From Fintech to Eco-Tech: The Catalytic Role of Digital Inclusion in China's Green Productivity Surge

From Fintech to Eco-Tech: The Catalytic Role of Digital Inclusion in China's Green Productivity Surge | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article From Fintech to Eco-Tech: The Catalytic Role of Digital Inclusion in China's Green Productivity Surge Ning Ma, Tsun Se Cheong, Shuaiyi Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8102488/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Digital financial inclusion (DFI) is of extraordinary significance for green total factor productivity (GTFP). To estimate the impact on the efficiency of the green economy through digital financial inclusion, this paper analyzes and develops an innovative approach: the regression with artificial neural network (ANN) and bootstrapping (RAB) method. This study is the first to employ machine learning methods in examining the correlation between digital financial inclusion and GTFP. Our study makes a vital contribution by unveiling the potential non-linear relationship between the two variables, using the ANN model complemented by advanced machine learning techniques. We find that how inclusion in digital finance would impact an economy’s sustainable development varies, depending on the economy’s current intensity of involvement in DFI. Explore the combined effect of DFI and some other driving factors on GTFP. Eight variables are selected, encompassing aspects such as demographic change, industrial structure, human capital, technological development, and foreign influences. The results reveal that urbanization, industrialization, and industrial upgrading can promote green initiatives, particularly when the economy is still in its early stages of development. The relationships between human capital, public expenditure, and the GEE are complex, as a wide range of context-specific factors collectively shape them. An “inverted U-shaped” or a “U-shaped” relationship is observed, respectively, when it comes to the correlation between GTFP and foreign influences or GTFP and the government’s expenditure on science and technology development. Business and commerce/Economics Social science/Economics Earth and environmental sciences/Environmental social sciences Business and commerce/Finance Social science/Finance Green total factor productivity (GTFP) Digital financial inclusion (DFI) Artificial neural network (ANN) China Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction China's economy has consistently achieved medium-high-speed growth since the implementation of economic reforms and opening up. As a result, it has now emerged as the world's second-largest economy, following the United States. Simultaneously, alongside the swift economic expansion, environmental pollution has emerged as a significant concern that impacts societal progress (Lu et al., 2021 ). In light of this context, the Fourteenth Five-Year Plan aims to “facilitate environmentally friendly progress and a balanced coexistence between humans and nature”. It provides instructive suggestions on “enhancing the integrity and durability of ecosystems”, “sustainably enhancing environmental standards”, and “expediting the adoption of eco-friendly development approaches”. The report of the 20th CPC National Congress reiterated the need to “advance comprehensive environmental pollution management, and uphold precise, scientific, and lawful pollution control”. The issue of cities being the primary contributors to environmental pollution and the necessity of altering the approach to economic development to enhance the green total factor productivity (GTFP) have emerged as crucial concerns for both scholars and professionals, requiring immediate attention. The advancement of a sustainable economy in urban areas is intricately linked to the robust backing of the banking sector (Tamazian et al., 2009 ). Providing sufficient financial assistance can have a dual impact on the city's companies. It can stimulate the development of green technological innovation and also expedite the transformation and advancement of industries. This, in turn, can raise overall productivity and improve the urban GTFP (Zhu et al., 2023 ). In the 21st century, digital finance has experienced rapid growth in China, driven by the advancement and widespread adoption of digital technologies such as big data and cloud computing. This has led to the transformation of China's industrial development landscape, characterized by digital finance and intelligent business models (Li et al., 2020 ). Digital finance, in contrast to traditional finance, efficiently lowers the barriers and expenses associated with financial services by utilizing digital technology. This effectively addresses the financial limitations experienced by numerous small and micro firms (Jain and Gabor, 2020 ). What effect might the rise of digital finance have on the effectiveness of urban GTFP? This question's response can offer a theoretical foundation and point of reference for the green transition of the urban economic growth model. Prior research has examined the variables that influence the effectiveness of urban GTFP from several angles. From an industrial development standpoint, scientists have seen a “U-shaped” relationship between manufacturing agglomeration and the GTFP of cities, typified by initial inhibition followed by promotion (Wang et al., 2023 ). The concentration of the productive service industry contributes to enhancing the environmental efficiency of the city's economy (Du and Zhang, 2023 ). Furthermore, the combined clustering of industrial and logistics sectors contributes to the continuous enhancement of cities' economic efficiency (Zhang and Tao, 2023 ). Regarding policy formulation, scholars have examined the effects of environmental regulation and determined that both formal and informal rules play a crucial role in enhancing the GTFP of cities. Additionally, a spatial spillover effect is associated with this role (Shuai and Fan, 2020 ). Regarding the technology aspect, experts commonly acknowledge that green technological innovation has the potential to improve the urban GTFP (Liu and Dong, 2021 ). Furthermore, other researchers have examined the influence of policies related to the digital economy, industrial structure upgrading, and national credit system development, and have determined that all these policies have a discernible positive impact (Liu et al., 2022 ; Chen et al., 2022 ). To summarize, existing research has created a foundation for the elements that influence the urban GTFP. However, there is a lack of literature that analyzes explicitly the effects of digital finance on these factors from a financial standpoint. The enhancement of urban GTFP is reliant on financial backing. To effectively enhance urban GTFP, it is necessary to direct funding into low-carbon and environmentally friendly sectors. Digital finance, resulting from the convergence of financial innovation and technical innovation, brings about significant changes in the distribution of capital elements and facilitates the unrestricted exchange of information and digital elements. Therefore, this paper integrates digital finance and urban GTFP into a cohesive analytical framework. It empirically investigates the relationship between these two factors. The aim is to provide empirical evidence that contributes to the advancement of urban GTFP. This study makes substantial contributions to various fields in economics, including methodology, data, and findings. This study represents the first endeavor to utilize machine learning methods in examining the correlation between digital financial inclusion and GTFP. Therefore, this study offers a unique perspective and successfully fills a gap in the existing body of literature regarding the approach. Additionally, through a thorough examination of nonlinearity, our technique accurately represents the genuine correlation between the variables. Furthermore, the authors developed an innovative technique called the regression utilizing an artificial neural network (ANN) and bootstrapping (RAB) approach. This approach combines bootstrapping methods with artificial neural network (ANN) models to present their empirical findings. The unique strategy not only provides similar information to the usual econometric method but also demonstrates greater performance. The subsequent portions of this work are organized in the following manner. Section 2 presents the theoretical framework and a detailed literature review, identifying research gaps and proposing hypotheses. Section 3 details the data. Section 4 of the paper provides an in-depth analysis of the methodology employed in the study. The discussion of empirical findings is presented in Sections 5 and 6 . The conclusions are outlined in Section 7 . 2. Theoretical framework and Literature review 2.1. Theoretical background Digital finance constitutes an emergent financial intermediation mechanism that leverages information and communication technologies (ICT) to enable the digitization, network integration, and intelligent automation of financial services via internet-based and mobile telecommunication infrastructures. In comparison to conventional monetary systems, this innovation has the potential to enhance the allocative efficiency of urban green economies significantly. First, digital finance mitigates financing constraints for green economic transitions by operationalizing platforms that facilitate improved access to capital formation channels for environmentally aligned enterprises and projects (Lee et al., 2023 ). Such platforms reduce asymmetric information frictions, thereby mobilizing capital inflows toward green sectors and accelerating industrial scalability. Concurrently, the digitization of financial flows generates verifiable audit trails, which elevate the credibility of green financial instruments and amplify market-driven signals for sustainable investment, further optimizing urban green economic efficiency. Second, the integration of digital financial services with algorithmic financial instruments, including AI-driven analytics, enhances operational productivity in green economic systems. By streamlining green investment appraisal, stochastic risk modeling, and dynamic resource allocation, these tools reduce transaction costs, mitigate resource misallocation, and attenuate negative environmental externalities, thereby elevating systemic GTFP (Pang et al., 2024 ). Third, digital finance augments regulatory oversight of green economic outcomes through blockchain-enabled supervisory platforms. These systems enable real-time monitoring of environmental externalities generated by municipal green initiatives, providing granular data for empirically grounded policymaking. Such ex-post evaluative frameworks ensure adaptive calibration of urban green development strategies, closing feedback loops between regulatory interventions and sustainability targets. Collectively, these mechanisms—capital mobilization, operational optimization, and regulatory precision—establish digital finance as a catalytic institution for advancing urban GTFP under conditions of technological convergence. 2.2 Literature Review Being a byproduct of Internet technology, digital technology is extensively debated in various multidimensional domains, including economic, social, and ecological fields. A significant study has been conducted on the connotations, characteristics, measurements, and internal relationships of digital finance. Tapscott ( 1996 ) has explored its connotations, Unctad (2017) has examined its features, Watanabe et al., ( 2018 ) have focused on its measures, and Hjort and Poulsen ( 2019 ) have investigated its internal ties with economic growth. Additional subjects encompass technological innovation (Hoenig and Henkel 2015 ), optimization and enhancement of industrial structure (Vaisman and Nikiforova 2018 ), the advancement of total factor productivity (Loebbeckea and Picotb, 2015 ), and similar areas of study. From an economic standpoint, digital technology can help businesses analyze and identify the trajectory of environmentally friendly advancements, their potential, and the path to achieving them. This prompts manufacturers to transition from relying on experience to relying on data-driven approaches (Johnson et al., 2017 ). Simultaneously, encouraging the advancement of environmentally friendly technologies, mitigating the potential risks associated with innovation, and effectively controlling transaction costs can enable firms to conserve energy, decrease emissions, and enhance their surroundings. Due to its high-tech overflow nature, digital finance requires personnel to possess advanced abilities. Human capital and national economies can be improved by leveraging knowledge spillover and information diffusion (Michaels et al., 2014 ). This allows for the transcendence of traditional production constraints, leading to the emergence of innovative business models and practices (Bukht and Heeks, 2018 ). Furthermore, it encourages investment in production factors, reduces energy consumption, and enhances overall production efficiency. Industrial structure upgrading is a crucial initial step towards promoting sustainable economic growth. The reliance on information technology is contingent upon the development of sectors associated with information and communication technology (Kim et al., 2002 ; Lee et al., 2009 ). The distinct interconnection, dissemination, and overflow impacts of information and communication technology (ICT) facilitate the enhancement of industrial frameworks. This technology facilitates the rapid movement and reorganization of production resources in high-tech sectors with minimal energy consumption, thereby enhancing the efficiency of aligning supply and demand (Peitz and Waldfogel 2012 ). It facilitates the coordination of different components to enhance advanced productive capabilities and seamlessly incorporates into the economy, utilizing digital technology to streamline the monitoring and administration of production processes. It enhances marketing operations and innovations, leading to changes in production and organization, ultimately improving the efficiency of the green economy (Moyer and Hughes 2012 ). There is no consensus on the relationship between digital finance and GTFP. Li and Xu ( 2023 ) found that in terms of the overall effect, digital financial development is conducive to improving urban GTFP. Huang et al., ( 2023 ) revealed that the digital economy has a positive impact on GTFP in Chinese cities. Luo et al., ( 2022 ) used 108 Chinese cities’ panel data and found that the digital economy significantly promotes GTFP. Chen et al., ( 2023 ) concluded that the digital economy could substantially improve forestry GTFP. Gu et al., ( 2022 ) examined the impact of digitalization on the social sphere on GTFP. The basic results showed that the development of the digital economy in the social sphere has a positive influence on the growth of GTFP, and a spatial spillover effect was observed. Hao et al., ( 2023 ) concluded that the development of the digitalization level effectively promotes green economic growth. Hong et al., ( 2023 ) found that the digital economy has a continuous driving effect on the development of green agriculture and with the passage of time, this effect becomes more and more prominent. Liu et al., ( 2022 ) argued that the digital economy can significantly improve China’s GTFP; however, there are apparent regional differences. Wang et al., ( 2022 ) found that boosting the digital economy can effectively promote urban low-carbon sustainable development. Wang et al., ( 2023 ) concluded that digital inclusive finance can promote the spatial convergence of the GTFP, with a more significant promotion effect in the Western regions than in the Eastern and Central regions of China. Li et al., ( 2021a ) studied the nexus of digital economy development and environmental quality for 217 cities in China from 2003 to 2018. Specifically, this study evaluated the degree of coupling coordination between the digital economy system and the ecological system. Results showed that the coupling coordination degree between the digital economy system and the environmental system shows a fluctuating rise from 2003 to 2018. Jiang et al., ( 2022 ) empirically analyzed the impact of the digital economy on agricultural green development and the underlying mechanism, using panel data from 30 Chinese provinces from 2011 to 2020. The results revealed that the digital economy can significantly enhance China's agricultural green development level. Chen ( 2022 ) examined the impact of the digital economy using a double fixed effects model and a spatial econometric model, analyzing 276 cities in China from 2011 to 2019. The author found that the digital economy can drive clean energy development. Lee et al., ( 2022 ) concluded that digitalization has significantly improved GTFP, and this finding remains valid after a series of robust analyses. Li et al., ( 2021b ) studied the panel data of 277 cities in China from 2011 to 2018. The paper constructs the Digital Economy Index and the GTFP Index. The research found that the digital economy has significantly improved the efficiency of the green economy in the region. Tian and Pang ( 2022 ) illustrated that internet development not only has a significant direct positive effect on GTFP, but also indirectly promotes GTFP through technology innovation and industrial structure upgrade. Wang et al., ( 2022 ) examined the relationship between financial inclusion and GTFP in the context of China, based on city-level data for the period 2011–2015. The result suggested that development of financial inclusion can enhance green economic efficiency. Zhang et al., ( 2022 ) concluded that the digital economy improves carbon emission performance. In contrast to the above literature, Li and Wang ( 2022 ) found that the relationship between the digital economy and carbon emissions is inverted U-shaped. Similarly, the spatial spillover effect of the digital economy on carbon emissions is also an inverted-U shape. Pertinent studies have established a solid groundwork for investigating the correlation between digital finance and GTFP, although specific inadequacies remain. Previous studies have primarily examined the general operational characteristics and their impact on the economic and environmental performance of the digital economy, as demonstrated by Graetz and Michaels ( 2018 ), Lederman and Zouaidi ( 2022 ), and Ma et al., ( 2022 ). Nevertheless, it is imperative to perform studies on the impact of digital finance on GTFP. Furthermore, the accuracy of the conclusions is compromised due to the constraints imposed by statistical data and research techniques, as most current studies are conducted at the provincial level. Hence, this study provides empirical evidence on the impact of digital finance on GTFP by constructing a regression utilizing an artificial neural network (ANN) and a bootstrapping (RAB) approach and examining the underlying process within the context of China. To fill this void in the literature, we advance the following research hypothesis: Hypothesis 1 GTFP and corporate DFI exhibit a nonlinear association. 