A comprehensive study evaluates the evolution of economic efficiency, regional technological disparities, and total factor productivity (TFP) changes in China’s industrial sector between 2000 and 2022. Using advanced analytical methods such as SBM-DEA, meta-frontier analysis, and the Malmquist–Luenberger index, the research examines how national and provincial policies have influenced industrial performance across 31 mainland provinces. The findings reveal significant regional imbalances in technology adoption and productivity growth, with eastern provinces consistently outperforming central and western regions. n nThe analysis shows that economic efficiency has improved over time, particularly in areas benefiting from targeted government initiatives like “Made in China 2025” and the Belt and Road Initiative. These programs have promoted innovation, advanced manufacturing, and digital transformation. Investments in infrastructure, education, and clean technology have also contributed to gains in efficiency and sustainability. However, disparities persist due to uneven access to modern production technologies and varying levels of institutional support. n nMeta-frontier analysis highlights a persistent technology gap ratio (TGR), indicating that less-developed regions operate under outdated industrial methods compared to the national technological frontier. While policy efforts have encouraged technology transfer and regional collaboration, progress remains slower in inland provinces. The study identifies technological change (TC) as a stronger driver of TFP growth than efficiency change (EC), suggesting that innovation and modernization are more impactful than incremental efficiency improvements. n nThe Malmquist–Luenberger index further confirms that productivity gains are concentrated in technologically advanced regions, particularly along the eastern coast. Provinces like Beijing, Shanghai, Guangdong, Hainan, and Tibet lead in both financial resource utilization efficiency and TFP performance. Meanwhile, northwestern and northeastern areas lag due to constraints in skilled labor, managerial capacity, and digital integration. n nStatistical testing via the Kruskal-Wallis method confirms significant differences across China’s four major regions in terms of efficiency, technology gaps, and productivity shifts. The authors recommend strengthening inter-regional cooperation, expanding R&D incentives in underdeveloped areas, and improving digital infrastructure to ensure more balanced industrial development. By addressing these disparities, China can enhance its long-term industrial competitiveness and sustainable growth trajectory. n— news from Springer Naturen
— News Original —nEconomic efficiency evaluation, regional technological heterogeneity, and total factor productivity change in the industrial sector of ChinanEconomic growth is paramount for a country or region’s overall prosperity and welfare, as it improves living standards, alleviates poverty, and promotes innovation. Governments are empowered to allocate funds towards infrastructure development and social services, fostering entrepreneurship and small enterprises and encouraging global competitiveness (N. Li et al. 2022) (Rodrik 2007) (Hung and Thanh 2022). Furthermore, the economy’s advancement fosters social stability and harmony while promoting environmental sustainability. To enhance the well-being of individuals and ensure a prosperous future for future generations, it is crucial to achieve consistent and long-term economic growth (Pais et al. 2019). The industrial sector is crucial to any country’s economic development and progress. Firstly, it functions as a fundamental base for economic productivity through producing goods and generating employment prospects. Industrial operations substantially contribute to the GDP, export revenues, and technological progress, therefore driving economic expansion (Singh and Singh, 2022). Moreover, the industrial sector fosters innovation and advances technology, enhancing efficiency, productivity, and competitiveness in domestic and global markets. Industrialization is key to the growth and advancement of supplementary industries, including transportation, infrastructure, and services, generating a multiplier effect that enhances sustainable economic growth (Jiao and Sun 2021) (Amin et al. 2022). n nThe industrial sector’s economic efficiency determines a country’s prosperity and competitiveness. Economic efficiency guarantees the most effective distribution and exploitation of resources, resulting in increased productivity and reduced production costs (Camanho et al. 2024). This enables various industries to increase their production of goods and services while reducing the required resources and improving profitability and competitiveness in domestic and international markets. Implementing effective industrial procedures reduces consumer costs and enhances their quality of life. Moreover, enhancing