economic benefits and minimizing CO2 emissions. The results showed that in the case of fixed total CO2 emissions, to improve the resource allocation efficiency, the quota should be increased in the regions with high efficiencies, and the quota should be reduced in the regions with low efficiencies. The results in this paper can help guide the future allocations of total CO2 emission in China.

Efficiency and effectiveness analysis based on educational inclusion and fairness of European countries

Inclusive and equitable quality education is at the top of the agenda of education authorities worldwide. However, frontier-based efficiency studies involving cross-country comparisons of education systems in terms of educational equity are still incipient. This paper elaborates on the concepts of efficiency and effectiveness from the perspective of inclusion and fairness to propose a conceptual framework for education systems. According to the proposed framework, the education system of a country could be optimal, selective, excessive, or deprived. We employed the framework for 26 European countries to illustrate its applicability. The Data Envelopment Analysis approach based on a directional distance function model with both desirable and undesirable outputs was used to measure effectiveness and efficiency. The comparison amongst education systems is based on all key-stages of education: early childhood, primary, lower secondary, upper secondary, and tertiary education. The empirical results indicate that European countries do not follow the common policy framework for ensuring inclusion and fairness in their education systems as well as within the country between key-stages. Furthermore, we demonstrate that economic categories such as effectiveness and efficiency have different connotations when applied to education and should be interpreted taking into account the peculiarities of national education systems.

Modeling and evaluating economic and ecological operation efficiency of smart city pilots

This study investigates whether China's smart city pilots (SCPs) have promoted efficiency in cities' economic and ecological operations and proposes a directional distance function model for super efficiency. Our model captures the economic flexibility of smart cities in China by exploiting slack aspects. We employ this model and other methods to study SCPs in China at the prefecture level. The results show that SCPs have a positive effect on both economic and total ecological efficiency (incorporating resource consumption and pollution emissions). However, the environmental protection effect is not as strong as the resource-preserving effect. These results may be related to China's current stage of development. These findings can help local governments understand the development effect of smart cities and formulate their plans accordingly, while providing valuable insights into the development of a new theory in this field.

Global and local banking crises and risk-adjusted efficiency of Indian banks: Are the impacts really perspective-dependent?

This paper explores the differences in the trajectory of bank efficiency in India in response to two recent episodes of banking crises: the global financial crisis (2007–2009) and local non-performing loans crisis (2013–2017). The study also seeks to find whether the observed impacts of these episodes of banking crises are uniform across two different perspectives of modelling bank efficiency. To obtain risk-adjusted bank efficiency estimates, we intently follow the suggestion of Simper et al. (2017) on choosing an optimum set of internal risk management control variables and employ a non-oriented directional distance function (DDF) model with quasi-fixed inputs. The results suggest that, by and large, public and private banks, irrespective of banking crises, are more efficient in pursuing the regulator’s objective of developing an efficient intermediation process rather than their own objective of profit-maximisation over the sample period from 2001 to 2019. Foreign banks are more adroit in accomplishing the goal of income maximisation. The findings indicate that both exogenous and endogenous banking crises have had distinctive, peculiar, asymmetric impacts on the efficiency levels in realising policy objectives by banks. The global financial crisis essentially has had no hostile effect on the bank’s efficiency in achieving the regulator’s goal. In stark contrast, the local banking crisis has had a significant adverse effect on the income-generating efficiency of all the bank groups. Overall, the impacts of the underlined banking crises are observed to be perspective-dependent.

Carbon emission efficiency measurement and influencing factor analysis of nine provinces in the Yellow River basin: based on SBM-DDF model and Tobit-CCD model.

The Yellow River basin (YRB) is China’s most critical energy consumption and coal production area. The improvement of carbon emission reduction efficiency in this area is the key for the Chinese government to achieve the 2030 carbon peak and 2060 carbon neutral (“30.60”). Given this, this study first calculates the carbon emission efficiency of YRB from 2005 to 2019 based on the slack-based measured directional distance function (SBM-DDF) model and combined with Malmquist–Luenberger (ML) index and decomposes the carbon emission efficiency of each province. Then, a panel Tobit model with random effect is constructed to measure the influencing factors and their influence degree of carbon emission efficiency of YRB. Finally, the main influencing factors are selected, and policy suggestions on how to improve the carbon emission efficiency of each province are put forward with the help of the coupling coordination degree (CCD) model. The results show that first, the carbon emission efficiency of each province is significantly different, but it shows a fluctuating upward trend on the whole. Second, the reasons for the rise or decline of the ML index in different provinces are different. Therefore, the development strategies of different provinces should be formulated from the perspective of accelerating technological progress and improving technical efficiency. Finally, the calculation results of influencing factors and coupling coordination degrees show that provinces with high coupling coordination degrees should focus on developing per capita power consumption and controlling per capita power consumption to consolidate the actual urbanization process and industrial structure adjustment. Provinces with low coupling coordination degrees should focus on maintaining the urbanization process and increasing the development of the tertiary industry. Therefore, to fundamentally reduce carbon emissions in YRB areas, we need to consider implementing differentiated emission reduction schemes based on national strategic objectives and in combination with the development characteristics of various provinces.