3. Data This study focuses on an extensive sample of 297 Chinese cities at the prefecture and above-prefecture levels from 2011 to 2017. The data was obtained from the China Statistical Yearbook (CSY), China Urban Statistical Yearbook (CUSY), and China Science and Technology Statistical Yearbook (CSTSY). The data on digital financial inclusion are sourced from the China Digital Inclusive Finance Index, released by the Digital Finance Research Centre of Peking University (Guo et al., 2020 ). The objective is to encompass a wide range of independent variables, as multicollinearity is generally not a significant concern in this context. Table 1 provides a list of the independent variables employed in this study, with GTFP serving as the dependent variable. This paper measures the GTFP using the SBM-DDF method and employs the GML index (Li et al., 2022 ). It includes multiple input and output elements, and it not only reflects the efficiency of economic development but also considers the degree of environmental protection, allowing for a well-reflective assessment of the objective requirements of green development. Input indicators include the urban capital stock level and labour input. We select the city's electricity consumption each year to represent the energy input. Output indicators include each city’s GDP in 2000 constant prices, which is chosen to represent the expected output. Unexpected output consists of the industrial wastewater, SO 2 , and smoke and dust of each prefecture-level city. GML index can divide GTFP into efficiency change ( EC ) and technology change ( TC ), and their expressions are as follows: $$\:{GTFP}_{i}^{(t,t+1)}={EC}_{i}^{(t,t+1)}\times\:{TC}_{i}^{(t,t+1)}$$ 1 $$\:{EC}_{i}^{(t,t+1)}=\frac{{D}_{i}^{t+1}({x}_{t+1},{y}_{t+1})}{{D}_{i}^{t}(x,y)}$$ 2 $$\:{TE}_{i}^{(t,t+1)}={[\frac{{D}_{i}^{t}\left({x}_{t+1},{y}_{t+1}\right)}{{D}_{i}^{t+1}\left({x}_{t+1},{y}_{t+1}\right)}\times\:\frac{{D}_{i}^{t}\left({x}_{t},{y}_{t}\right)}{{D}_{i}^{t+1}\left({x}_{t},{y}_{t}\right)}]}^{1/2}$$ 3 In the above equations, Dt (⋅) and Dt + 1 (⋅) express the Shephard distance at year t and t + 1, respectively. EC reflects the distance change from the present production level to the frontier level. If EC is above 1, it means there is an improvement in production efficiency; otherwise, it indicates production degradation. TC indicates the distance change of production compared with technical activities. If TC is larger than 1, it indicates technology advancement. Conversely, it means technology regression. To ensure the thoroughness of this analysis, we have incorporated nearly all the variables utilized in previous studies (excluding a few unavailable data series). Consequently, this study stands as the most comprehensive to date in terms of the breadth of independent variables considered. As recommended by previous researchers, the selected independent variables span various crucial domains, including policy, demographic, macroeconomic, and polity variables. To account for the disparate units and ranges of the independent variables, a standardization process was implemented during data preparation. Before model processing and training, the data underwent appropriate data transformations. Subsequently, the forecasted results were subjected to a reverse transformation to restore them to the original units of the data. The dataset was divided into a training dataset and a testing dataset. The training dataset was used during the training phase, while the model's accuracy was assessed using the testing dataset. Table 1 Independent Variables list Variables Measure Data Source Related Literature Digital financial inclusion Digital financial inclusion index Digital Finance Research Center, Peking University Li and Xu ( 2023 ); Huang et al., 2023 ; Luo et al., 2022 ; Chen et al., 2023 ; Gu et al., 2022 ; Hao et al., 2023 ; Hong et al., 2023 ; Liu et al., 2022 ; Wang et al., 2022 ; Wang et al., 2023 ; Li et al., 2021a ; Jiang et al., 2022 ; Chen ( 2022 ); Lee et al., 2022 ; Li et al., 2021b ; Li and Wang 2022 ; Tian and Pang 2022 ; Wang et al., 2021 ; Zhang et al., 2022 Energy consumption Ratio of total electricity supply to total population; Ratio of total gas supply to total population; Ratio of total LPG supply to total population CSY, CUSY, CSTSY Gu et al., 2022 ; Li and Wang 2022 ; Tian and Pang 2022 ; Zhang et al., 2022 Foreign investment Proportion of foreign capital utilized to GDP CSY, CUSY, CSTSY Li and Xu ( 2023 ); Wang et al., 2022 ; Chen ( 2022 ); Li et al., 2021; Li and Wang 2022 ; Tian and Pang 2022 Government expenditure Proportion of government expenditure to GDP CSY, CUSY, CSTSY Li and Xu ( 2023 ); Luo et al., 2022 ; Chen et al., 2023 ; Gu et al., 2022 ; Hao et al., 2023 ; Liu et al., 2022 ; Wang et al., 2022 ; Jiang et al., 2022 ; Lee et al., 2022 ; Li et al., 2021a ; Tian and Pang 2022 ; Wang et al., 2021 ; Zhang et al., 2022 Higher education Proportion of students in the university CSY, CUSY, CSTSY Huang et al., 2023 ; Luo et al., 2022 ; Gu et al., 2022 ; Hong et al., 2023 ; Liu et al., 2022 ; Wang et al., 2023 ; Chen ( 2022 ); Wang et al., 2021 Income Per capita disposable income (constant 2011 RMB) CSY, CUSY, CSTSY Hong et al., 2023 ; Zhang et al., 2022 Industrial rationalization Dispersion of the ratio of industrial output to the employed population CSY, CUSY, CSTSY Wang et al., 2022 ; Li et al., 2021a ; Lee et al., 2022 Industrial upgrading Proportion of added value of the tertiary industry to GDP CSY, CUSY, CSTSY Li and Xu ( 2023 ); Luo et al., 2022 ; Chen et al., 2023 ; Liu et al., 2022 ; Wang et al., 2022 ; Wang et al., 2023 ; Li et al., 2021a ; Chen ( 2022 ); Lee et al., 2022 ; Li et al., 2021b ; Wang et al., 2021 ; Zhang et al., 2022 Industrialization Share of industrial value added in GDP CSY, CUSY, CSTSY Huang et al., 2023 ; Gu et al., 2022 Patent Proportion of patent authorizations to the total population CSY, CUSY, CSTSY Luo et al., 2022 ; Gu et al., 2022 ; Liu et al., 2022 ; Li et al., 202a1; Li and Wang 2022 ; Wang et al., 2021 Population density Number of people per square kilometer CSY, CUSY, CSTSY Li and Xu ( 2023 ); Gu et al., 2022 ; Chen ( 2022 ); Lee et al., 2022 ; Li and Wang 2022 Real GDP GDP (constant 2011 RMB) CSY, CUSY, CSTSY Luo et al., 2022 ; Gu et al., 2022 ; Hao et al., 2023 ; Wang et al., 2023 ; Li et al., 2021a ; Chen ( 2022 ); Li et al., 2021b ; Li and Wang 2022 Support of science, technology, and education Ratio of fiscal expenditure on science, technology, and education CSY, CUSY, CSTSY Huang et al., 2023 ; Jiang et al., 2022 ; Lee et al., 2022 Trade openness Amount of foreign capital utilization CSY, CUSY, CSTSY Huang et al., 2023 ; Luo et al., 2022 ; Gu et al., 2022 ; Hao et al., 2023 ; Liu et al., 2022 ; Wang et al., 2022 ; Wang et al., 2023 ; Lee et al., 2022 ; Li and Wang 2022 ; Wang et al., 2021 ; Zhang et al., 2022 Urbanization Share of urban population in total population CSY, CUSY, CSTSY Chen et al., 2023 ; Wang et al., 2022 ; Li and Wang 2022 ; Zhang et al., 2022 Source: author’s own compilation 4. Methodology 4.1 Artificial Neural Network Model In a seminal work, Hornik ( 1991 ) established the multilayer feedforward network, a specific type of artificial neural network (ANN), as a universal approximator capable of faithfully reproducing the underlying functional form and the actual relationship between the dependent variable and the independent variables. This groundbreaking research laid a solid foundation for advancements in artificial intelligence and huge language models (LLMs). These models, such as ChatGPT, have proven indispensable in various applications, including chatbots, autonomous driving systems, machine translation, face and voice recognition, and other domains requiring high forecasting accuracy. In terms of mean squared error (MSE), the ANN consistently outperforms traditional econometric models. Notably, conventional econometric models struggle to handle nonlinear functions, such as trigonometric functions and those involving the logarithm of the sum of independent variables. In contrast, the ANN possesses an exceptional capacity to simulate all functional forms, making it a universal approximator. It excels in identifying complex nonlinear relationships among independent variables. Given that most econometric approaches are linear in nature, the ANN holds great promise for researchers aiming to explore complex nonlinear relationships, as it can accurately replicate any underlying functional form. Moreover, the ANN model is highly valuable as it does not rely on the assumption of a linear relationship, thereby allowing the data to speak for themselves without being constrained by any assumptions about the underlying functional form. Unfortunately, the adoption of machine learning (ML) technologies, including ANN, in economic and financial research remains limited (for a discussion on potential areas of application, refer to Mullainathan and Spiess 2017 ). One possible reason for this is the challenge of presenting the results to economists who are familiar with econometric techniques but not well-versed in the ANN approach. To address this issue, Cheong et al., ( 2022 ) introduced Regression by ANN with Bootstrapping (RAB) approach, aiming to enhance the communication of findings. By bridging the gap between the ANN method and conventional econometric models, the RAB approach facilitates the exploration of highly nonlinear relationships between variables. Consequently, both the ANN model and the RAB approach were employed in this study to uncover the intricate nonlinear relationships between the variables. The architecture of the ANN model employed in this study follows a two-stage approach, encompassing a neural network for classification in the first stage and function approximation in the second stage. This design significantly enhances the model's accuracy. Initially, a classifier is employed to categorize the data into four distinct groups, ensuring that the data within each group exhibits similarity based on its intrinsic features. For this purpose, a self-organizing map (SOM) neural network is employed in the first step. The classified data from the first stage is then passed on to the second stage, which comprises four separate function approximation ANNs. Adopting this two-stage technique enhances the efficiency of the training process. It improves the accuracy of the function approximation ANN for each group, as the data within each group are inherently similar. This design has also been utilized by Zhang et al., ( 2004 ), Weng et al., ( 2009 ), Nourani et al., ( 2014 ), Lin et al., ( 2016 ), and Cheong et al., ( 2022 ). The foundational element of an ANN is the neuron, which is composed of a series of formulas. Assuming that the neuron's inputs consist of i independent variables ( X 1 , X 2 , ..., X i ), each neuron is characterized by a constant known as the bias and j weights. The initial output of neuron j is determined by the sum of its bias and the product of its inputs and weights. The following equation can represent this relationship: $$\:{S}_{j}={\sum\:}_{k=1}^{i}{X}_{k}{W}_{j,k}+{B}_{j}$$ 4 where the weight of input k is denoted as W j,k , and the bias is represented by B j . Subsequently, the output of neuron j is passed through the activation function, also referred to as the transfer function, to calculate the final output. While the activation function frequently takes the form of a sigmoid function, it can also encompass various other types, such as the logistic function, hyperbolic tangent, rectified linear unit, and others. In the case of the four-function approximation ANNs, the inputs are initially directed to the input layer of the ANN model. Neurons are then established within the hidden layer based on the equation. The outputs of all hidden layer neurons are subsequently consolidated through an activation function in the output layer, which combines the outputs from the hidden layer neurons. Hornik ( 1991 ) demonstrated that this configuration of neurons can replicate the functional relationships between dependent and independent variables across diverse forms. To optimize the neural network, the biases and weights of the neurons are iteratively adjusted in each iteration, employing the backpropagation and gradient descent methods. Gradients are computed using the chain rule and the backpropagation technique. By continuously modifying the biases and weights in the direction of the steepest descent, as determined by the negative gradient, the MSE is progressively reduced towards its local minimum through gradient descent. Following each iteration, the parameter values are updated to systematically reduce the MSE to the desired level. The following equation can represent the gradient descent algorithm: $$\:{\theta\:}_{i,\:t+1}={\theta\:}_{i,t}-\alpha\:\frac{\partial\:}{\partial\:{\theta\:}_{i,t}}J\left({\theta\:}_{i,t}\right)$$ 5 where \(\:{\theta\:}_{i,t}\) is the initial value of the parameter \(\:{\theta\:}_{i}\) in iteration t before the update, and \(\:{\theta\:}_{i,t+1}\:\) is the value of the parameter \(\:{\theta\:}_{i}\) after updating, \(\:\alpha\:\) is the learning rate, \(\:J\left({\theta\:}_{i,t}\right)\) is the MSE function in terms of \(\:{\theta\:}_{i,t}\) , and \(\:\frac{\partial\:}{\partial\:{\theta\:}_{i,t}}J\left({\theta\:}_{i,t}\right)\) represents the gradient of \(\:{\theta\:}_{i,t}\) . One of the significant challenges encountered in machine learning techniques is the issue of overfitting, not overtraining. This occurs when a model becomes so adept at learning from the training data that it can almost perfectly reproduce the same data. However, when confronted with entirely new data that was not part of the training dataset, the model struggles to handle it effectively. Consequently, the model's ability to generalize beyond the training data is compromised, making it unsuitable for data from sources other than the training dataset. To mitigate this issue, techniques such as dropout, early stopping, regularization, and reducing the model's architectural complexity can be employed. In this study, the complexity of the neural network was deliberately constrained to achieve a balance between flexibility and generalization. The equation below provides the optimal number of neurons for the model: $$\:\:N=(\frac{S{P}_{t}{N}_{O}-{N}_{O}}{{I}_{O}+{N}_{O}+1}-1)/{F}_{L}$$ 6 where S represents the total number of samples available for analysis. The limiting factor F L , set to a value of 10 based on the approach followed by Cheong et al. ( 2022 ), serves to constrain the flexibility of the ANN. N signifies the suggested number of hidden neurons in the ANN, used as a reference point for determining the actual number of neurons in the model. P t is the proportion of samples utilized during the training process and classified as the training set. At the same time, N O is the number of output neurons, and I O is the total number of independent variables. To facilitate training and evaluation, the dataset was split randomly into two smaller subsets. The training dataset encompassed 90% of the total data, while the remaining 10% constituted the testing dataset. This division of data is a common practice in machine learning, enabling an unbiased assessment of model accuracy. Following the training of the model using the training dataset, its performance was evaluated using the testing dataset. The model exhibiting the lowest MSE when tested on the testing dataset was considered the most optimal. It is worth noting that the concept of endogeneity, which poses challenges in conventional linear regression, does not apply to the analysis of ANN. Unlike linear regression, ANNs do not rely on linear relationships and, therefore, do not involve slope parameters. This distinction is crucial as endogeneity can introduce bias in the estimation of slope parameters, highlighting the advantages of utilizing ANNs in capturing complex data relationships. 4.2 Regression by ANN with Bootstrapping Approach (RAB) This research employed the regression by ANN with bootstrapping (RAB) approach introduced by Cheong et al., ( 2022 ) to investigate the underlying relationship between the dependent variable and its determinants. The RAB approach offers significant advantages over traditional econometric research by providing comprehensive insights into relationships that are difficult to obtain through conventional linear regression analysis. The classical linear regression framework consists of three essential components: the MSE of the linear line, the slope parameter of the line, and the statistical test conducted on the slope parameter. Notably, the RAB approach surpasses traditional linear regression in all three areas. The primary distinction between the ANN model and conventional linear regression lies in their accuracy. The ANN model, serving as a universal approximator and capable of capturing complex nonlinear relationships, exhibits superior accuracy compared to the linear regression model. If the underlying relationship is linear, both models will yield similar MSE values. However, when faced with nonlinear relationships, the ANN model will outperform the conventional linear regression model in terms of accuracy. Consequently, the linear regression model, with its limited flexibility in representing only a straight line, can be considered a simplified form of an ANN. Unlike the conventional linear regression model, which relies on the computation of the slope parameter ( beta ) to illustrate the relationship between the dependent variable and the independent variables, the ANN model does not depend on beta. It is important to note that beta represents the ratio of the change in the dependent variable to the change in the independent variable, serving as the slope parameter. Consequently, the conventional linear regression model primarily focuses on changes in variables rather than levels. Another limitation of the linear regression model is its assumption of a constant slope parameter across the entire range of independent variables. In contrast, the RAB approach utilizes a two-dimensional curve that allows for variable slopes throughout the whole range, effectively capturing highly nonlinear relationships. Moreover, while the linear regression model emphasizes changes in independent variables, the RAB approach provides a holistic depiction of the relationship between variables at different levels. The third distinction lies in the statistical testing methodology. The conventional linear regression model employs statistical tests conducted on the slope parameter. In contrast, the RAB approach utilizes bootstrapping techniques to calculate the confidence interval for each incremental value of the independent variables at each level. Specifically, the bootstrapping method generated 6,000 samples for each incremental value. Unlike the linear regression model, which focuses on the confidence interval of the slope parameter, the RAB approach directly presents the confidence interval of the independent variable, making it superior to the conventional linear regression model. 