Non-Linear Impacts and Spatial Spillover of Digital Finance on Green Total Factor Productivity: An Empirical Study of Smart Cities in China

Abstract

Smart cities are important digital economy vehicles that can fully exploit the green attributes and spatial penetration of digital finance. Using panel data for 100 cities selected as pilot smart cities in China from 2011 to 2019, this paper applies a spatial econometric model to analyze the non-linear impacts of digital finance on GTFP and its spatial spillovers. Furthermore, it utilizes mediation models to study their transmission mechanisms. The results show that digital finance first inhibits and then promotes GTFP, with spatial spillovers in four dimensions: geography, information, technology, and human capital. Its mediating mechanisms are innovation effects, structural effects, and scale effects. The statistical significance of the U-shaped relationship is regionally heterogeneous, according to different levels of human capital, informatization, urbanization, and financial marketization. Based on digital finance’s U-shaped and heterogeneous impacts on GTFP, policy recommendations are to adopt differentiated development strategies according to specific levels of digital finance and underlying conditions in smart cities. Stimulating the innovation and structural effects and suppressing the scale effects will help digital finance breakthrough inflection points, and will positively promote GTFP. It is also necessary to encourage inter-regional cooperation among smart cities to fully release spatial spillover dividends through technology sharing, information transfer, and talent exchange to promote the linked improvement of GTFP.

1. Introduction

China has made notable progress in its economic development since the “reform and opening up” in 1978. However, trade-offs among environmental pollution, energy consumption, and economic growth have become increasingly acute. Large amounts of energy consumption are accrued during industrialization and urbanization, thereby increasing environmental pressures [1]. Therefore, urban development must change from a high energy-consumption model to a low-carbon pattern. Green development pursues the win-win goals of economic and ecological benefits, making it more advantageous than traditional development patterns [2]. As an essential indicator of green growth, green total factor productivity (GTFP) considers both factor inputs and resource constraints, which can effectively reflect the sustainable economic development of a region. Accordingly, the focus on urban economic development should shift from the traditional total factor productivity to GTFP.

Digital finance is a new financial form manifested in the infusion of digital technology into traditional finance. Its natural green attributes play an essential role in enhancing GTFP. Firstly, digital finance facilitates an increase in expected outputs. Relying on digital and information technology, digital finance can better combine data elements and financial elements, break through regional and time constraints, accelerate the profit-oriented flow of various factors across regional boundaries [3], and improve resource allocation efficiency. Secondly, digital finance enables reductions in undesired outputs. It can reduce the asymmetry of information between investors and financiers to achieve efficient capital-matching, and reduce the investment risk of green projects. The penetration of big data, the internet, and artificial intelligence-based technologies can also facilitate the diffusion of knowledge, and improve energy use efficiency. Digital finance also takes financial transactions such as credit, payment, and investment online, reducing the resource consumption associated with physical financial activities.

However, when digital finance development is low, GTFP may be inhibited. Digital finance can exacerbate resource mismatches through the digital divide. Firms also use digital finance for short-term speculation and arbitrage in virtual economy industries. These phenomena can be mitigated by improved digital infrastructure and coordination between digital technology and financial services [4,5]. In addition, the initial growth effects of digital finance have led to large amounts of pollutant emissions, which can be alleviated by enhancing energy-saving technologies [6]. Moreover, the positive environmental impacts of digital finance depend on specific digital infrastructure, and lower levels of digitization inhibit its emission-reducing effects [7]. Therefore, digital finance may have a U-shaped effect on GTFP.

In addition, digital finance has spillover effects. Digital finance links material, capital, talent, technology and other resources through data flows, and breaks through physical space limitations to achieve financial services across borders, thereby offering a wider scope and stronger spatial penetration than traditional finance. Furthermore, digital finance can accelerate the spatial spillover of explicit knowledge through network effects, expand the spillover channels of tacit knowledge through the movement of labor [8], and improve the productivity of neighboring regions. Meanwhile, based on the imitation effect of environmental policies in neighboring cities and the comparative effect of urban development, digital finance can also affect the environment of surrounding cities [2].