economic efficiency fosters innovation and technological progress within the industrial domain, facilitating ongoing enhancements in productivity, quality, and sustainability (Y. Li et al. 2022). Economic efficiency facilitates the ability of industries to effectively respond to dynamic market conditions, sustain competitiveness, and promote sustainable economic growth and development by optimizing output and minimizing input. Therefore, it is imperative to prioritize economic efficiency within the industrial sector to improve overall economic performance, foster innovation, and provide lasting prosperity for the country (Ginevičius et al. 2022). n nThe growth of total factor productivity (TFP) plays a crucial role in any country’s industrial sector, as it is vital to economic efficiency, innovation, and competitiveness. TFP growth enables economies to increase their output using the same inputs or sustain output with reduced inputs, reducing production costs and improving productivity (J. Xu et al. 2023). It fosters innovation, produces innovative goods and procedures, and guarantees flexibility in response to evolving market circumstances. The growth of TFP growth plays a significant role in promoting economic growth and sustainability through the expansion of production opportunities and the promotion of resource efficiency (Chen et al. 2022). Total factor productivity (TFP) serves as a fundamental driver of industrial sector growth, reflecting the efficiency with which labor, capital, and other inputs are transformed into output. Higher TFP levels signal improved resource allocation, technological progress, and innovation—critical factors for enhancing global competitiveness. Importantly, TFP growth enables sustainable economic expansion by decoupling output gains from input increases, making it indispensable for long-term industrial development. To maintain continuous growth in the industrial sector, economic efficiency, and prosperity, policymakers and industry leaders need to prioritize policies that encourage Total Factor Productivity (TFP) growth (Lee and Xuan 2019) (Zeng et al. 2022). Similarly, the improvement of production technology significantly enhances the economic efficiency of regions and countries. By increasing efficiency and productivity, it reduces expenses and improves competitiveness. Advanced technologies foster innovation, generate high-skilled employment opportunities, and promote economic expansion, guaranteeing sustained prosperity and international competitiveness. Hence, investing in manufacturing technology is crucial for ensuring long-term economic growth and optimizing operational effectiveness (Albiman and Sulong 2018) (Ananiashvili and Papava 2012). The presence of diverse production technologies at the regional level can positively and negatively affect economic efficiency. Various production technologies enable regions to focus on their strengths and exploit their comparative advantages. This promotes innovation and the ability to adapt to challenges. However, if there are differences in how these technologies are adopted, it can lead to wider gaps in productivity and limit overall economic progress. Regions with obsolete technologies may face difficulties competing with more technologically sophisticated places, resulting in economic inequities. Therefore, to promote economic efficiency and prosperity in countries and regions, collaboration and the spread of technologies between different regions are of significant importance (Shah et al. 2024b). n nThe Chinese government has introduced several measures to improve economic efficiency and promote total factor productivity (TFP) growth within its industrial sector. A primary emphasis has been placed on fostering innovation and promoting development powered by technology (Tian et al. 2023). This is demonstrated by prominent endeavours like the “Made in China 2025” and the “Belt and Road Initiative.” These programs aim to enhance industrial capacities, encourage research and development, and facilitate the implementation of modern technologies such as artificial intelligence, robots, and renewable energy (Li 2018) (Ma, 2022). In addition, China has undertaken policies to enhance resource allocation and minimize inefficiencies. These policies include the reorganization of state-owned businesses, the promotion of market-oriented reforms, and the encouragement of entrepreneurship and the development of the private sector. Efforts to upgrade infrastructure, education, and skills training also enhance economic efficiency and production (Liu et al. 2023). In addition, the government has placed a high importance on environmental sustainability, decreasing pollution, and improving the efficiency of resources. This is achieved through implementing more stringent rules and allocating funds to develop and adopt clean technology (Qian et al. 2022). The Chinese government aims to enhance the efficiency, competitiveness, and