5. Results and Discussions 5.1 The impact of digital financial inclusion on green total factor productivity The relationship between GTFP and the Digital Financial Inclusion Index (DFII) is illustrated in Fig. 1 . While digital financial inclusion (DFI) is found to play an overall positive role in boosting GTFP, other observations merit attention. First and foremost, the curve transitions from a convex to a concave shape with the inflection point occurring within the range of DFII values between 150 and 200. At very low levels of DFII, an increment in its value slightly diminishes GTFP. A positive correlation is observed between the two, as DFII increases beyond 75. The value of GTFP increases rapidly until DFII reaches a value of 200, after which the rate of increase slows down gradually. Secondly, the value of GTFP stays above 1 only if the value of DFII exceeds 125. Thirdly, the distance of the confidence intervals narrows markedly when the value of DFII falls into the interval of 150 to 200. The interplay between GTFP and DFI remains underexplored in the literature. After investigating the limited existing studies, we find that a vast majority would presume a linear relationship between the two variables, thus implying a uniform impact of DFI on GTFP. It remains debatable whether DFI improves GTFP as various strands of studies have derived mixed and contradicting regression results when employing the workhorse linear regression technique. Our study makes its key contribution by unveiling the potential non-linear relationship between the two variables, using an ANN model complemented by advanced machine learning techniques. We find that how inclusion in digital finance would exert its impact on an economy’s sustainable development varies, depending on the economy’s current intensity of involvement in DFI. As target audience of DFI is mainly the underprivileged group residing in less-developed areas, when economy is at the initial stage of developing DFI (value of DFII stays below 75), areas of policy focus include scaling up the delivery of regional telecommunication infrastructure, enhancing availability and accessibility of affordable electronic devices accompanied with secure digital financial services as well as nurturing digital financial literacy within the group. Since infrastructure projects like cell tower installation and network implementation can be energy-intensive, a remarkable amount of energy consumption (mainly in the form of fossil fuel as they are more cost-effective and thus more wildly used in marginalized areas) and environmental deterioration would be foreseeable byproducts when developing digital infrastructure for the underserved community. Furthermore, promoting digital financial products and providing training programs on the use of digital finance can also be resource-intensive, considering the human resources and long-distance transportation costs involved. All the production activities that lead to an expansion of the production scale in both intensive and extensive manner violate the realization of reducing energy exploitation and environmental waste and therefore may put a strain on the green development of the economy. It alerts one to the fact that GTFP may even fall below the critical value of 1 at this phase, which is quite unpromising as only if its value goes above 1 can one anticipate GTFP growth. Source: authors' calculations. Nevertheless, the impact of DFI on GTFP reverses when the economy is becoming increasingly mature in DFI (value of DFII surpassing the threshold of 75), where GTFP rises in line with DFII. When the economy is at a moderate level of DFI or when the value of DFII falls into the range of 125 to 225, DFI and GTFP are supposed to be complementary to each other. Particularly, the economy enters its “golden era” of sustainable development when the value of DFII falls into the interval of 150 to 200, where GTFP proliferates stringently with the mildest uncertainties as captured by the narrowest distance between different confidence intervals. Policymakers are advised to fully leverage the benefits of DFI in promoting sustainability at this stage. There are a few possible mechanisms that may contribute to the emergence of this “golden era”. First, as the digital and telecommunication infrastructure is a public good that is non-excludable and non-rivalrous in nature, and since one cell tower can support Internet access for the entire nearby neighborhood, we expect no further exhaustion of resources in this regard. Apart from that, knowledge spillovers among target users of digital financial services would effectively reduce resource depletion from training and education initiatives. Additionally, it may put individuals or firms in unfavorable situations when counterparts are utilizing the benefits of digital financial services while they remain hesitant to test the waters. For instance, when it comes to one of the significant components of DFI, digital payment services, deals halt when one party to a transaction only accepts digital payments (even on-street hawkers in less-developed areas are found to use QR codes to accept payments nowadays in China). Businesses are at risk of losing clients to their competitors if the demand side prefers electronic payments due to their convenience and cost efficiency. All these initiatives would likely arouse interest in the community regarding digital finance and expedite the economy’s digital transition. Conservation of resources and alleviation of environmental degradation often accompany the elimination of paper-based transactions and physical trades, primarily due to digitalization. Once the majority experience the sweet taste of digital finance, enterprises and entrepreneurs seeking product differentiation to secure market share and competitiveness will, by no means, take no further actions. They may, through innovation and research, strive to provide market-leading digital finance platforms, energy-efficient devices, and cutting-edge services that are at the forefront of market trends and relevant to customer needs. This would reinforce the growth in GTFP, thanks to both lower resource input and reduced undesirable output, resulting from higher operational efficiency. It has reached a consensus among scholars that digital finance lowers credit limits and loosens financial constraints for low-income groups, enabling them to access funds and capital more broadly and easily. Apart from that, we believe that promoting digital finance may also help improve the financial literacy of the target group and ultimately contribute to the performance of GTFP. As reaching out to financial services can be done through mobile apps or online platforms rather than via physical banks or institutions, and the former is much simplified by virtue of electronic memory, digital finance gives individuals more time from their daily routines to care for financial planning affairs. It paves the way for energy-saving knowledge spillovers. It is worth mentioning that we treat annual electricity consumption as an energy input, while environmental waste is considered an undesirable output when computing GTFP. Additionally, providing financial services in an online mode can be electricity-intensive. In China, coal still accounts for a dominant proportion of power consumption for electricity generation, as it is more abundant and affordable compared to other forms of fuel, such as natural gas. Therefore, if GTFP is observed to be increasing in tandem with DFII, there must have been some forms of upgrades in digital platforms and devices to improve energy efficiency or shift power towards cleaner energy sources, such as wind and solar. GTFP transits from a phase of rapid growth into a trajectory of stable development when the economy enters a later stage of DFI (value of DFII exceeds 225) as the curve in Fig. 1 gets flatter towards its right end. At this stage, the low-hanging fruit has been picked, and it is challenging to unblock the technology bottlenecks. Moreover, at an advanced stage of digital development, it is reasonable to anticipate an oligopoly in the technology and smartphone market. A few new firms may wish to enter this mature market, where stagnant buying habits and low customer loyalty prevail. Innovation occurs slowly due to weak incentives. These collectively explain the diminishing marginal incremental gains in GTFP. Regarding all the above, we highlight the following policy implications. Firstly, attention should be drawn to those that are currently underperforming in DFI (i.e., the value of DFII stays below 125). The primary policy goal should be to accelerate digital inclusion and promptly increase the value of DFII. Bolstering basic communication and technology infrastructure is needed. A promotion campaign aiming at raising awareness of the digital era and bridging the digital literacy gap should be put on the agenda. To minimize resource exhaustion or environmental externalities during this period, for instance, policymakers can identify cities with comparative advantages in digital sectors and nurture them into regional hubs in DFI via target investment. Pilot programs in training and education can be carried out first in local policy and research institutes to foster the top-down knowledge spillover effect. Secondly, for those cities that are moderately involved in DFI or where the value of DFII ranges from 125 to 225, as basic infrastructure should be well-established, while elementary education on digital finance should have been accomplished, policymakers are advised to devote their efforts to encouraging innovation and digital evolution to revamp DFI’s reinforcing impact on environmental practices. Subsidies and grants can be provided to reward creativity. Law and regulations aimed at correcting market failures while fostering fair and multifaceted competition should be implemented. Cross-sector collaboration on research and development can be inspired and so forth. Lastly, when the economy’s development of DFI is near completion or when the value of DFII exceeds 225, the positive impact of DFI on GTFP weakens. Outcome-based policymakers may consider gradually reallocating resources towards some other thriving industries or sectors to maximize the impact of interventions. The discussions above underscore the need for a nuanced method to explore the correlation between DFI and GTFP. Linear regression techniques with a uniform correlation as the concluding remark would often lead to implausible one-way policy implications. Our work, on the contrary, makes a significant contribution to disclosing the non-linear relationship between DFI and GTFP by utilizing powerful machine learning techniques within an ANN model. Our work can guide policymakers to tailor policies and design targeted interventions based on the specific stage of DFI development. 5.2 The driving factors behind the impact of DFI on GTFP In this section, we explore the combined effect of DFI and some other driving factors on an economy’s GTFP. A total of eight variables are chosen, which cover aspects such as demographic change, industrial structure, human capital, technological development, and foreign influences. 5.2.1 Demographic change 5.2.1.1 Urbanization Figure 2 plots the joint effect of DFI and urbanization on the performance of GTFP. One could observe that the positive correlation in a “convex concave” shape as shown in Fig. 1 still exists at various levels of urbanization and it is more visible when urbanization is relatively low. This is consistent with our previous statement that less-developed remote areas, which are in crucial need of telecommunication and digital infrastructure, are more likely to experience a reduction in GTFP at an early stage of promoting DFI. Source: authors' calculation. From another perspective, at a given value of DFII, urbanization generally facilitates growth in GTFP. The positive relationship between the two manifests more evidently when the value of DFII ranges from 43 to 124. If mass rural-urban migration occurs in the background of rural areas lagging in DFI with no basic telecommunication infrastructure, the migrated rural population would share the benefits of those well-established telecommunication amenities in the city, making part of the planned initially digital infrastructure in rural areas redundant. Resource consumption from infrastructure construction could be reasonably avoided. On top of that, knowledge spillover works more smoothly in agglomeration economies which accelerate human capital formation within the migrated group. It also frees up manpower and resources for training and educational activities. However, if an economy’s DFI development is already nearly completed, to continuously moving into intensive urban growth may be detrimental to the economy’s green ambitions. At this stage, the gap in digital finance between rural and urban areas is trivial. Mass and rapid migration lead to significant congestion costs, placing pressure on both resources and the environment. As we include environmental undesirables, such as dust, in the computation of the GTFP index, it is conceivable to witness a dramatic increase in such undesirable outputs, which would ultimately drive down the value of GTFP. As a result, urbanization is believed to complement DFI strongly and works towards an economy’s sustainable development when the economy is still in its infancy of DFI. It may not necessarily aid economic growth in favor of green transition in those economies that lead in digital inclusive finance. 5.2.1.2 Population density We then investigate another indicator that describes an economy’s demographic change, population density. As we analyze the performance of data at city levels, urbanization and population density are expected to be positively associated with each other. With rapid rural-urban migration, the concentration of the population in a limited urban space will result in higher population density. It is interesting to note in Fig. 3 the staircase shape of the curve, indicating a non-linear relationship between population density and GTFP. The value of population density, 1545, is identified as a breakpoint at which the step occurs, whereas on either thread, GTFP does not fluctuate much. This discontinuity coincides with our previous conclusion about urbanization. At the initial stage of urbanization, population density remains below the benchmark value of 1545, and GTFP remains relatively high. As urbanization progresses to a later stage, when population density surpasses the benchmark, urban areas become too crowded to sustain their population, which negatively impacts their green performance. There are two other attention-getting observations in Fig. 3 . Firstly, the vertical distance between the two threads, or the height of the riser, increases as DFII rises, indicating a sharper plunge in GTFP. Secondly, on the lower thread, where population density exceeds the threshold of 1545, GTFP slightly increases with an increment in population density. It is found to increase less intensely when the level of DFII reaches a plateau. This further underlines the fact that urbanization may be unpropitious to green efficiency for those economies that are already at the forefront of DFI. Source: authors' calculation. 5.2.2 Industrial structure For the industrial structure, we conduct a compare-and-contrast analysis on two related indicators, the proportion of secondary and tertiary industry in gross regional product (GRP). As shown in Figs. 4 and 5 , respectively, the interaction effect of DFI and the two indicators on GTFP resembles each other. The “convex concave” positive relationship in Fig. 1 remains robust across different levels of industry share in GRP (more noticeable when the proportion of either industry is relatively lower), and an increase in the percentage share of either industry tends to lift the value of GTFP across most of the levels of DFI. Both patterns are more observable in Fig. 5 . Source: authors' calculation. The first observation reiterates our earlier conclusion that marginalized areas which are often considered to be lacking in well-developed digital infrastructure, may predictably experience a deficiency in GTFP during the initial stage of DFI development. While it may be self-evident that an enlarging percentage share of the tertiary industry, or interpreted differently, industrial upgrading, would contribute to an economy’s green development, it is worth commenting on the transmission mechanism through which a booming secondary industry may affect the economy’s sustainable development. At first glance, it may be counterintuitive to one that capital-intensive and highly polluted secondary industry can grease the wheels of green growth to a certain extent. Referring to the graph in Fig. 4 in more detail, GTFP is found to be monotonically increasing as industrialization (interpreted as an increasing percentage share of secondary industry in GRP) progresses, provided the economy’s level of DFII remains between the values of 65 and 220. This suggests that the degree of industrialization's impact on the economy’s green growth will be influenced by the economy’s current level of involvement in digital finance. Despite the long-standing consensus that industrialization tends to impair an economy’s green initiatives, it is noteworthy that the primary industry may generate waste and pollutants at a level equal to that of industrial activities. Typical undesirable outputs, such as wastewater from agricultural activities or SO2 from natural resource-based activities like mining and quarrying, are both taken into account in the measurement of GTFP. Therefore, the increasing dominance of the secondary sector in GRP, together with a modest increase in the value of GTFP, can be attributed to a shift from primary to secondary industry. From another perspective, industrialization and urbanization often go hand in hand as the former is considered to draw mass rural-urban migration by providing job opportunities in the cities where production and assembly lines are located. Our previous finding regarding the impact of urbanization on an economy’s green performance is confirmed once more. Source: authors' calculation. 