From the above analysis, we can infer that non-linearity and spatial spillover are critical features when analyzing digital finance’s impact on GTFP. The existing literature has studied the non-linear effects of digital finance on total factor productivity and environmental quality [4,6,7,9,10,11,12], as well as the spatial spillover mentioned in some papers [2,3,6,8,13]. However, little attention has been paid to the non-linear effects of digital finance on GTFP under spatial spillovers. Furthermore, existing studies mainly focus on province, industry, and city levels, while the investigation of smart cities is neglected. Smart cities integrate urbanization with information technology and act as an important vehicle for digital economic operation. The green attributes of digital finance can be embodied more effectively in the operation of smart cities. Smart cities can make full use of the platform-based and shared features of digital information technology to reduce waste of resources and energy consumption, and thereby establish a new model for green urban development. On the other hand, smart cities can amplify the spillover of digital finance. They are all-around sensing cities built upon modern information technology, with a variety of characteristics such as high intelligence, interconnection, integration, exchange and sharing [14]. Spatial interactions between cities occur due to geographical adjacency, exchanging and sharing of talents, technology and information. Therefore, smart cities will more effectively utilize digital finance’s green attributes and spatial penetration, thus giving full play to its role in promoting GTFP.

Based on the above analysis, some questions deserve to be explored in depth. What is the specific manifestation of the U-shaped impact of digital finance on GTFP in smart cities? Are there spillover effects? Through which channels do such non-linear impacts operate? Does the regional heterogeneity of smart cities result in differences in non-linear effects? To answer these questions, this paper constructs spatial econometric models based on panel data from 100 cities selected as pilot smart cities in China, exploring the non-linear impacts of digital finance on GTFP, and its mechanism and spatial effects. It is important to study this issue to fully exploit digital finance’s role in promoting sustainable urban green development.

Our contributions are as follows. Firstly, the analysis of smart city construction, digital finance and GTFP is integrated into a unified analytical framework, which enriches the related literature. Secondly, the mechanism of non-linear effects is studied from three perspectives—innovation effects, structural effects, and scale effects—providing a theoretical framework for analyzing the double-edged impact of digital finance on GTFP. Thirdly, spillover effects are analyzed in four dimensions—geographical distance, informatization level, technological innovation, and human capital—taking into account the interconnection of smart cities and the mobile characteristics of digital finance. Fourth, the heterogeneity of the non-linear impact is analyzed by considering the different endowment characteristics of smart cities. The research provides a policy basis for digital finance to break through inflection points and realize its role in promoting GTFP under spillover effects.

2. Literature Review and Hypothesis Development

2.1. The Impact of Digital Finance on GTFP

Many studies focus on the linear relationship of digital finance and GTFP. At the county level, digital finance promotes GTFP through the intermediary effect of industrial structure [15]. At the urban level, digital finance significantly improves the GTFP of cities. The effects of cities in western China are stronger than those in eastern and central regions [16]. Digital finance has improved GTFP by alleviating capital and labor mismatching, and such enhancement is more evident in the eastern region and key cities [17]. In general, digital finance can promote the GTFP by encouraging technological innovation, optimizing industrial structure, and alleviating resource mismatches [18]. At the provincial level, digital finance improves GTFP mainly through the dimensions of coverage, usage and digitization [19]. Its impact is mainly realized through technological innovation and regional entrepreneurship [20]. At the industry level, digital finance positively promotes the GTFP of agricultural industries by improving their technical efficiency [21] and optimizing the agricultural industrial structure [22].

There is little discussion of digital finance’s non-linear impact on GTFP in the existing literature, especially with regard to smart cities. Digital finance has multifaceted effects on economic efficiency and the environment, and these forces jointly determine its overall impact [5]. In fact, digital finance enhances GTFP through increasing desired outputs and reducing undesired outputs (i.e., polluting emissions). This can be achieved by improving both resource allocation efficiency and the environmental quality; both of these are closely related to the development of digital finance, and have “U”-shaped characteristics.