sustainable growth of its industrial sector in the global economy by implementing these initiatives (Xia et al. 2022). Moreover, the Chinese government has implemented many initiatives to ensure equitable access to industrial technology throughout all its regions and provinces, with the goal of improving economic efficiency and minimizing technological disparities. Fostering technology transfer and diffusion initiatives facilitates the dissemination of modern industrial methods from developed areas to less-developed ones (L. Xu et al. 2023). It entails offering subsidies, tax benefits, and assistance for research and development endeavors in less developed areas to stimulate technology acceptance and innovation advancement (Yue et al. 2023). In addition, the government has made significant investments in enhancing infrastructure, such as transportation networks and internet access, to guarantee that all areas possess the essential infrastructure to facilitate the implementation and exploitation of contemporary manufacturing technology (Zhou et al. 2018). Furthermore, the Chinese government has enacted regulations to promote cooperation and knowledge-sharing throughout regions, facilitating alliances between corporations, research institutes, and universities across several provinces. China aims to diminish regional disparities, foster inclusive economic growth, and improve overall economic efficiency by equalizing access to industrial technology (Zhao et al. 2022). n nThe purpose of this study is to identify the Chinese provincial and central government’s level of success in enhancing the economic efficiency of the industrial sector and the level of technology curtailment in the different regions by appraising economic efficiency, technology gap ratio, and total factor economic productivity change in the different regions across the country. During the chattels of the Chinese provincial and central government’s dedicated initiatives to enhance economic efficiency, reduce technological heterogeneity in production, and increase total-factor economic productivity growth, exploring the level of success in these endeavors is significant. Concocting policy implications to alter or continue the economic policy is of interest. To this end, the study investigated the level of change in the economic efficiency of the industrial sector of China in the study period of 2000–2022 using SBM-DEA in the first stage. The level of success ratio of the policies by Chinese central and provincial governments in enhancing the economic efficiency of the industrial sectors is evaluated. In the second stage of the study, the Chinese provinces are grouped into 4 different regions. The study evaluates the production technology heterogeneity in different geographical regions through Meta frontier analysis. It also evaluates the level of success of the policies by the Chinese government to curtail the difference in the technology of production of the industrial sector. The study used the Malmquist–Luenberger index in the third stage to check on the total factor economic productivity change in the industrial sector of China in the study period and both geographical regions and 31 mainland provinces. The TFEPC will further be decomposed into EC and TC. The study finds the main determinant in TFPC: EC or TC. It further investigates which factors need to be improved to change TFP in China’s industrial sector. To invalidate the study results, the Kruskal Wallis test was used to test the significant statistical difference among all 4 regions concerning economic efficiency, technology gap ratio, and total factor economic productivity change. The rest of the study is bifurcated as follows. Section “Literature review” gives a detailed literature review on economic efficiency, production technology heterogeneity, and TFEPC in different regions globally. Section ”Methodology” reveals the DEA methodology used for the current study. The data collection and variable selection process are explained in section “Variable Selection and Data Collection”. Results and discussion of the study are represented in Section “Results and Discussion”. Conclusion and policy implications are shown in Section “Conclusion and policy recommendations”. n nThe following 3 subsections illustrate the comprehensive literature review on economic efficiency, production technology heterogeneity, and Total factor economic productivity change in the different regions and industries around the globe. n nEconomic efficiency in different regions and industries n nCamanho et al. (2024) contributed to the current research on Data Envelopment Analysis (DEA) economic efficiency assessments by extensively examining technological advancements. The study explored core models that aim to optimize costs, revenues, and profits. It emphasized the widespread use of detailed data on quantities and prices. Furthermore, it highlighted the dominance of research focusing on