5.2.3 Human capital To provide insights into how human capital interacts with DFI to impact an economy’s green efficiency jointly, we calculate the proportion of students enrolled in regular and short-cycle courses in higher education as a percentage of the population and treat it as a proxy for the economy’s level of human capital. The result is plotted in Fig. 6 as below. Consistently, we notice in Fig. 6 as well the existence of the curve pattern in Fig. 1 , which is more pronounced at lower levels of human capital. An increase in the percentage share of student enrollment is found to enhance the performance of GTFP when the value of DFII is either less than 80 or greater than 249. There is found to be a slight “U-shaped” relationship between the two variables when the value of DFII lies in the range of 80 to 129. At the same time, GTFP decreases monotonically with an increase in the level of human capital when DFII ranges from 129 to 249. Source: authors' calculation. In this regard, we conclude that the intensity of an economy’s involvement in DFI would affect the way in which human capital plays its role in sustainable development. The highly non-linear correlation between human capital and GTFP, as summarized in the previous paragraph, should be shaped by mutually opposing forces, or, in other words, there are policy trade-offs. On the one hand, strengthening literacy helps nurture environmental awareness and encourage innovation in green projects, which are likely the leading factors contributing to the positive correlation between human capital and green efficiency when the value of DFII falls within a specific range (less than 80 or more than 249, respectively). On the other hand, education in the digital era can be electricity-intensive and thus environmental-unfriendly. If one chooses not to pursue higher education, they are more likely to end up as a low-skilled worker. They would probably be employed in less human capital- and digitally intensive sectors. Compared to a typical university student who needs their laptop on throughout the day or a peer worker who deals with information and communications technology (ICT), the low-skilled worker is believed to be living a life that is relatively “power-efficient.” This explains why when the value of DFII ranges from 129 to 249, an enhancement in the human capital may, to some extent, contradict an economy’s sustainability motivations. While we cannot sacrifice the accumulation of human capital to achieve green growth, we are obliged to promote and implement energy-saving measures in schools, such as turning off lights and air conditioners when leaving, shutting down unused electrical equipment between consecutive lessons, and so on. 5.2.4 Technology development We continue to investigate how a tech-savvy government might influence an economy’s green transition. Two other related variables are selected for analysis: total government expenditure and the percentage share of government expenditure allocated to science and technology development. When referring to Fig. 7 , one could notice that the interplay between public expenditure and performance of GTFP varies across different levels of DFII. There is observed to be a “U-shaped” relationship between the two when the value of DFII stays below 36, while a hump-shaped behavior when DFII ranks above 183. A “convex concave” pattern similar to that in Fig. 1 is identified when DFII falls into the range between 36 and 183. Nevertheless, when it comes to the other driver, a specific amount of government expenditure on science and technology development, DFII does not play a significant role in the interaction effect as the U-shaped curve observed in Fig. 8 remains consistent across all levels of DFII. However, it is more evident at lower levels of DFII. Source: authors' calculation. Source: authors' calculation. As public expenditure can be allocated towards various directions and utilized in projects that may happen to be either eco-friendly or eco-hostile (and this explains the sophisticated pattern in Fig. 7 ), more information on the allocation and management of the fund is needed before arriving at a solid conclusion about the impact of total government expenditure on green transition. Regarding the specific amount of government expenditure on science and technology development, we believe that a response lag helps explain the initial deficiency in GTFP, despite budget growth in this direction. Research and innovation take time so a period between the time the fiscal policy is implemented and the time the policy impact is felt would commonly exist. 5.2.5 Foreign influences Lastly, we examine the potential impact of foreign sectors on the domestic economy’s evolution in terms of green efficiency. The annual actual use of foreign capital as a percentage of GRP is used to depict the influence from abroad. From Fig. 9 , one could still acknowledge a quite noticeable “convex concave” pattern, particularly in those economies that are relatively underutilizing foreign capital. There exists a hump-shaped curve when examining the correlation between foreign capital and GTFP at a given level of DFII, which is found to be more right-skewed when DFII stays low. Whilst the introduction of foreign capital may be beneficial in terms of knowledge and expertise transfer, an overutilization of foreign capital may put a strain on the domestic market and reduce innovation incentives. Moreover, the pollution-haven-seeking behavior of some highly polluting foreign firms is anticipated to hinder the sustainable growth of the targeted investment zones. These drawbacks would be more prominently seen in marginalized areas, considering their immature market structure and weak regulations on inbound investments, which justifies the more noticeable right-skewed hump-shaped curve, particularly when the value of DFII stays low. Source: authors' calculation. 6. Model Accuracy To evaluate the accuracy of the models, we computed the mean squared error (MSE) for both the traditional linear regression method (LRM) and our RAB approach. The findings reveal a considerable decrease in error when using the machine learning technique. Specifically, employing a self-organizing map (SOM) to identify the optimal model for running the artificial neural network (ANN), which maximizes MSE improvement, requires balancing the number of data observations per model with the total number of models to promote effective competitive learning (Cheong et al., 2022 ). After performing several thousand trial-and-error runs, we selected four models for implementation within the ANN framework. Table 2 illustrates the MSE improvements achieved with the RAB approach compared to the traditional linear regression model. Among these models, Model 4 demonstrated the most substantial reduction in MSE with the RAB approach. We also derived the ANN functions for the selected variables in each model and integrated them into combined LRM and ANN models to reanalyze the data. The results in the “Overall” row indicate an overall MSE reduction of 8.26%. In conclusion, our SOM-ANN framework consistently demonstrates a significant improvement in capturing the empirical relationships among the relevant variables, as evidenced by the reductions in MSE across models. Table 2 Comparison of MSE between LRM and ANN method LRM ANN Overall 0.001943 0.001783 Model 1 0.001381 0.001364 Model 2 0 0.001498 Model 3 0.002334 0.002091 Model 4 0.001211 0.000889 7. Conclusion We identify a non-linear relationship between GTFP and its level of inclusion in digital finance through the lens of the powerful machine learning techniques. Heterogeneous impacts from digital financial inclusion (DFI) on GTFP are found to prevail across different stages of the economy’s development in DFI. When an economy is still in its infancy of DFI, GTFP diminishes slightly against a greater degree of involvement in DFI. At this stage, the value of the Digital Financial Inclusion Index (DFII) remains under 75. GTFP becomes positively associated with DFII thereafter, as the latter continues to rise, and the mushrooming occurs when the economy is moderately mature in DFI (the value of DFII ranges from 150 to 200). The upsurge in GTFP slows down though when development of DFI is close to completion (value of DFII surpasses 225). These discrepancies in the interplay between DFI and GTFP across different phases of DFI development should be carefully considered when designing policy interventions aimed at promoting sustainable growth. Building up Infrastructure and improving digital literacy, encouraging innovation, and regulating the market together with reallocating resources for practical purposes are core issues that should take precedence respectively during the initial, moderate, and mature stages of DFI development. We also point out that urbanization, industrialization, and industrial upgrading in general promote green initiatives, particularly when the economy has not yet entered an advanced stage of DFI. Policymakers may leverage the complementarity between each of the three aforementioned drivers and DFI in facilitating sustainable development. The relationships between human capital, public expenditure, and the economy’s green efficiency are complex, as a wide range of context-specific factors collectively shape them. Nevertheless, implementing energy-saving measures in educational institutions or direct public expenditure on human capital and green projects is believed to help bolster green efficiency. An “inverted U-shaped” or a “U-shaped” relationship is observed, respectively, when it comes to the correlation between GTFP and foreign influences or GTFP and the government’s expenditure on science and technology development. Local governors should propose stringent regulations on inbound investment to ensure that it is environmentally friendly and market-friendly, and that they continue to expand the budget for science and technology development in marginalized areas that are currently lagging in DFI. Declarations Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contribution N.M: Conceptualization, Writing- Original draft, Data curation, Visualization, preparation, Writing- Reviewing and Editing; T.C:Methodology, Writing- Original draft, Visualization, preparation, Writing- Reviewing and Editing; S.L: Writing- Original draft. Acknowledgements: This work was supported by the Philosophy and Social Science Planning Projects in Hainan Province (HNSK(ZC)23–155), Hainan College of Economics and Business (hnjmk2021301), Hainan Province Education Teaching Reform Research and Scientific Research Projects (Hnjgwt2025-7). Data Availability Data will be made available on request. References Bukht, R and Heeks, R. 2018. Defining, conceptualizing, and measuring the digital economy. 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Synergistic agglomeration of manufacturing and logistics industries and urban green economy efficiency: influence and upgrading. Mathematical Problems in Engineering . 8118981. Zhang, W., Liu, X., Wang, D and Zhou, J. 2022. Digital economy and carbon emission performance: evidence at China’s city level. Energy Policy . 165, 112927. Zhang, B., Zeng, C., Wang, S and Xie, P., 2004. Forecasting Market-Clearing Price in Day-Ahead Market, Using SOM-ANN. 39th International Universities Power Engineering Conference, 2004. UPEC 2004, 2004 Bristol, UK. IEEE, 390-393. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8102488","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":552502353,"identity":"7d6b59db-a3f2-4322-858f-521ece7efaf1","order_by":0,"name":"Ning Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYJCCAwwMNglA2oCBgY14LWkkagGCwyRo0W0/e/Bwwa/zefztzRsYPpQdZuCf3YBfi9mZvITDM/tuF0ucOVbAOOPcYQaJOwcIaDmQY3CYt+d24gaJHANm3rbDDAYSCQS0nH8D0nIucYP8GwPmv0RpuQG0hefHAaAtPAbMjMRpAdnSkJw440xawcGec+k8EjcIOizH+DPPH7vE/vbDGx/8KLOW459BQAsYMLZB6ANAzEOEehD4Q6S6UTAKRsEoGJkAABj1Si3i2bFwAAAAAElFTkSuQmCC","orcid":"","institution":"Hainan College of Economics and Business","correspondingAuthor":true,"prefix":"","firstName":"Ning","middleName":"","lastName":"Ma","suffix":""},{"id":552502354,"identity":"c17f5f8e-f17e-4fb5-8e3f-c253b7ba3650","order_by":1,"name":"Tsun Se Cheong","email":"","orcid":"","institution":"The Hang Seng University of Hong Kong","correspondingAuthor":false,"prefix":"","firstName":"Tsun","middleName":"Se","lastName":"Cheong","suffix":""},{"id":552502355,"identity":"d029b652-406d-4234-afdc-0a2828d9fa9d","order_by":2,"name":"Shuaiyi 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1","display":"","copyAsset":false,"role":"figure","size":54450,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with confidence intervals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculations.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/e46dd56425edeb3c0eca6544.png"},{"id":97141937,"identity":"cd4d4ea6-8eb7-4f69-adfe-e7107b3c47e3","added_by":"auto","created_at":"2025-12-01 10:07:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":72175,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying degrees of urbanization\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/070788fdc14c416e41372ca4.png"},{"id":97141367,"identity":"7be256e6-32cd-4357-bbfe-07b3d0ccedcf","added_by":"auto","created_at":"2025-12-01 10:06:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":111118,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying density of population\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/315db498b51996d917b91eab.png"},{"id":97141886,"identity":"68c0eaf4-0dd1-4b9c-b2ce-0851e3e06a57","added_by":"auto","created_at":"2025-12-01 10:07:08","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":85875,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying percentage share of secondary industry in GRP\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/334b4ef79574d6ab069b4eb8.png"},{"id":97112386,"identity":"610b13d3-7097-49e2-9e77-9f6e31edc497","added_by":"auto","created_at":"2025-12-01 06:47:42","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":77849,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying percentage share of the tertiary industry in GRP\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/736376de8e0f1e8b98499739.png"},{"id":97112388,"identity":"85f1c442-1acb-44db-8040-b91aec413d16","added_by":"auto","created_at":"2025-12-01 06:47:42","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":68043,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying percentage share of students enrolled in regular and short-cycle courses in higher education\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/eb1e1a3bfd570243239b51f1.png"},{"id":97112393,"identity":"7b208dfc-a4e5-4b8a-9fc8-457013b63b9d","added_by":"auto","created_at":"2025-12-01 06:47:42","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":83783,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying percentage share of regional general public budget expenditure in GRP\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/2248153a4dbbf77dee3abc45.png"},{"id":97112385,"identity":"f0fc2896-530a-47a3-8f22-02a7317f7f27","added_by":"auto","created_at":"2025-12-01 06:47:42","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":107969,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying percentage share of government expenditure on science and technology\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/89733d4e3eb7dfab0d7e70de.png"},{"id":97112389,"identity":"da101898-0dd2-4c7e-a798-049ad771ecdd","added_by":"auto","created_at":"2025-12-01 06:47:42","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":66842,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between GTFP and DFII with varying percentage share of annual actual use of foreign capital in GRP\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: authors' calculation.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/f5e1c760525092b160bc9e60.png"},{"id":100406099,"identity":"e3d950e9-e2df-4387-93ca-64d7e0cb6bc5","added_by":"auto","created_at":"2026-01-16 12:40:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1809056,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8102488/v1/4c333e18-1dfc-418f-93f0-ea53d692587f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"From Fintech to Eco-Tech: The Catalytic Role of Digital Inclusion in China's Green Productivity Surge","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eChina's economy has consistently achieved medium-high-speed growth since the implementation of economic reforms and opening up. As a result, it has now emerged as the world's second-largest economy, following the United States. Simultaneously, alongside the swift economic expansion, environmental pollution has emerged as a significant concern that impacts societal progress (Lu et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In light of this context, the Fourteenth Five-Year Plan aims to \u0026ldquo;facilitate environmentally friendly progress and a balanced coexistence between humans and nature\u0026rdquo;. It provides instructive suggestions on \u0026ldquo;enhancing the integrity and durability of ecosystems\u0026rdquo;, \u0026ldquo;sustainably enhancing environmental standards\u0026rdquo;, and \u0026ldquo;expediting the adoption of eco-friendly development approaches\u0026rdquo;. The report of the 20th CPC National Congress reiterated the need to \u0026ldquo;advance comprehensive environmental pollution management, and uphold precise, scientific, and lawful pollution control\u0026rdquo;. The issue of cities being the primary contributors to environmental pollution and the necessity of altering the approach to economic development to enhance the green total factor productivity (GTFP) have emerged as crucial concerns for both scholars and professionals, requiring immediate attention.\u003c/p\u003e\u003cp\u003eThe advancement of a sustainable economy in urban areas is intricately linked to the robust backing of the banking sector (Tamazian et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Providing sufficient financial assistance can have a dual impact on the city's companies. It can stimulate the development of green technological innovation and also expedite the transformation and advancement of industries. This, in turn, can raise overall productivity and improve the urban GTFP (Zhu et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In the 21st century, digital finance has experienced rapid growth in China, driven by the advancement and widespread adoption of digital technologies such as big data and cloud computing. This has led to the transformation of China's industrial development landscape, characterized by digital finance and intelligent business models (Li et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Digital finance, in contrast to traditional finance, efficiently lowers the barriers and expenses associated with financial services by utilizing digital technology. This effectively addresses the financial limitations experienced by numerous small and micro firms (Jain and Gabor, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). What effect might the rise of digital finance have on the effectiveness of urban GTFP? This question's response can offer a theoretical foundation and point of reference for the green transition of the urban economic growth model.