First, digital finance has a U-shaped impact on resource allocation efficiency. A Pareto-optimal state of resource allocation is realized in the process of the free flow of factors under the conditions of a market with sufficient information and perfect competition. Traditional financial transaction costs are relatively high, and incomplete information and imperfect markets lead to resource mismatching. Digital finance relies on information technology to collect and intelligently analyze different types of information from enterprises, reducing information collection costs and effectively identifying innovative entities, correcting capital and labor distortions, and optimizing resource allocation [23]. Smart cities use digitization as a means to achieve the intelligent operation and management of cities. Smart production empowered by digitization can effectively integrate data resources based on production and transactions, solve the problem of information asymmetry, reduce resource waste, and provide basic guarantees for green development [24]. Therefore, digital finance in smart cities can effectively combine digital and financial factors, breaking regional and temporal restrictions. Then, digital finance can promote the profit-oriented flow of various factors across regional boundaries in a reticulated space [3], thereby correcting resource mismatches and improving desired output.

However, there are some prerequisites for the implementation of the resource allocation function. It is only possible for digital finance to fully play its role in optimizing the allocation of production factors once it has reached a certain level. Much capital flows from banks to digital investment and financing platforms in the initial stage. The idling of funds caused by imperfect digital finance will distort capital allocation in industries and regions [5], thus inhibiting the normal function of resource allocation. In addition, digital finance may exacerbate resource mismatches as a result of the “digital divide”. This phenomenon may be corrected with an increase in coordination between digital technology and financial services [4]. Therefore, digital finance improving GTFP through optimal resource allocation will be a long-term process.

Second, digital finance has a U-shaped impact on the environment. We can illustrate this point in two ways. First, digital technology, which digital finance depends on, is vital for the non-linear impact. Digital finance affects carbon emission through two mechanisms: the industrialization of digital technology and the digitization of traditional industries. This impact follows a non-linear trend [9]. Smart cities use digital technologies to intelligently analyze and manage city operations. Cloud-based big data analysis enables more accurate credit assessment, which reduces the operating costs of social and economic systems that occur due to credit failure [25], and reduces waste of resources in information search processes. Digital technology also helps overcome the “digital island” formed by the difficulty of sharing information, enabling various scenarios and service platforms to cooperate in the sharing of information, again avoiding a waste of resources and duplication of construction [26]. Some new green financial instruments driven by digital finance, such as green remittances, can direct remittances to target green infrastructure projects, combining remittances, sustainable development and capital investment, reducing transaction costs and providing a new path to achieving sustainability goals [27]. However, digitization has some degree of “green blindness,” leading to increased carbon emissions and other negative environmental externalities. In the early stages of digitization, the penetration of digital technology can consume large amounts of resources, resulting in environmental problems [28].

Further, digital finance’s influences on environmental performance relies on specific types of infrastructure; this reliance induces non-linear effects. The positive impact of digital finance on environmental performance relies on specific infrastructure, and is unlikely to positively encourage energy saving and emissions reduction if the level of digitization is low [7]. When digital finance develops to a high level, carbon dioxide emissions are expected to decrease due to reduced pollution control costs and improved infrastructure. When this happens, digital finance will fully play its role in promoting GTFP. Therefore, we propose the following:

Hypothesis 1 (H1). 

Digital finance initially inhibits then promotes GTFP in smart cities, showing a “U”-shaped relationship.

2.2. Spatial Spillovers of Digital Finance on GTFP

Plentiful literature has focused on the spillovers of digital finance on total factor productivity, economic growth, and environmental pollution. Technical innovation drives total factor productivity through two channels. One is based on the network effect, which accelerates the spatial spillover of explicit knowledge; the other is based on the mobility effect, which accelerates the spatial spillover of tacit knowledge [8]. Digital finance also drives the spatial linkage of total factor productivity, thus generating a strong spatial effect on total factor productivity in neighboring provinces, and tends to increase year by year [3]. Additionally, digital finance integrates digital and internet technologies, breaking the spatial constraints of financial services and promoting local economic development. Still, due to the siphoning effect, it has negative spillovers on economic growth in adjacent areas [29]. In terms of environmental effects, digital finance reduces carbon emissions in local cities, but improves carbon emissions in adjacent cities [2]. A similar relationship has been observed between digital finance and haze pollution, in that digital finance alleviates local haze pollution but aggravates haze pollution in adjacent areas [13]. However, digital finance positively impacts environmental total factor productivity in surrounding areas. The reason for this is that digital finance helps financial resources to absorb into city centers, and also concentrates environmental pollution within them, thus relieving environmental pressure on surrounding cities [6]. Therefore, we can infer that digital finance also has spatial effects on GTFP, but this has not received much attention. Such spatial spillovers are based upon several aspects.