input-related factors, particularly cost efficiency. Wang et al. (2022) conducted an analysis of the green economy of financial inclusion intersection in China sustainability and utilized the city-level data for the years 2011 to 2015. This model has approached the evaluation of financial inclusion in a manner that is quite holistic to give the desired results and has put so much emphasis on promoting the phasing in digital finance. The results showed that improving financial inclusion will help improve the efficiency of the green economy. The primary source through which the green economy has been enhanced is imposing more stringent credit limits on manufacturing companies known for causing pollution. The analysis of the relationship between digital and green economy development later receded in China. In their study, Kong and Li, (2023) used ArcGIS spatial analysis to analyze the provincial data between 2011 and 2019. It also helped uncover spatial patterns related to growth in digital economy development and the effectiveness of the developed green economy. Some other statistical models were employed in this analysis, and different models were used, such as fixed effect and Geographical Durbin Models. Quantities were easily verified, showing that digital economy expansion positively affects the efficiency of the green economy, and this is felt more in the Eastern and Central regions. Moreover, the study has also revealed that digital industrialization is critical because it accounts for forty percent of the overall effect and the necessity of the digital economy. Regional green economy efficiency has also been enhanced, positively impacting the neighboring regions. Strielkowski et al. (2020) investigated the determinants that impact economic efficiency and energy stability in smart urban areas. The main emphasis is enhancing infrastructure by implementing LED street lighting systems commonly found in innovative city projects. The findings emphasized the substantial energy-saving capacity of LED lighting and proposed the incorporation of smart grids to achieve even more significant efficiency improvements. The research presented novel estimations for the average European city and highlighted the significance of robust leadership networks and local energy storage technologies in promoting sustainable smart city growth. Aparicio et al. (2023) presented essential criteria for the allocative efficiency component in economic efficiency. This study detected disparities among different decomposition techniques and highlighted the need to accurately represent allocative efficiency in economic efficiency measurements. The study provided a framework for assessing allocative efficiency, which helps better understand economic efficiency breakdowns, specifically price inefficiencies. Besides this, numerous research studies employed the DEA to evaluate the economic efficiency in different regions around the globe (Bednárová et al. 2023; Chen et al. 2024; Frančeškin and Bojnec, 2022; Appiah-Twumasi et al. 2022; Sanina et al. 2023). n nRegional production technology heterogeneity n nAdom and Adams, (2020) highlighted Africa’s agriculture sector’s crucial importance in achieving economic development and the Sustainable Development Goals (SDGs). Although the sector is significant, its productivity development is slower than in other regions, emphasizing the need for a more thorough investigation of technical inefficiencies. The analysis revealed tremendous unrealized potential in agricultural productivity in 49 African countries from 1990 to 2016 due to ongoing technical inefficiency. These findings stressed the need for enduring agricultural policies to tackle ongoing inefficiencies and promote regional progress in food security, poverty alleviation, and sustainable development. Zhang et al. (2020) examined how variations in manufacturing technology affect evaluations of logistical efficiency and carbon emissions across different provinces in China. The study analyzed the origins of logistical inefficiency by employing a meta-frontier data envelopment analysis (DEA) technique and investigated regional disparities from 2011 to 2017. The findings indicated a generally low level of logistics efficiency in China, characterized by notable geographical disparities and a range of factors contributing to inefficiencies. Lin et al. (Lin et al. 2024) highlighted the importance of considering geographical and temporal variations when evaluating ecological efficiency (eco-efficiency) due to the ongoing impact of technology and the differing economic power and resources in different places. The study assessed eco-efficiency, emissions inefficiency, and technological gaps in 30 Chinese provinces from 2016 to 2020, considering numerous aspects such as management, geography, and time. The results revealed regional disparities in management eco-efficiency, with central provinces outperforming those in the east. Additionally, the