\u003c/p\u003e\u003cp\u003ePrior research has examined the variables that influence the effectiveness of urban GTFP from several angles. From an industrial development standpoint, scientists have seen a \u0026ldquo;U-shaped\u0026rdquo; relationship between manufacturing agglomeration and the GTFP of cities, typified by initial inhibition followed by promotion (Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The concentration of the productive service industry contributes to enhancing the environmental efficiency of the city's economy (Du and Zhang, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Furthermore, the combined clustering of industrial and logistics sectors contributes to the continuous enhancement of cities' economic efficiency (Zhang and Tao, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Regarding policy formulation, scholars have examined the effects of environmental regulation and determined that both formal and informal rules play a crucial role in enhancing the GTFP of cities. Additionally, a spatial spillover effect is associated with this role (Shuai and Fan, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Regarding the technology aspect, experts commonly acknowledge that green technological innovation has the potential to improve the urban GTFP (Liu and Dong, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Furthermore, other researchers have examined the influence of policies related to the digital economy, industrial structure upgrading, and national credit system development, and have determined that all these policies have a discernible positive impact (Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). To summarize, existing research has created a foundation for the elements that influence the urban GTFP. However, there is a lack of literature that analyzes explicitly the effects of digital finance on these factors from a financial standpoint. The enhancement of urban GTFP is reliant on financial backing. To effectively enhance urban GTFP, it is necessary to direct funding into low-carbon and environmentally friendly sectors. Digital finance, resulting from the convergence of financial innovation and technical innovation, brings about significant changes in the distribution of capital elements and facilitates the unrestricted exchange of information and digital elements. Therefore, this paper integrates digital finance and urban GTFP into a cohesive analytical framework. It empirically investigates the relationship between these two factors. The aim is to provide empirical evidence that contributes to the advancement of urban GTFP.\u003c/p\u003e\u003cp\u003eThis study makes substantial contributions to various fields in economics, including methodology, data, and findings. This study represents the first endeavor to utilize machine learning methods in examining the correlation between digital financial inclusion and GTFP. Therefore, this study offers a unique perspective and successfully fills a gap in the existing body of literature regarding the approach. Additionally, through a thorough examination of nonlinearity, our technique accurately represents the genuine correlation between the variables.\u003c/p\u003e\u003cp\u003eFurthermore, the authors developed an innovative technique called the regression utilizing an artificial neural network (ANN) and bootstrapping (RAB) approach. This approach combines bootstrapping methods with artificial neural network (ANN) models to present their empirical findings. The unique strategy not only provides similar information to the usual econometric method but also demonstrates greater performance.\u003c/p\u003e\u003cp\u003eThe subsequent portions of this work are organized in the following manner. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the theoretical framework and a detailed literature review, identifying research gaps and proposing hypotheses. Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3\u003c/span\u003e details the data. Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e4\u003c/span\u003e of the paper provides an in-depth analysis of the methodology employed in the study. The discussion of empirical findings is presented in Sections \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Sec19\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The conclusions are outlined in Section \u003cspan refid=\"Sec20\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e"},{"header":"2. Theoretical framework and Literature review","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Theoretical background\u003c/h2\u003e\u003cp\u003eDigital finance constitutes an emergent financial intermediation mechanism that leverages information and communication technologies (ICT) to enable the digitization, network integration, and intelligent automation of financial services via internet-based and mobile telecommunication infrastructures. In comparison to conventional monetary systems, this innovation has the potential to enhance the allocative efficiency of urban green economies significantly. First, digital finance mitigates financing constraints for green economic transitions by operationalizing platforms that facilitate improved access to capital formation channels for environmentally aligned enterprises and projects (Lee et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Such platforms reduce asymmetric information frictions, thereby mobilizing capital inflows toward green sectors and accelerating industrial scalability. Concurrently, the digitization of financial flows generates verifiable audit trails, which elevate the credibility of green financial instruments and amplify market-driven signals for sustainable investment, further optimizing urban green economic efficiency.\u003c/p\u003e\u003cp\u003eSecond, the integration of digital financial services with algorithmic financial instruments, including AI-driven analytics, enhances operational productivity in green economic systems. By streamlining green investment appraisal, stochastic risk modeling, and dynamic resource allocation, these tools reduce transaction costs, mitigate resource misallocation, and attenuate negative environmental externalities, thereby elevating systemic GTFP (Pang et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThird, digital finance augments regulatory oversight of green economic outcomes through blockchain-enabled supervisory platforms. These systems enable real-time monitoring of environmental externalities generated by municipal green initiatives, providing granular data for empirically grounded policymaking. Such ex-post evaluative frameworks ensure adaptive calibration of urban green development strategies, closing feedback loops between regulatory interventions and sustainability targets. Collectively, these mechanisms\u0026mdash;capital mobilization, operational optimization, and regulatory precision\u0026mdash;establish digital finance as a catalytic institution for advancing urban GTFP under conditions of technological convergence.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Literature Review\u003c/h2\u003e\u003cp\u003eBeing a byproduct of Internet technology, digital technology is extensively debated in various multidimensional domains, including economic, social, and ecological fields. A significant study has been conducted on the connotations, characteristics, measurements, and internal relationships of digital finance. Tapscott (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1996\u003c/span\u003e) has explored its connotations, Unctad (2017) has examined its features, Watanabe et al., (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) have focused on its measures, and Hjort and Poulsen (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) have investigated its internal ties with economic growth. Additional subjects encompass technological innovation (Hoenig and Henkel \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), optimization and enhancement of industrial structure (Vaisman and Nikiforova \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), the advancement of total factor productivity (Loebbeckea and Picotb, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), and similar areas of study.\u003c/p\u003e\u003cp\u003eFrom an economic standpoint, digital technology can help businesses analyze and identify the trajectory of environmentally friendly advancements, their potential, and the path to achieving them. This prompts manufacturers to transition from relying on experience to relying on data-driven approaches (Johnson et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Simultaneously, encouraging the advancement of environmentally friendly technologies, mitigating the potential risks associated with innovation, and effectively controlling transaction costs can enable firms to conserve energy, decrease emissions, and enhance their surroundings. Due to its high-tech overflow nature, digital finance requires personnel to possess advanced abilities. Human capital and national economies can be improved by leveraging knowledge spillover and information diffusion (Michaels et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). This allows for the transcendence of traditional production constraints, leading to the emergence of innovative business models and practices (Bukht and Heeks, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Furthermore, it encourages investment in production factors, reduces energy consumption, and enhances overall production efficiency.\u003c/p\u003e\u003cp\u003eIndustrial structure upgrading is a crucial initial step towards promoting sustainable economic growth. The reliance on information technology is contingent upon the development of sectors associated with information and communication technology (Kim et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Lee et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). The distinct interconnection, dissemination, and overflow impacts of information and communication technology (ICT) facilitate the enhancement of industrial frameworks. This technology facilitates the rapid movement and reorganization of production resources in high-tech sectors with minimal energy consumption, thereby enhancing the efficiency of aligning supply and demand (Peitz and Waldfogel \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIt facilitates the coordination of different components to enhance advanced productive capabilities and seamlessly incorporates into the economy, utilizing digital technology to streamline the monitoring and administration of production processes. It enhances marketing operations and innovations, leading to changes in production and organization, ultimately improving the efficiency of the green economy (Moyer and Hughes \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThere is no consensus on the relationship between digital finance and GTFP. Li and Xu (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) found that in terms of the overall effect, digital financial development is conducive to improving urban GTFP. Huang et al., (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) revealed that the digital economy has a positive impact on GTFP in Chinese cities. Luo et al., (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) used 108 Chinese cities\u0026rsquo; panel data and found that the digital economy significantly promotes GTFP. Chen et al., (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) concluded that the digital economy could substantially improve forestry GTFP. Gu et al., (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) examined the impact of digitalization on the social sphere on GTFP. The basic results showed that the development of the digital economy in the social sphere has a positive influence on the growth of GTFP, and a spatial spillover effect was observed. Hao et al., (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) concluded that the development of the digitalization level effectively promotes green economic growth. Hong et al., (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) found that the digital economy has a continuous driving effect on the development of green agriculture and with the passage of time, this effect becomes more and more prominent. Liu et al., (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) argued that the digital economy can significantly improve China\u0026rsquo;s GTFP; however, there are apparent regional differences. Wang et al., (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) found that boosting the digital economy can effectively promote urban low-carbon sustainable development. Wang et al., (\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) concluded that digital inclusive finance can promote the spatial convergence of the GTFP, with a more significant promotion effect in the Western regions than in the Eastern and Central regions of China. Li et al., (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e) studied the nexus of digital economy development and environmental quality for 217 cities in China from 2003 to 2018. Specifically, this study evaluated the degree of coupling coordination between the digital economy system and the ecological system. Results showed that the coupling coordination degree between the digital economy system and the environmental system shows a fluctuating rise from 2003 to 2018. Jiang et al., (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) empirically analyzed the impact of the digital economy on agricultural green development and the underlying mechanism, using panel data from 30 Chinese provinces from 2011 to 2020. The results revealed that the digital economy can significantly enhance China's agricultural green development level. Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) examined the impact of the digital economy using a double fixed effects model and a spatial econometric model, analyzing 276 cities in China from 2011 to 2019. The author found that the digital economy can drive clean energy development. Lee et al., (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) concluded that digitalization has significantly improved GTFP, and this finding remains valid after a series of robust analyses. Li et al., (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e) studied the panel data of 277 cities in China from 2011 to 2018. The paper constructs the Digital Economy Index and the GTFP Index. The research found that the digital economy has significantly improved the efficiency of the green economy in the region. Tian and Pang (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) illustrated that internet development not only has a significant direct positive effect on GTFP, but also indirectly promotes GTFP through technology innovation and industrial structure upgrade. Wang et al., (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) examined the relationship between financial inclusion and GTFP in the context of China, based on city-level data for the period 2011\u0026ndash;2015. The result suggested that development of financial inclusion can enhance green economic efficiency. Zhang et al., (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) concluded that the digital economy improves carbon emission performance.\u003c/p\u003e\u003cp\u003eIn contrast to the above literature, Li and Wang (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) found that the relationship between the digital economy and carbon emissions is inverted U-shaped. Similarly, the spatial spillover effect of the digital economy on carbon emissions is also an inverted-U shape.\u003c/p\u003e\u003cp\u003ePertinent studies have established a solid groundwork for investigating the correlation between digital finance and GTFP, although specific inadequacies remain. Previous studies have primarily examined the general operational characteristics and their impact on the economic and environmental performance of the digital economy, as demonstrated by Graetz and Michaels (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), Lederman and Zouaidi (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and Ma et al., (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Nevertheless, it is imperative to perform studies on the impact of digital finance on GTFP. Furthermore, the accuracy of the conclusions is compromised due to the constraints imposed by statistical data and research techniques, as most current studies are conducted at the provincial level. Hence, this study provides empirical evidence on the impact of digital finance on GTFP by constructing a regression utilizing an artificial neural network (ANN) and a bootstrapping (RAB) approach and examining the underlying process within the context of China.\u003c/p\u003e\u003cp\u003eTo fill this void in the literature, we advance the following research hypothesis:\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eHypothesis 1\u003c/strong\u003e\u003cp\u003eGTFP and corporate DFI exhibit a nonlinear association.\u003c/p\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Data","content":"\u003cp\u003eThis study focuses on an extensive sample of 297 Chinese cities at the prefecture and above-prefecture levels from 2011 to 2017. The data was obtained from the China Statistical Yearbook (CSY), China Urban Statistical Yearbook (CUSY), and China Science and Technology Statistical Yearbook (CSTSY). The data on digital financial inclusion are sourced from the China Digital Inclusive Finance Index, released by the Digital Finance Research Centre of Peking University (Guo et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The objective is to encompass a wide range of independent variables, as multicollinearity is generally not a significant concern in this context. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e provides a list of the independent variables employed in this study, with GTFP serving as the dependent variable. This paper measures the GTFP using the SBM-DDF method and employs the GML index (Li et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). It includes multiple input and output elements, and it not only reflects the efficiency of economic development but also considers the degree of environmental protection, allowing for a well-reflective assessment of the objective requirements of green development. Input indicators include the urban capital stock level and labour input. We select the city's electricity consumption each year to represent the energy input. Output indicators include each city\u0026rsquo;s GDP in 2000 constant prices, which is chosen to represent the expected output. Unexpected output consists of the industrial wastewater, SO\u003csub\u003e2\u003c/sub\u003e, and smoke and dust of each prefecture-level city.\u003c/p\u003e\u003cp\u003eGML index can divide GTFP into efficiency change (\u003cem\u003eEC\u003c/em\u003e) and technology change (\u003cem\u003eTC\u003c/em\u003e), and their expressions are as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{GTFP}_{i}^{(t,t+1)}={EC}_{i}^{(t,t+1)}\\times\\:{TC}_{i}^{(t,t+1)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{EC}_{i}^{(t,t+1)}=\\frac{{D}_{i}^{t+1}({x}_{t+1},{y}_{t+1})}{{D}_{i}^{t}(x,y)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{TE}_{i}^{(t,t+1)}={[\\frac{{D}_{i}^{t}\\left({x}_{t+1},{y}_{t+1}\\right)}{{D}_{i}^{t+1}\\left({x}_{t+1},{y}_{t+1}\\right)}\\times\\:\\frac{{D}_{i}^{t}\\left({x}_{t},{y}_{t}\\right)}{{D}_{i}^{t+1}\\left({x}_{t},{y}_{t}\\right)}]}^{1/2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn the above equations, \u003cem\u003eDt (\u0026sdot;) and Dt\u0026thinsp;+\u0026thinsp;1 (\u0026sdot;)\u003c/em\u003e express the Shephard distance at year \u003cem\u003et\u003c/em\u003e and \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1, respectively. \u003cem\u003eEC\u003c/em\u003e reflects the distance change from the present production level to the frontier level. If \u003cem\u003eEC\u003c/em\u003e is above 1, it means there is an improvement in production efficiency; otherwise, it indicates production degradation. \u003cem\u003eTC\u003c/em\u003e indicates the distance change of production compared with technical activities. If \u003cem\u003eTC\u003c/em\u003e is larger than 1, it indicates technology advancement. Conversely, it means technology regression.