Efficiency of the Education System (Primary, Secondary and Tertiary) in Particular Voivodeships of Poland

The reform of the Polish education system (both lower and higher education) that was carried out in recent years has shown the need to improve the efficiency of schools. Therefore, it is reasonable to analyse and evaluate the efficiency of educational centres before implementing reforms. Educational units influence the development of human capital, which should translate into an increase in the wealth of a given region. To our knowledge, there is a lack of research on the technical efficiency of the primary, secondary and tertiary education systems in particular Polish voivodeships. Therefore, the aim of this paper was to present the results of studies on the efficiency of the three levels of the Polish education sector in 2016. The non-radial Slack-Based Directional Distance Function (SBDDF) model, which belongs to the nonparametric Data Envelopment Analysis (DEA) method, was used to test the efficiency. The number of teachers employed in particular voivodeships, as well as the number of schools and universities were assumed as inputs. The number of pupils and students was assumed as outputs. We hypothesise that there is a positive correlation between the efficiency of the education system and the labour market economic indicators in the province. The hypothesis was verified positively as the findings showed that the higher the education system efficiency indicator in a given voivodeship, the greater the number of the SME sector companies per 10,000 inhabitants, the higher the gross Domestic Product (GDP) per capita and the lower the percentage of the unemployed in the region. The study results may be of use to various groups of stakeholders, in particular, employees of ministries responsible for the functioning of primary, secondary and tertiary education. The limitations of the study concern the selection of variables adopted on the input and output side. Moreover, the conducted analysis is static (in one year). Therefore, there is a need to continue research using a dynamic approach.

Directional distance based efficiency decomposition for series system in network data envelopment analysis

The multiplier network directional distance function (DDF) model capable of handling negative data received little attention in the field of data envelopment analysis (DEA). The series system is a basic network one. Under the assumption of variable returns to scale (VRS), this paper extends the multiplier series DEA model for use with the DDF. The proposed series DDF model is non-oriented and can deal with negative data. The resulting system efficiency score can be decomposed as a weighted average of process efficiency scores. In the context of DDF, the issue of possible alternate process efficiencies is addressed. The proposed model can also be applied to the assumption of constant returns to scale (CRS). Moreover, we derive the mathematical relationship between the CRS form of our series DDF model and the series CCR model. Two empirical examples in the literature illustrate the applicability and advantages of the new model.

Government debt and fiscal execution efficiency

Governments have used deficit policies in recent years, yet many still face fiscal debt problems. Thus, this research uses Range Directional Measure Dynamic Directional Distance Function model with negative data to explore the financial efficiency of local governments in Taiwan from 2011 to 2018. This article has three major contributions: (1) The research uses RDM Dynamic DDF model with negative data to solve the problem of negative values on input and output data and uses dynamic models to make up for the deficiencies of past research. (2) Due to the differences in regions, local governments have different fiscal budgets. Therefore, this article uses the Wilcoxon Test to explore the efficiency differences of local governments in different regions. (3) This article analyzes the impact of central subsidies and government deficits (debts) of local governments on fiscal efficiency, and discusses the efficiency of government fiscal execution. The results are as follows. (1) Seven counties and cities with the best efficiency, and seven local governments with poor efficiency. (2) The fiscal performances of outlying islands and eastern local governments are better than those of western local governments. (3) Kaohsiung City has the highest accumulated debt and Tainan City exhibits poor financial performance.

Inclusive ecological efficiency analysis in China's Hainan Island: an extended meta-frontier DEA approach.

China is advocating the ecological civilization for a sustainable society and resource-economic-environmental system due to its environmental and climate problems. As a special resource-economic-environmental system, island systems are facing severe challenges due to the vulnerable coordination ability between ecological environment and economic development. To measure the sustainable performance of island systems more directly and specifically, this paper extends the concept of ecological efficiency to inclusive ecological efficiency. For the first time, we analyze the inclusive eco-efficiency of Hainan Island, the second largest island in China, from 2008 to 2017. Due to the large technological heterogeneity among the diverse industries, this paper combines inclusive eco-efficiency with meta-frontier data envelopment analysis (DEA). And we propose a revised meta-frontier slack-based measure (SBM) model and meta-frontier non-radial directional distance function (NRDDF) model, which makes the technology gap rate (TGR) no larger than 1. The empirical results show that the average inclusive total factor energy efficiency (ITFEE) of the tertiary industry under the group-frontier is the largest while the average ITFEE of the primary industry is the highest under the meta-frontier. Moreover, the technology gap rate of the primary industry is the largest. Policy implementations are presented based on the empirical results.