utilization of sophisticated technology in the eastern region had a significant role in achieving higher eco-efficiency. The research emphasized prioritizing environmental governance, improving regional collaboration, and implementing policies to reduce technology inequities. Zhou et al. (2024) researched the impact of introducing industrial robots on pollution emissions. By implementing industrial robots, they found that pollution emissions intensity decreased significantly in the country’s provinces. This is explained by the decrease in energy use and the application of pollution reduction technologies. The importance of this work lies in the information obtained, which allows one to understand to what extent the application of industrial robots will contribute to greener production in the future. The article is also important for understanding ways to control pollution emissions. Xu et al. (2024) consider the effect of financial resources FRUE, the regional technological gap TGR, and the change in the total factor productivity TFPC on the formation of sports infrastructure in China. The data of 31 provinces and 3 regions of China from 2014 to 2021 were used. The authors used DEA-SBM, Meta-frontier analysis, and the Malmquist productivity index to conduct their work. As a result, it was found that FRUE has a significant potential for growth, and the Eastern region is the most efficient and significantly ahead of the Western and Central regions. The authors discovered that the Eastern region’s production technology is more advanced and leads to total factor productivity. The main leading regions in FRUE and TFPC are Beijing, Shanghai, Tibet, Hainan, and Guangdong. Shah et al. (2024b) highlighted the significance of maintaining sustainable, efficient agricultural production in the face of climate change’s influence on global food security. Examining China’s instance, the study examined the impact of climate change on agricultural productivity and found locations like the Sichuan Basin to be the most successful. The results underscored the importance of climate considerations in influencing technological advancements, validating the existence of regional differences in agricultural output. Shah et al. (2022a) investigated the worldwide concerns around energy efficiency and emissions reduction in light of the twenty-first century’s rapid economic and infrastructural development. The focus was on China’s significant transition in energy policy in 2011, shifting from a focus on security to prioritizing efficiency and long-term economic growth. The study utilized data envelopment analysis (DEA-SBM) to evaluate the energy efficiency of Chinese provinces between 2004 and 2017. The findings emphasized notable advancements in the transition of energy policies. Nevertheless, it observed a slow rate of progress in attaining energy efficiency goals, explicitly in central and western areas. It emphasized the need to enhance manufacturing technologies and energy efficiency levels to boost national energy efficiency. Further, many studies have applied meta-frontier analysis to evaluate the region’s production technology heterogeneity in different parts of the globe (Chen et al. 2023; Kumbhakar et al. 2023; Meng et al. 2021; Shao et al. 2018). n nTotal factor economic productivity change in different global regions n nAfter analyzing the data from 1998 to 2012 in China’s manufacturing sector, Ruihui et al. (2023) concluded that enhancing the cleaner production index has a positive effect on the overall efficiency of environmentally detrimental businesses, among which total factor productivity in industries with high levels of pollution becomes more productive, as well as big and Western companies due to adoption of clean production methods, implementation of advanced production equipment, and employment of high-qualified workers to achieve economies of scale. The authors also gave empirical evidence and policy recommendations to promote the high-quality development of the manufacturing sector. Kryszak et al. (2023) utilized bibliometric analysis to examine total factor productivity (TFP) in agricultural economics and policy. The study identified three primary research areas: the rise of total factor productivity (TFP) in developing countries during policy changes, the issues related to agricultural TFP, and the non-parametric decomposition of TFP using secondary data. The findings offer valuable understanding for future research, highlighting the requirement of expanding the range of TFP concepts to include policy, environmental, and technical matters in developing countries. They provide a comprehensive overview of the existing body of knowledge on agricultural Total Factor Productivity (TFP). Erken et al. (2018) addressed the dearth of data regarding the persistent association between entrepreneurship and economic growth in academic literature. The study incorporated entrepreneurship into four established