\u003c/p\u003e\u003cp\u003eTo ensure the thoroughness of this analysis, we have incorporated nearly all the variables utilized in previous studies (excluding a few unavailable data series). Consequently, this study stands as the most comprehensive to date in terms of the breadth of independent variables considered. As recommended by previous researchers, the selected independent variables span various crucial domains, including policy, demographic, macroeconomic, and polity variables.\u003c/p\u003e\u003cp\u003eTo account for the disparate units and ranges of the independent variables, a standardization process was implemented during data preparation. Before model processing and training, the data underwent appropriate data transformations. Subsequently, the forecasted results were subjected to a reverse transformation to restore them to the original units of the data. The dataset was divided into a training dataset and a testing dataset. The training dataset was used during the training phase, while the model's accuracy was assessed using the testing dataset.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eIndependent Variables list\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariables\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMeasure\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eData Source\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRelated Literature\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDigital financial inclusion\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDigital financial inclusion index\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDigital Finance Research Center, Peking University\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLi and Xu (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e); Huang et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Luo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hao et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Hong et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e; Jiang et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Tian and Pang \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnergy consumption\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRatio of total electricity supply to total population; Ratio of total gas supply to total population; Ratio of total LPG supply to total population\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eGu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Tian and Pang \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eForeign investment\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProportion of foreign capital utilized to GDP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLi and Xu (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e); Wang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Li et al., 2021; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Tian and Pang \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGovernment expenditure\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProportion of government expenditure to GDP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLi and Xu (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e); Luo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hao et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Jiang et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e; Tian and Pang \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHigher education\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProportion of students in the university\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHuang et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Luo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hong et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIncome\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePer capita disposable income (constant 2011 RMB)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHong et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIndustrial rationalization\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDispersion of the ratio of industrial output to the employed population\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eWang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e; Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIndustrial upgrading\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProportion of added value of the tertiary industry to GDP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLi and Xu (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e); Luo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e; Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIndustrialization\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eShare of industrial value added in GDP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHuang et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePatent\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProportion of patent authorizations to the total population\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLuo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., 202a1; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePopulation density\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of people per square kilometer\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLi and Xu (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e); Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eReal GDP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGDP (constant 2011 RMB)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLuo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hao et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e; Chen (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); Li et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSupport of science, technology, and education\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRatio of fiscal expenditure on science, technology, and education\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHuang et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Jiang et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTrade openness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAmount of foreign capital utilization\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHuang et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Luo et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hao et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Lee et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUrbanization\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eShare of urban population in total population\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCSY, CUSY, CSTSY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eChen et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li and Wang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003eSource: author\u0026rsquo;s own compilation\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"4. Methodology","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Artificial Neural Network Model\u003c/h2\u003e\u003cp\u003eIn a seminal work, Hornik (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) established the multilayer feedforward network, a specific type of artificial neural network (ANN), as a universal approximator capable of faithfully reproducing the underlying functional form and the actual relationship between the dependent variable and the independent variables. This groundbreaking research laid a solid foundation for advancements in artificial intelligence and huge language models (LLMs). These models, such as ChatGPT, have proven indispensable in various applications, including chatbots, autonomous driving systems, machine translation, face and voice recognition, and other domains requiring high forecasting accuracy.\u003c/p\u003e\u003cp\u003eIn terms of mean squared error (MSE), the ANN consistently outperforms traditional econometric models. Notably, conventional econometric models struggle to handle nonlinear functions, such as trigonometric functions and those involving the logarithm of the sum of independent variables. In contrast, the ANN possesses an exceptional capacity to simulate all functional forms, making it a universal approximator. It excels in identifying complex nonlinear relationships among independent variables. Given that most econometric approaches are linear in nature, the ANN holds great promise for researchers aiming to explore complex nonlinear relationships, as it can accurately replicate any underlying functional form. Moreover, the ANN model is highly valuable as it does not rely on the assumption of a linear relationship, thereby allowing the data to speak for themselves without being constrained by any assumptions about the underlying functional form.\u003c/p\u003e\u003cp\u003eUnfortunately, the adoption of machine learning (ML) technologies, including ANN, in economic and financial research remains limited (for a discussion on potential areas of application, refer to Mullainathan and Spiess \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). One possible reason for this is the challenge of presenting the results to economists who are familiar with econometric techniques but not well-versed in the ANN approach. To address this issue, Cheong et al., (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) introduced Regression by ANN with Bootstrapping (RAB) approach, aiming to enhance the communication of findings. By bridging the gap between the ANN method and conventional econometric models, the RAB approach facilitates the exploration of highly nonlinear relationships between variables. Consequently, both the ANN model and the RAB approach were employed in this study to uncover the intricate nonlinear relationships between the variables.\u003c/p\u003e\u003cp\u003eThe architecture of the ANN model employed in this study follows a two-stage approach, encompassing a neural network for classification in the first stage and function approximation in the second stage. This design significantly enhances the model's accuracy. Initially, a classifier is employed to categorize the data into four distinct groups, ensuring that the data within each group exhibits similarity based on its intrinsic features. For this purpose, a self-organizing map (SOM) neural network is employed in the first step. The classified data from the first stage is then passed on to the second stage, which comprises four separate function approximation ANNs. Adopting this two-stage technique enhances the efficiency of the training process. It improves the accuracy of the function approximation ANN for each group, as the data within each group are inherently similar. This design has also been utilized by Zhang et al., (\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), Weng et al., (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), Nourani et al., (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), Lin et al., (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), and Cheong et al., (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe foundational element of an ANN is the neuron, which is composed of a series of formulas. Assuming that the neuron's inputs consist of \u003cem\u003ei\u003c/em\u003e independent variables (\u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, ..., \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), each neuron is characterized by a constant known as the bias and \u003cem\u003ej\u003c/em\u003e weights. The initial output of neuron \u003cem\u003ej\u003c/em\u003e is determined by the sum of its bias and the product of its inputs and weights. The following equation can represent this relationship:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{S}_{j}={\\sum\\:}_{k=1}^{i}{X}_{k}{W}_{j,k}+{B}_{j}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere the weight of input \u003cem\u003ek\u003c/em\u003e is denoted as \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k\u003c/em\u003e\u003c/sub\u003e, and the bias is represented by \u003cem\u003eB\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e. Subsequently, the output of neuron \u003cem\u003ej\u003c/em\u003e is passed through the activation function, also referred to as the transfer function, to calculate the final output.\u003c/p\u003e\u003cp\u003eWhile the activation function frequently takes the form of a sigmoid function, it can also encompass various other types, such as the logistic function, hyperbolic tangent, rectified linear unit, and others. In the case of the four-function approximation ANNs, the inputs are initially directed to the input layer of the ANN model. Neurons are then established within the hidden layer based on the equation. The outputs of all hidden layer neurons are subsequently consolidated through an activation function in the output layer, which combines the outputs from the hidden layer neurons. Hornik (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) demonstrated that this configuration of neurons can replicate the functional relationships between dependent and independent variables across diverse forms.\u003c/p\u003e\u003cp\u003eTo optimize the neural network, the biases and weights of the neurons are iteratively adjusted in each iteration, employing the backpropagation and gradient descent methods. Gradients are computed using the chain rule and the backpropagation technique. By continuously modifying the biases and weights in the direction of the steepest descent, as determined by the negative gradient, the MSE is progressively reduced towards its local minimum through gradient descent. Following each iteration, the parameter values are updated to systematically reduce the MSE to the desired level. The following equation can represent the gradient descent algorithm:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\theta\\:}_{i,\\:t+1}={\\theta\\:}_{i,t}-\\alpha\\:\\frac{\\partial\\:}{\\partial\\:{\\theta\\:}_{i,t}}J\\left({\\theta\\:}_{i,t}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e is the initial value of the parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e in iteration \u003cem\u003et\u003c/em\u003e before the update, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{i,t+1}\\:\\)\u003c/span\u003e\u003c/span\u003eis the value of the parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e after updating, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e is the learning rate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:J\\left({\\theta\\:}_{i,t}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the MSE function in terms of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:}{\\partial\\:{\\theta\\:}_{i,t}}J\\left({\\theta\\:}_{i,t}\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the gradient of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eOne of the significant challenges encountered in machine learning techniques is the issue of overfitting, not overtraining. This occurs when a model becomes so adept at learning from the training data that it can almost perfectly reproduce the same data. However, when confronted with entirely new data that was not part of the training dataset, the model struggles to handle it effectively. Consequently, the model's ability to generalize beyond the training data is compromised, making it unsuitable for data from sources other than the training dataset. To mitigate this issue, techniques such as dropout, early stopping, regularization, and reducing the model's architectural complexity can be employed. In this study, the complexity of the neural network was deliberately constrained to achieve a balance between flexibility and generalization. The equation below provides the optimal number of neurons for the model:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\:N=(\\frac{S{P}_{t}{N}_{O}-{N}_{O}}{{I}_{O}+{N}_{O}+1}-1)/{F}_{L}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003eS\u003c/em\u003e represents the total number of samples available for analysis. The limiting factor \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e, set to a value of 10 based on the approach followed by Cheong et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), serves to constrain the flexibility of the ANN. \u003cem\u003eN\u003c/em\u003e signifies the suggested number of hidden neurons in the ANN, used as a reference point for determining the actual number of neurons in the model. \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e is the proportion of samples utilized during the training process and classified as the training set. At the same time, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e is the number of output neurons, and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e is the total number of independent variables.\u003c/p\u003e\u003cp\u003eTo facilitate training and evaluation, the dataset was split randomly into two smaller subsets. The training dataset encompassed 90% of the total data, while the remaining 10% constituted the testing dataset. This division of data is a common practice in machine learning, enabling an unbiased assessment of model accuracy.\u003c/p\u003e\u003cp\u003eFollowing the training of the model using the training dataset, its performance was evaluated using the testing dataset. The model exhibiting the lowest MSE when tested on the testing dataset was considered the most optimal. It is worth noting that the concept of endogeneity, which poses challenges in conventional linear regression, does not apply to the analysis of ANN. Unlike linear regression, ANNs do not rely on linear relationships and, therefore, do not involve slope parameters. This distinction is crucial as endogeneity can introduce bias in the estimation of slope parameters, highlighting the advantages of utilizing ANNs in capturing complex data relationships.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Regression by ANN with Bootstrapping Approach (RAB)\u003c/h2\u003e\u003cp\u003eThis research employed the regression by ANN with bootstrapping (RAB) approach introduced by Cheong et al., (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) to investigate the underlying relationship between the dependent variable and its determinants. The RAB approach offers significant advantages over traditional econometric research by providing comprehensive insights into relationships that are difficult to obtain through conventional linear regression analysis. The classical linear regression framework consists of three essential components: the MSE of the linear line, the slope parameter of the line, and the statistical test conducted on the slope parameter. Notably, the RAB approach surpasses traditional linear regression in all three areas.