Multiplier dynamic data envelopment analysis based on directional distance function: An application to mutual funds

This paper extends the multiplier dynamic data envelopment analysis (DEA) by using directional distance function (DDF). Based on the duality theory, a multiplier network DDF model is proposed for the dynamic system which consists of a sequence of periods linked by carryovers. The proposed multiplier dynamic model is non-oriented and is able to handle negative data that possibly exist in inputs, carryovers and outputs. The overall efficiency score calculated by the proposed multiplier dynamic model can be decomposed into a weighted average of period efficiency scores. The approach that determines a unique efficiency score for each period is also proposed. To demonstrate the validity and practicality of the proposed dynamic model, we apply it to evaluate the performance of mutual funds in the American market. The empirical results show that the proposed multiplier dynamic model has strong ability to discriminate performance and good practice value for the actual portfolio selection.

Chinese liquor company management efficiency from a social responsibility perspective: a two stage dynamic directional distance function

Because the liquor industry is an important industry in China, alcohol companies have greater social responsibilities when upgrading their production processes to improve efficiencies. Two main data envelopment analysis (DEA) methods have been used for efficiency analyses: radial models, such as CCR (Charnes, Cooper, Rhodes) and BCC (Banker, Charnes, Cooper) and non-radial methods such as SBM (slacks-based model); however, both have disadvantages. The radial DEA model ignores the non-radial slacks and the non-radial DEA model ignores the characteristics of the same proportion in the radial DEA model. Therefore, this research used a dynamic two-stage directional distance function (DDF) model to analyse the production efficiencies of Chinese listed liquor companies from 2016 to 2018 by evaluating each company’s poverty alleviation input efficiencies, business operations efficiencies, and their social responsibility efficiencies, which was based on their wastewater treatment efficiencies. To overcome the disadvantages in traditional data envelopment models, the DDF model consisted of both input and output direction vectors, the indicator values for which indicated their relative importance or priorities. The analyses found that the indicator efficiencies at most liquor companies had declined, with the poverty alleviation indicator efficiencies being generally lower than the wastewater treatment indicator efficiencies. Several policy and management recommendations are given to improve the overall corporate efficiency and social responsibility in the Chinese liquor industry.

Empirical Analysis on How Financial Development Influences Low-Carbon Economic Gain Efficiency Considering the Panel Data of Yangtze River Economic Corridor

This paper establishes an evaluation metric system (EMS) for low-carbon economic gain efficiency (LCEGE) containing the carbon sink element, and measures the LCEGEs in the 11 provincial administrative regions in the Yangtze River Economic Corridor (YREC) of 2000-2017 with the directional distance function (DDF) model. Furthermore, the Tobit model was selected for the empirical analysis on the influence of financial development on LCEGE. The results show that: the provinces in YREC had certain disparities in LCEGE. Most provinces achieved desirable LCEGEs, but a few provinces failed to do so. The LCEGE in the lower part changed little in the target period, while that in the middle part and upper part varied in two phases. Besides, there are obvious differences in the mean LCEGE between the lower part, middle part, and upper part. In the target period, the three parts of the YREC can be ranked as lower part, middle part, and upper part by LCEGE. The results of Tobit model reveal that the LCEGE in the YREC can be greatly promoted by financial scale, and clearly suppressed by financial structure. Among the control variables, foreign direct investment significantly promotes LCEGE; technical innovation, and energy structure significantly suppresses LCEGE; industrial structure and environmental regulation have an insignificant influence on LCEGE.

Dynamic evolution and influencing factors of industrial green total factor energy efficiency in China

This paper sets up an evaluation index system (EIS) for industrial green total factor energy efficiency (IGTFEE), which contains undesired outputs. Next, the directional distance function (DDF) model was adopted to evaluate the IGTFEEs in 2003–2017 of 30 provincial administrative regions (provinces) in China. The results show that: The 30 provinces differed greatly in mean IGTFEE through the sample period. Most eastern coastal provinces had relatively high IGTFEE, while most inland provinces had undesirable IGTFEE. Eastern region had far better IGTFEE than central and western regions, while central and western regions had similar IGTFEEs. Through kernel density estimation (KDE), it is learned that the kernel density curves of IGTFEE in most years have only one peak, and moved to the left with the elapse of time, revealing the declining trend of China’s IGTFEE. The results of the Tobit model indicate that IGTFEE is greatly promoted by technological progress, opening-up, and environmental regulation, obviously suppressed by energy structure, and insignificantly promoted by human capital.