models that describe total factor productivity in twenty OECD countries from 1969 to 2010. These models have previously neglected the role of entrepreneurship. The results showed that entrepreneurship, measured by the company ownership rate adjusted for GDP per capita, significantly influenced total factor productivity in all models. This highlights entrepreneurship’s crucial role in driving economic growth dynamics. Pan et al. (2022) used the pooled regression analysis method to analyze the digital economy’s impact on the Chinese total factor productivity with a special emphasis on innovation. Applying the method, the scholars concluded that TFP has a curved reaction to the digital economy index of a certain province t. It was also stated that the digital economy index played an important role in advancing the sustained and effective development of TFP. However, given that digital technology was integrated into the median in the process, it can be noted that the eastern part of the country was more interested in advancing its economics, which most likely can be explained by the fact that the high-quality development of total factor productivity has significantly increased. As for central and western parts of the country, the results differed, and the technology was integrated significantly slower. Significance can also be gained by the work of Chang et al. (2023), who has also conducted an empirical analysis to understand how the increase in numbers of the digital economy influences the TFP of the manufacturing department by using data from Chinese manufacturing enterprises from a comprehensive database system, which has been obtained from 2011 to 2020.The findings suggest that the growth of the digital economy has a notable and favorable effect on the overall productivity of the industrial sector. Regional variation demonstrates that coastal regions, namely the eastern coastline area, witness the most prominent enhancement. However, regions like the middle reaches of the Yellow River, the middle reaches of the Yangtze River, and the southwest also receive significant benefits. However, the lack of noticeable influence in the northwest and northeast regions may be attributed to obstacles in the labor force composition, technological advancement, and managerial abilities, which restrict the successful utilization of digital benefits and the implementation of strategies, thus affecting productivity improvement. Wen et al. (2022) examined how the process of digitization and environmental restrictions affected the overall efficiency of Chinese manufacturing companies listed from 2008 to 2019. The difference-in-difference approach was used to analyze the data. The results demonstrated substantial improvements in total factor productivity (TFP) due to digitalization implementation and environmental standards enforcement. The process of digitalization has been shown to reduce transaction costs, facilitate the provision of services, and encourage investment in innovation. Additionally, environmental regulations have compelled manufacturing companies to transform and improve total factor productivity (TFP). Nevertheless, the correlation between ecological legislation and digitalization hurt total factor productivity (TFP), indicating a lack of synchronization between the transition towards cleaner practices and the adoption of digital technologies. Numerous research studies have utilized the DEA to gauge the TFPC in different regions and industries around the globe (Wang, 2023; Cheng et al. 2023; Zhang and Zhang, 2023; Šlander Wostner et al. 2023; Chen et al. 2023). n nThe use of the Data Envelopment Analysis (DEA) technique, developed in the late 1970s by Charnes et al. (1978), represented notable progress in operations research and efficiency analysis. DEA is a non-parametric method used to assess the relative efficiency of decision-making units, such as enterprises, organizations, or institutions. It achieves this by comparing their input-output connections. Unlike conventional approaches that require explicit functional forms, DEA enables the simultaneous assessment of numerous inputs and outputs. This makes it well-suited for evaluating intricate systems where quantifying or comparing inputs and outcomes may be challenging. Over time, the DEA has been widely used in several industries, such as banking, healthcare, education, and manufacturing. Its application has helped to enhance efficiency and production in various areas. n nDEA-SBM with undesirable output n nWe assume there are n Decision Making Units (DMUs), each comprising three distinct elements: inputs, desirable outputs, and undesirable outputs, represented by vectors (x in {R}^{m},{y}^{g} in {R}^{s1} ) and ({y}^{b} in {R}^{S2} ) respectively. Matrices ( chi = left[{x}_{1}, ldots ,{x}_{n} right] in {R}^{m times n},{Y}^{g}= left[{y}_{1}^{g}, ldots ,{y}_{n}^{g} right] in {R}^{s1 times n} ), and ({Y}^{b}= left lfloor {y}_{1}^{b}, ldots ,{y}_{n}^{b} right rfloor in {R}^{{s}_{2} times n} ). We stipulate that (X > 0,{Y}^{b} > 0 ) and ({Y}^{b} > 0 ). Consequently, the production possibility set (P) is defined as follows: n n$$P= left { left(x,{y}^{g},{y}^{b} right){ rm{| }}x ge X lambda ,{y}^{g} le {Y}^{g} lambda ,{y}^{b} ge {Y}^{b} lambda , lambda ge 0 right },$$ n n(1) n nIn this context, we utilize the intensity vector λ ∈ R ^ n. The concept of “constant returns to scale assumption” can be applied within this framework. Even when the model incorporates undesirable outputs, the efficiency of DMU _0 (x_0,y_0^g,y_0^b) can still be determined. If there is no vector ( left(x,{y}^{g},{y}^{b} right) in P ) such that ({x}_{0} ge x,{y}_{0}^{g} le {y}^{g} ) and ({{ rm{y}}}_{0}^{{ rm{b}}} ge {{ rm{y}}}^{{ rm{b}}} ) with at least one strict inequality, the DMU is deemed efficient regardless of undesirable output. SBM can be adjusted as follows: n n$$ left[{ rm{SBM}}-{ rm{Undesirable}} right] ,{p}* = min frac{1- frac{1}{m}{ sum }_{i=1}^{m} frac{{s}_{i}^{-}}{{x}_{i0}}}{1+ frac{1}{{s}_{1}+{s}_{2}} left({ Sigma }_{r=1}^{{s}_{1}} frac{{s}_{r}^{g}}{{y}_{{ro}}}+{ sum }_{r=1}^{{s}_{2}} frac{{s}_{r}^{b}}{{y}_{r0}^{b}} right)}$$ n n(2) n nSubject to n n$${{ boldsymbol{x}}}_{0}=X{ boldsymbol{ lambda }}+{s}^{-}$$ n n(3) n n$${y}_{0}^{g}={Y}^{g} lambda -{s}^{g}$$ n n(4) n n$${y}_{0}^{b}={Y}^{b} lambda +{s}^{b}$$ n n(5) n n$${s}^{-} ge 0,{s}^{g} ge 0,{s}^{b} ge 0, lambda ge 0$$ n n(6) n nThe vectors ({s}^{-} in {R}^{m} ) and ({s}^{b} in {R}^{{s}_{2}} ) represent excessive inputs and undesirable outputs, respectively, while ({s}^{g} in {R}^{{s}_{1}} ) indicates shortages in desirable outputs. Objective function (2) exhibits strict decreasing behavior concerning ({s}_{i}^{-}( forall i),{s}_{r}^{g}( forall r) ) and ({s}_{r}^{b}( forall r) ), and the objective value adheres to (0 < p* le 1 ). The optimal solution for the problem above is ( left({ lambda }^{* },{s}^{-* },{s}^{{g}^{* }},{s}^{{b}^{* }} right) ). To incorporate Return to Scale (RTS) characteristics, the following constraint can be added to [SBM-Undesirable], defining production possibility as: n n$$ ,L le e lambda le U$$ n n(7) n nIn this scenario, (=(1, ldots ,1) in {R}^{n} ) and, (L( le 1) ) and (U( ge 1) )) represent the lower and upper constraints on the intensity, λ, respectively. The conditions ((L=1,U=1),(L=0,U=1) ) and (L = 1, U = ∞) correspond to variable returns to scale (VRS), decreasing returns to scale (DRS), and increasing returns to scale (IRS), respectively. In the initial phase of the empirical analysis, SBM-DEA was employed to assess economic efficiency across Chinese provinces annually from 2000 to 2022. n nDEA-Meta frontier Model n nUtilizing the Meta-frontier Model enhances the precision of assessing the efficiency of DMUs across various groups. As different groups of DMUs may operate with distinct technologies, a more accurate comparison can be achieved when they are evaluated within the same group possessing homogeneous technology levels (Wang et al. 2013). The Meta-frontier ratio (MTR) serves to quantify the technology gaps among different groups, with MTR for group I being represented as (Wang et al. 2018; Hang et al. 2015). n n$${ rm{TGR}}= frac{{MEcoE}}{{GEecoEi}}$$ n n(8) n nWhere ({{GEcoE}}_{i} ) is the economic efficiency of an individual DMU within a group, but MEcoE is Meta-economics efficiency for all DMUs under technology contains all DMUs under consideration. TGR is the mean technological gap ratio between group and meta-frontier technology for different regions with different physiographic characteristics (Chiu et al. 2012). A higher TGR indicates that the group frontier technology is relatively close to the meta-frontier technology because both technology functions are positive and, therefore, have moved in opposite directions. When (TGR = 1), it indicates that there is no technological difference between group and meta frontier. n nMalmquist–Luenberger index n nNevertheless, the DEA model is limited in its capacity to analyze dynamic variations in economic efficiency, as it can only evaluate technical efficiency (TE) over a predetermined period. The Malmquist index is a useful instrument for analyzing variations in productivity. Chung et al. renamed it the Malmquist-Luenberger index (Chung et al. 1997). This model includes an unwanted directional distance function, which introduces two separate components: the efficiency component (EC) and the technology component (TC), as described by Färe et al. (Färe et al. 1992). The ML index undergoes the following changes from time t to t + 1: n n$$M{L}^{t+1}={ left { frac{ left[1+ vec{{D}_{0}^{t}} left({x}^{t},{y}^{t},{b}^{* };{y}^{t},-{b}^{t} right) right]}{ left[1+ vec{{D}_{0}^{t}} left({x}^{t+1},{y}^{+1},{b}^{t+1};{y}^{t+1},-{b}^{t+1} right) right]} times frac{ left[1+ vec{{D}_{0}^{t+1}} left({x}^{t},{y}^{t},{b}^{t};{y}^{t},-{b}^{t} right) right]}{ left[1+ vec{{D}_{0}^{t+1}} left({x}^{t+1},{y}^{+1},{b}^{++1};{y}^{t