\u003c/p\u003e\u003cp\u003eThe primary distinction between the ANN model and conventional linear regression lies in their accuracy. The ANN model, serving as a universal approximator and capable of capturing complex nonlinear relationships, exhibits superior accuracy compared to the linear regression model. If the underlying relationship is linear, both models will yield similar MSE values. However, when faced with nonlinear relationships, the ANN model will outperform the conventional linear regression model in terms of accuracy. Consequently, the linear regression model, with its limited flexibility in representing only a straight line, can be considered a simplified form of an ANN.\u003c/p\u003e\u003cp\u003eUnlike the conventional linear regression model, which relies on the computation of the slope parameter (\u003cem\u003ebeta\u003c/em\u003e) to illustrate the relationship between the dependent variable and the independent variables, the ANN model does not depend on beta. It is important to note that beta represents the ratio of the change in the dependent variable to the change in the independent variable, serving as the slope parameter. Consequently, the conventional linear regression model primarily focuses on changes in variables rather than levels. Another limitation of the linear regression model is its assumption of a constant slope parameter across the entire range of independent variables. In contrast, the RAB approach utilizes a two-dimensional curve that allows for variable slopes throughout the whole range, effectively capturing highly nonlinear relationships. Moreover, while the linear regression model emphasizes changes in independent variables, the RAB approach provides a holistic depiction of the relationship between variables at different levels.\u003c/p\u003e\u003cp\u003eThe third distinction lies in the statistical testing methodology. The conventional linear regression model employs statistical tests conducted on the slope parameter. In contrast, the RAB approach utilizes bootstrapping techniques to calculate the confidence interval for each incremental value of the independent variables at each level. Specifically, the bootstrapping method generated 6,000 samples for each incremental value. Unlike the linear regression model, which focuses on the confidence interval of the slope parameter, the RAB approach directly presents the confidence interval of the independent variable, making it superior to the conventional linear regression model.\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Results and Discussions","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e5.1 The impact of digital financial inclusion on green total factor productivity\u003c/h2\u003e\u003cp\u003eThe relationship between GTFP and the Digital Financial Inclusion Index (DFII) is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. While digital financial inclusion (DFI) is found to play an overall positive role in boosting GTFP, other observations merit attention.\u003c/p\u003e\u003cp\u003eFirst and foremost, the curve transitions from a convex to a concave shape with the inflection point occurring within the range of DFII values between 150 and 200. At very low levels of DFII, an increment in its value slightly diminishes GTFP. A positive correlation is observed between the two, as DFII increases beyond 75. The value of GTFP increases rapidly until DFII reaches a value of 200, after which the rate of increase slows down gradually. Secondly, the value of GTFP stays above 1 only if the value of DFII exceeds 125. Thirdly, the distance of the confidence intervals narrows markedly when the value of DFII falls into the interval of 150 to 200.\u003c/p\u003e\u003cp\u003eThe interplay between GTFP and DFI remains underexplored in the literature. After investigating the limited existing studies, we find that a vast majority would presume a linear relationship between the two variables, thus implying a uniform impact of DFI on GTFP. It remains debatable whether DFI improves GTFP as various strands of studies have derived mixed and contradicting regression results when employing the workhorse linear regression technique. Our study makes its key contribution by unveiling the potential non-linear relationship between the two variables, using an ANN model complemented by advanced machine learning techniques. We find that how inclusion in digital finance would exert its impact on an economy\u0026rsquo;s sustainable development varies, depending on the economy\u0026rsquo;s current intensity of involvement in DFI.\u003c/p\u003e\u003cp\u003eAs target audience of DFI is mainly the underprivileged group residing in less-developed areas, when economy is at the initial stage of developing DFI (value of DFII stays below 75), areas of policy focus include scaling up the delivery of regional telecommunication infrastructure, enhancing availability and accessibility of affordable electronic devices accompanied with secure digital financial services as well as nurturing digital financial literacy within the group.\u003c/p\u003e\u003cp\u003eSince infrastructure projects like cell tower installation and network implementation can be energy-intensive, a remarkable amount of energy consumption (mainly in the form of fossil fuel as they are more cost-effective and thus more wildly used in marginalized areas) and environmental deterioration would be foreseeable byproducts when developing digital infrastructure for the underserved community. Furthermore, promoting digital financial products and providing training programs on the use of digital finance can also be resource-intensive, considering the human resources and long-distance transportation costs involved.\u003c/p\u003e\u003cp\u003eAll the production activities that lead to an expansion of the production scale in both intensive and extensive manner violate the realization of reducing energy exploitation and environmental waste and therefore may put a strain on the green development of the economy. It alerts one to the fact that GTFP may even fall below the critical value of 1 at this phase, which is quite unpromising as only if its value goes above 1 can one anticipate GTFP growth.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculations.\u003c/p\u003e\u003cp\u003eNevertheless, the impact of DFI on GTFP reverses when the economy is becoming increasingly mature in DFI (value of DFII surpassing the threshold of 75), where GTFP rises in line with DFII. When the economy is at a moderate level of DFI or when the value of DFII falls into the range of 125 to 225, DFI and GTFP are supposed to be complementary to each other. Particularly, the economy enters its \u0026ldquo;golden era\u0026rdquo; of sustainable development when the value of DFII falls into the interval of 150 to 200, where GTFP proliferates stringently with the mildest uncertainties as captured by the narrowest distance between different confidence intervals. Policymakers are advised to fully leverage the benefits of DFI in promoting sustainability at this stage.\u003c/p\u003e\u003cp\u003eThere are a few possible mechanisms that may contribute to the emergence of this \u0026ldquo;golden era\u0026rdquo;. First, as the digital and telecommunication infrastructure is a public good that is non-excludable and non-rivalrous in nature, and since one cell tower can support Internet access for the entire nearby neighborhood, we expect no further exhaustion of resources in this regard. Apart from that, knowledge spillovers among target users of digital financial services would effectively reduce resource depletion from training and education initiatives.\u003c/p\u003e\u003cp\u003eAdditionally, it may put individuals or firms in unfavorable situations when counterparts are utilizing the benefits of digital financial services while they remain hesitant to test the waters. For instance, when it comes to one of the significant components of DFI, digital payment services, deals halt when one party to a transaction only accepts digital payments (even on-street hawkers in less-developed areas are found to use QR codes to accept payments nowadays in China). Businesses are at risk of losing clients to their competitors if the demand side prefers electronic payments due to their convenience and cost efficiency. All these initiatives would likely arouse interest in the community regarding digital finance and expedite the economy\u0026rsquo;s digital transition. Conservation of resources and alleviation of environmental degradation often accompany the elimination of paper-based transactions and physical trades, primarily due to digitalization.\u003c/p\u003e\u003cp\u003eOnce the majority experience the sweet taste of digital finance, enterprises and entrepreneurs seeking product differentiation to secure market share and competitiveness will, by no means, take no further actions. They may, through innovation and research, strive to provide market-leading digital finance platforms, energy-efficient devices, and cutting-edge services that are at the forefront of market trends and relevant to customer needs. This would reinforce the growth in GTFP, thanks to both lower resource input and reduced undesirable output, resulting from higher operational efficiency.\u003c/p\u003e\u003cp\u003eIt has reached a consensus among scholars that digital finance lowers credit limits and loosens financial constraints for low-income groups, enabling them to access funds and capital more broadly and easily. Apart from that, we believe that promoting digital finance may also help improve the financial literacy of the target group and ultimately contribute to the performance of GTFP. As reaching out to financial services can be done through mobile apps or online platforms rather than via physical banks or institutions, and the former is much simplified by virtue of electronic memory, digital finance gives individuals more time from their daily routines to care for financial planning affairs. It paves the way for energy-saving knowledge spillovers.\u003c/p\u003e\u003cp\u003eIt is worth mentioning that we treat annual electricity consumption as an energy input, while environmental waste is considered an undesirable output when computing GTFP. Additionally, providing financial services in an online mode can be electricity-intensive. In China, coal still accounts for a dominant proportion of power consumption for electricity generation, as it is more abundant and affordable compared to other forms of fuel, such as natural gas. Therefore, if GTFP is observed to be increasing in tandem with DFII, there must have been some forms of upgrades in digital platforms and devices to improve energy efficiency or shift power towards cleaner energy sources, such as wind and solar.\u003c/p\u003e\u003cp\u003eGTFP transits from a phase of rapid growth into a trajectory of stable development when the economy enters a later stage of DFI (value of DFII exceeds 225) as the curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e gets flatter towards its right end. At this stage, the low-hanging fruit has been picked, and it is challenging to unblock the technology bottlenecks. Moreover, at an advanced stage of digital development, it is reasonable to anticipate an oligopoly in the technology and smartphone market. A few new firms may wish to enter this mature market, where stagnant buying habits and low customer loyalty prevail. Innovation occurs slowly due to weak incentives. These collectively explain the diminishing marginal incremental gains in GTFP.\u003c/p\u003e\u003cp\u003eRegarding all the above, we highlight the following policy implications. Firstly, attention should be drawn to those that are currently underperforming in DFI (i.e., the value of DFII stays below 125). The primary policy goal should be to accelerate digital inclusion and promptly increase the value of DFII. Bolstering basic communication and technology infrastructure is needed. A promotion campaign aiming at raising awareness of the digital era and bridging the digital literacy gap should be put on the agenda. To minimize resource exhaustion or environmental externalities during this period, for instance, policymakers can identify cities with comparative advantages in digital sectors and nurture them into regional hubs in DFI via target investment. Pilot programs in training and education can be carried out first in local policy and research institutes to foster the top-down knowledge spillover effect.\u003c/p\u003e\u003cp\u003eSecondly, for those cities that are moderately involved in DFI or where the value of DFII ranges from 125 to 225, as basic infrastructure should be well-established, while elementary education on digital finance should have been accomplished, policymakers are advised to devote their efforts to encouraging innovation and digital evolution to revamp DFI\u0026rsquo;s reinforcing impact on environmental practices. Subsidies and grants can be provided to reward creativity. Law and regulations aimed at correcting market failures while fostering fair and multifaceted competition should be implemented. Cross-sector collaboration on research and development can be inspired and so forth.\u003c/p\u003e\u003cp\u003eLastly, when the economy\u0026rsquo;s development of DFI is near completion or when the value of DFII exceeds 225, the positive impact of DFI on GTFP weakens. Outcome-based policymakers may consider gradually reallocating resources towards some other thriving industries or sectors to maximize the impact of interventions.\u003c/p\u003e\u003cp\u003eThe discussions above underscore the need for a nuanced method to explore the correlation between DFI and GTFP. Linear regression techniques with a uniform correlation as the concluding remark would often lead to implausible one-way policy implications. Our work, on the contrary, makes a significant contribution to disclosing the non-linear relationship between DFI and GTFP by utilizing powerful machine learning techniques within an ANN model. Our work can guide policymakers to tailor policies and design targeted interventions based on the specific stage of DFI development.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e5.2 The driving factors behind the impact of DFI on GTFP\u003c/h2\u003e\u003cp\u003eIn this section, we explore the combined effect of DFI and some other driving factors on an economy\u0026rsquo;s GTFP. A total of eight variables are chosen, which cover aspects such as demographic change, industrial structure, human capital, technological development, and foreign influences.\u003c/p\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003e5.2.1 Demographic change\u003c/h2\u003e\u003cdiv id=\"Sec13\" class=\"Section4\"\u003e\u003ch2\u003e5.2.1.1 Urbanization\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e plots the joint effect of DFI and urbanization on the performance of GTFP. One could observe that the positive correlation in a \u0026ldquo;convex concave\u0026rdquo; shape as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e still exists at various levels of urbanization and it is more visible when urbanization is relatively low. This is consistent with our previous statement that less-developed remote areas, which are in crucial need of telecommunication and digital infrastructure, are more likely to experience a reduction in GTFP at an early stage of promoting DFI.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003cp\u003eFrom another perspective, at a given value of DFII, urbanization generally facilitates growth in GTFP. The positive relationship between the two manifests more evidently when the value of DFII ranges from 43 to 124.\u003c/p\u003e\u003cp\u003eIf mass rural-urban migration occurs in the background of rural areas lagging in DFI with no basic telecommunication infrastructure, the migrated rural population would share the benefits of those well-established telecommunication amenities in the city, making part of the planned initially digital infrastructure in rural areas redundant. Resource consumption from infrastructure construction could be reasonably avoided. On top of that, knowledge spillover works more smoothly in agglomeration economies which accelerate human capital formation within the migrated group. It also frees up manpower and resources for training and educational activities.\u003c/p\u003e\u003cp\u003eHowever, if an economy\u0026rsquo;s DFI development is already nearly completed, to continuously moving into intensive urban growth may be detrimental to the economy\u0026rsquo;s green ambitions. At this stage, the gap in digital finance between rural and urban areas is trivial. Mass and rapid migration lead to significant congestion costs, placing pressure on both resources and the environment. As we include environmental undesirables, such as dust, in the computation of the GTFP index, it is conceivable to witness a dramatic increase in such undesirable outputs, which would ultimately drive down the value of GTFP.\u003c/p\u003e\u003cp\u003eAs a result, urbanization is believed to complement DFI strongly and works towards an economy\u0026rsquo;s sustainable development when the economy is still in its infancy of DFI. It may not necessarily aid economic growth in favor of green transition in those economies that lead in digital inclusive finance.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section4\"\u003e\u003ch2\u003e5.2.1.2 Population density\u003c/h2\u003e\u003cp\u003eWe then investigate another indicator that describes an economy\u0026rsquo;s demographic change, population density. As we analyze the performance of data at city levels, urbanization and population density are expected to be positively associated with each other. With rapid rural-urban migration, the concentration of the population in a limited urban space will result in higher population density.\u003c/p\u003e\u003cp\u003eIt is interesting to note in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e the staircase shape of the curve, indicating a non-linear relationship between population density and GTFP. The value of population density, 1545, is identified as a breakpoint at which the step occurs, whereas on either thread, GTFP does not fluctuate much. This discontinuity coincides with our previous conclusion about urbanization. At the initial stage of urbanization, population density remains below the benchmark value of 1545, and GTFP remains relatively high. As urbanization progresses to a later stage, when population density surpasses the benchmark, urban areas become too crowded to sustain their population, which negatively impacts their green performance.\u003c/p\u003e\u003cp\u003eThere are two other attention-getting observations in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Firstly, the vertical distance between the two threads, or the height of the riser, increases as DFII rises, indicating a sharper plunge in GTFP. Secondly, on the lower thread, where population density exceeds the threshold of 1545, GTFP slightly increases with an increment in population density. It is found to increase less intensely when the level of DFII reaches a plateau. This further underlines the fact that urbanization may be unpropitious to green efficiency for those economies that are already at the forefront of DFI.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\u003ch2\u003e5.2.2 Industrial structure\u003c/h2\u003e\u003cp\u003eFor the industrial structure, we conduct a compare-and-contrast analysis on two related indicators, the proportion of secondary and tertiary industry in gross regional product (GRP). As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, respectively, the interaction effect of DFI and the two indicators on GTFP resembles each other. The \u0026ldquo;convex concave\u0026rdquo; positive relationship in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e remains robust across different levels of industry share in GRP (more noticeable when the proportion of either industry is relatively lower), and an increase in the percentage share of either industry tends to lift the value of GTFP across most of the levels of DFI. Both patterns are more observable in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003cp\u003eThe first observation reiterates our earlier conclusion that marginalized areas which are often considered to be lacking in well-developed digital infrastructure, may predictably experience a deficiency in GTFP during the initial stage of DFI development. While it may be self-evident that an enlarging percentage share of the tertiary industry, or interpreted differently, industrial upgrading, would contribute to an economy\u0026rsquo;s green development, it is worth commenting on the transmission mechanism through which a booming secondary industry may affect the economy\u0026rsquo;s sustainable development. At first glance, it may be counterintuitive to one that capital-intensive and highly polluted secondary industry can grease the wheels of green growth to a certain extent.\u003c/p\u003e\u003cp\u003eReferring to the graph in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e in more detail, GTFP is found to be monotonically increasing as industrialization (interpreted as an increasing percentage share of secondary industry in GRP) progresses, provided the economy\u0026rsquo;s level of DFII remains between the values of 65 and 220. This suggests that the degree of industrialization's impact on the economy\u0026rsquo;s green growth will be influenced by the economy\u0026rsquo;s current level of involvement in digital finance.\u003c/p\u003e\u003cp\u003eDespite the long-standing consensus that industrialization tends to impair an economy\u0026rsquo;s green initiatives, it is noteworthy that the primary industry may generate waste and pollutants at a level equal to that of industrial activities. Typical undesirable outputs, such as wastewater from agricultural activities or SO2 from natural resource-based activities like mining and quarrying, are both taken into account in the measurement of GTFP. Therefore, the increasing dominance of the secondary sector in GRP, together with a modest increase in the value of GTFP, can be attributed to a shift from primary to secondary industry. From another perspective, industrialization and urbanization often go hand in hand as the former is considered to draw mass rural-urban migration by providing job opportunities in the cities where production and assembly lines are located. Our previous finding regarding the impact of urbanization on an economy\u0026rsquo;s green performance is confirmed once more.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\u003ch2\u003e5.2.3 Human capital\u003c/h2\u003e\u003cp\u003eTo provide insights into how human capital interacts with DFI to impact an economy\u0026rsquo;s green efficiency jointly, we calculate the proportion of students enrolled in regular and short-cycle courses in higher education as a percentage of the population and treat it as a proxy for the economy\u0026rsquo;s level of human capital. The result is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e as below.\u003c/p\u003e\u003cp\u003eConsistently, we notice in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e as well the existence of the curve pattern in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, which is more pronounced at lower levels of human capital. An increase in the percentage share of student enrollment is found to enhance the performance of GTFP when the value of DFII is either less than 80 or greater than 249. There is found to be a slight \u0026ldquo;U-shaped\u0026rdquo; relationship between the two variables when the value of DFII lies in the range of 80 to 129. At the same time, GTFP decreases monotonically with an increase in the level of human capital when DFII ranges from 129 to 249.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003cp\u003eIn this regard, we conclude that the intensity of an economy\u0026rsquo;s involvement in DFI would affect the way in which human capital plays its role in sustainable development. The highly non-linear correlation between human capital and GTFP, as summarized in the previous paragraph, should be shaped by mutually opposing forces, or, in other words, there are policy trade-offs. On the one hand, strengthening literacy helps nurture environmental awareness and encourage innovation in green projects, which are likely the leading factors contributing to the positive correlation between human capital and green efficiency when the value of DFII falls within a specific range (less than 80 or more than 249, respectively).\u003c/p\u003e\u003cp\u003eOn the other hand, education in the digital era can be electricity-intensive and thus environmental-unfriendly. If one chooses not to pursue higher education, they are more likely to end up as a low-skilled worker. They would probably be employed in less human capital- and digitally intensive sectors. Compared to a typical university student who needs their laptop on throughout the day or a peer worker who deals with information and communications technology (ICT), the low-skilled worker is believed to be living a life that is relatively \u0026ldquo;power-efficient.\u0026rdquo; This explains why when the value of DFII ranges from 129 to 249, an enhancement in the human capital may, to some extent, contradict an economy\u0026rsquo;s sustainability motivations.\u003c/p\u003e\u003cp\u003eWhile we cannot sacrifice the accumulation of human capital to achieve green growth, we are obliged to promote and implement energy-saving measures in schools, such as turning off lights and air conditioners when leaving, shutting down unused electrical equipment between consecutive lessons, and so on.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003e5.2.4 Technology development\u003c/h2\u003e\u003cp\u003eWe continue to investigate how a tech-savvy government might influence an economy\u0026rsquo;s green transition. Two other related variables are selected for analysis: total government expenditure and the percentage share of government expenditure allocated to science and technology development.\u003c/p\u003e\u003cp\u003eWhen referring to Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, one could notice that the interplay between public expenditure and performance of GTFP varies across different levels of DFII. There is observed to be a \u0026ldquo;U-shaped\u0026rdquo; relationship between the two when the value of DFII stays below 36, while a hump-shaped behavior when DFII ranks above 183. A \u0026ldquo;convex concave\u0026rdquo; pattern similar to that in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e is identified when DFII falls into the range between 36 and 183.\u003c/p\u003e\u003cp\u003eNevertheless, when it comes to the other driver, a specific amount of government expenditure on science and technology development, DFII does not play a significant role in the interaction effect as the U-shaped curve observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e remains consistent across all levels of DFII. However, it is more evident at lower levels of DFII.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003cp\u003eAs public expenditure can be allocated towards various directions and utilized in projects that may happen to be either eco-friendly or eco-hostile (and this explains the sophisticated pattern in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), more information on the allocation and management of the fund is needed before arriving at a solid conclusion about the impact of total government expenditure on green transition.\u003c/p\u003e\u003cp\u003eRegarding the specific amount of government expenditure on science and technology development, we believe that a response lag helps explain the initial deficiency in GTFP, despite budget growth in this direction. Research and innovation take time so a period between the time the fiscal policy is implemented and the time the policy impact is felt would commonly exist.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\u003ch2\u003e5.2.5 Foreign influences\u003c/h2\u003e\u003cp\u003eLastly, we examine the potential impact of foreign sectors on the domestic economy\u0026rsquo;s evolution in terms of green efficiency. The annual actual use of foreign capital as a percentage of GRP is used to depict the influence from abroad. From Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, one could still acknowledge a quite noticeable \u0026ldquo;convex concave\u0026rdquo; pattern, particularly in those economies that are relatively underutilizing foreign capital. There exists a hump-shaped curve when examining the correlation between foreign capital and GTFP at a given level of DFII, which is found to be more right-skewed when DFII stays low.\u003c/p\u003e\u003cp\u003eWhilst the introduction of foreign capital may be beneficial in terms of knowledge and expertise transfer, an overutilization of foreign capital may put a strain on the domestic market and reduce innovation incentives. Moreover, the pollution-haven-seeking behavior of some highly polluting foreign firms is anticipated to hinder the sustainable growth of the targeted investment zones. These drawbacks would be more prominently seen in marginalized areas, considering their immature market structure and weak regulations on inbound investments, which justifies the more noticeable right-skewed hump-shaped curve, particularly when the value of DFII stays low.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSource: authors' calculation.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"6. Model Accuracy","content":"\u003cp\u003eTo evaluate the accuracy of the models, we computed the mean squared error (MSE) for both the traditional linear regression method (LRM) and our RAB approach. The findings reveal a considerable decrease in error when using the machine learning technique. Specifically, employing a self-organizing map (SOM) to identify the optimal model for running the artificial neural network (ANN), which maximizes MSE improvement, requires balancing the number of data observations per model with the total number of models to promote effective competitive learning (Cheong et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). After performing several thousand trial-and-error runs, we selected four models for implementation within the ANN framework. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the MSE improvements achieved with the RAB approach compared to the traditional linear regression model.\u003c/p\u003e\u003cp\u003eAmong these models, Model 4 demonstrated the most substantial reduction in MSE with the RAB approach. We also derived the ANN functions for the selected variables in each model and integrated them into combined LRM and ANN models to reanalyze the data. The results in the \u0026ldquo;Overall\u0026rdquo; row indicate an overall MSE reduction of 8.26%. In conclusion, our SOM-ANN framework consistently demonstrates a significant improvement in capturing the empirical relationships among the relevant variables, as evidenced by the reductions in MSE across models.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of MSE between LRM and ANN method\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLRM\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eANN\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOverall\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001943\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001783\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001381\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001364\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001498\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel 3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.002334\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.002091\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel 4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001211\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000889\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"7. Conclusion","content":"\u003cp\u003eWe identify a non-linear relationship between GTFP and its level of inclusion in digital finance through the lens of the powerful machine learning techniques. Heterogeneous impacts from digital financial inclusion (DFI) on GTFP are found to prevail across different stages of the economy\u0026rsquo;s development in DFI.\u003c/p\u003e\u003cp\u003eWhen an economy is still in its infancy of DFI, GTFP diminishes slightly against a greater degree of involvement in DFI. At this stage, the value of the Digital Financial Inclusion Index (DFII) remains under 75. GTFP becomes positively associated with DFII thereafter, as the latter continues to rise, and the mushrooming occurs when the economy is moderately mature in DFI (the value of DFII ranges from 150 to 200). The upsurge in GTFP slows down though when development of DFI is close to completion (value of DFII surpasses 225).\u003c/p\u003e\u003cp\u003eThese discrepancies in the interplay between DFI and GTFP across different phases of DFI development should be carefully considered when designing policy interventions aimed at promoting sustainable growth. Building up Infrastructure and improving digital literacy, encouraging innovation, and regulating the market together with reallocating resources for practical purposes are core issues that should take precedence respectively during the initial, moderate, and mature stages of DFI development.\u003c/p\u003e\u003cp\u003eWe also point out that urbanization, industrialization, and industrial upgrading in general promote green initiatives, particularly when the economy has not yet entered an advanced stage of DFI. Policymakers may leverage the complementarity between each of the three aforementioned drivers and DFI in facilitating sustainable development.\u003c/p\u003e\u003cp\u003eThe relationships between human capital, public expenditure, and the economy\u0026rsquo;s green efficiency are complex, as a wide range of context-specific factors collectively shape them. Nevertheless, implementing energy-saving measures in educational institutions or direct public expenditure on human capital and green projects is believed to help bolster green efficiency.\u003c/p\u003e\u003cp\u003eAn \u0026ldquo;inverted U-shaped\u0026rdquo; or a \u0026ldquo;U-shaped\u0026rdquo; relationship is observed, respectively, when it comes to the correlation between GTFP and foreign influences or GTFP and the government\u0026rsquo;s expenditure on science and technology development. Local governors should propose stringent regulations on inbound investment to ensure that it is environmentally friendly and market-friendly, and that they continue to expand the budget for science and technology development in marginalized areas that are currently lagging in DFI.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eN.M: Conceptualization, Writing- Original draft, Data curation, Visualization, preparation, Writing- Reviewing and Editing; T.C:Methodology, Writing- Original draft, Visualization, preparation, Writing- Reviewing and Editing; S.L: Writing- Original draft.\u003c/p\u003e\u003ch2\u003eAcknowledgements:\u003c/h2\u003e\u003cp\u003eThis work was supported by the Philosophy and Social Science Planning Projects in Hainan Province (HNSK(ZC)23\u0026ndash;155), Hainan College of Economics and Business (hnjmk2021301), Hainan Province Education Teaching Reform Research and Scientific Research Projects (Hnjgwt2025-7).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData will be made available on request.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003eBukht, R and Heeks, R. 2018. 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IEEE, 390-393.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Green total factor productivity (GTFP), Digital financial inclusion (DFI), Artificial neural network (ANN), China","lastPublishedDoi":"10.21203/rs.3.rs-8102488/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8102488/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDigital financial inclusion (DFI) is of extraordinary significance for green total factor productivity (GTFP). To estimate the impact on the efficiency of the green economy through digital financial inclusion, this paper analyzes and develops an innovative approach: the regression with artificial neural network (ANN) and bootstrapping (RAB) method. This study is the first to employ machine learning methods in examining the correlation between digital financial inclusion and GTFP. Our study makes a vital contribution by unveiling the potential non-linear relationship between the two variables, using the ANN model complemented by advanced machine learning techniques. We find that how inclusion in digital finance would impact an economy\u0026rsquo;s sustainable development varies, depending on the economy\u0026rsquo;s current intensity of involvement in DFI. Explore the combined effect of DFI and some other driving factors on GTFP. Eight variables are selected, encompassing aspects such as demographic change, industrial structure, human capital, technological development, and foreign influences. The results reveal that urbanization, industrialization, and industrial upgrading can promote green initiatives, particularly when the economy is still in its early stages of development. The relationships between human capital, public expenditure, and the GEE are complex, as a wide range of context-specific factors collectively shape them. An \u0026ldquo;inverted U-shaped\u0026rdquo; or a \u0026ldquo;U-shaped\u0026rdquo; relationship is observed, respectively, when it comes to the correlation between GTFP and foreign influences or GTFP and the government\u0026rsquo;s expenditure on science and technology development.\u003c/p\u003e","manuscriptTitle":"From Fintech to Eco-Tech: The Catalytic Role of Digital Inclusion in China's Green Productivity Surge","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-01 06:47:37","doi":"10.21203/rs.3.rs-8102488/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"12911c31-d3e8-487d-af13-63838f76bb0d","owner":[],"postedDate":"December 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":58798385,"name":"Business and commerce/Economics"},{"id":58798386,"name":"Social science/Economics"},{"id":58798387,"name":"Earth and environmental sciences/Environmental social sciences"},{"id":58798388,"name":"Business and commerce/Finance"},{"id":58798389,"name":"Social science/Finance"}],"tags":[],"updatedAt":"2026-01-11T06:38:48+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-01 06:47:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8102488","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8102488","identity":"rs-8102488","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}