Firstly, there is spatial spillover based on the geographical dimension. Relying on internet and information technology, digital finance weakens spatial information isolation caused by geographical factors, reduces market transaction barriers, and facilitates the flow of talent, technology and knowledge. Smart cities are instrumented, interconnected, and intelligent, which integrates data sources from physical and virtual sensors into enterprise computing platforms and shares such information among various city services [30]. This enables regions to enhance linkages in the process of specialization and spatial cooperation. Information management in smart cities and the networking characteristics of digital finance strengthen the spatial correlations of smart cities at the geographical level.

Secondly, spatial spillover is based on the information and technology dimension. The intangibility of digital finance services breaks through the temporal and spatial limitations of physical outlets, significantly reduces transaction and information costs, and promotes information flow and knowledge exchange. This allows enterprises to quickly obtain innovative resources, and accelerates knowledge spillovers by improving innovation cooperation [31], thereby enabling green technology innovation entities to efficiently share information and technology with others. Smart cities integrate urban systems through data-driven and intelligent operation, shorten the spatial distance in traditional transactions, and effectively promote the exchange and dissemination of knowledge. These intelligent and digital operations improve green technology innovation and expand its spillover scope. As a result, local digital finance development drives the growth of GTFP in surrounding cities with similar information and technology levels.

Thirdly, spatial spillovers occur through a human capital dimension. Digital finance has a strong spatial agglomeration characteristic, which gives practitioners more opportunities to realize human capital appreciation through mutual communication, cooperation, and learning [32]. The rapid development of smart cities is attributable to the contribution of smart talent. Smart cities with a higher concentration of digital finance also have higher levels of human capital. These cities promote spatial spillover of human capital through the exchange of talent. Therefore, the agglomeration character of digital finance and the talent-driven mode in smart cities are conducive to the appreciation and spillover of human capital. Therefore, we propose:

Hypothesis 2 (H2). 

Digital finance has spillover effects on GTFP, which exist in the dimensions of geography, information, technology, and human capital.

2.3. The Mechanism of the “U”-Shaped Impact

Existing studies have analyzed the mediating channels through which digital finance affects the environment, including technological innovation, structural optimization, and scale expansion (yield effects). The first two are positive effects, while the latter is an inhibiting effect. Non-linear effects are determined by a combination of the positive and negative effects. The impact of digital finance on carbon emissions can be divided into a yield-increasing effect and an energy-saving effect. The former is the expanded coverage of digital finance, which expands output and increases carbon emissions. By contrast, the latter is the deeper usage and digitalization of digital finance, which promotes innovation and a reduction in carbon emissions [33]. Digital finance also increases household carbon emissions by expanding the scale of consumption, but could reduce household carbon emissions by promoting the structural effects of green consumption [34]. Furthermore, digital finance reduces polluting emissions by helping SMEs to accelerate technology innovation and upgrade industrial structure. However, digital finance also promotes polluting emissions by strengthening extensive growth and expanding the scale of consumption [35].

Some studies also argue that the strength of the above effects varies with digital finance development, as the scale effect works at the initial stage and the technology effect works later, thus creating a non-linear impact. In the initial stage, scale effects are greater than technology effects, with the result that digital finance increases the carbon intensity. However, if technology effects exceed scale effects in the mature stage, digital finance will reduce carbon emissions [12]. Additionally, when digital finance develops at a low level, its main effect on the environment is promoting economic growth. The emission of large amounts of pollutants in this process inhibits increases in environmental quality. With improvements in digital finance, however, clean technologies’ enhancement could weaken the inhibitory effect [6].

Three mediating effects tested in the existing literature are instructive for this paper’s analysis of the mechanism of the non-linear effects of digital finance on GTFP. However, the impact of digital finance on the intermediary channel, or the impact of the intermediary channel on the environment, is mainly linear in the related literature. In contrast, we analyze a non-linear intermediary effect. That is to say, digital finance affects the intermediate channel non-linearly, or the intermediate channel affects GTFP non-linearly, thus forming the basis for the non-linear analysis carried out below.

2.3.1. Innovation Effect

The innovation effect means improving GTFP through encouraging green technology innovation. Digital finance effectively breaks through geographical restrictions with the spatial-temporal advantages of digital technology. Therefore, it is conducive to easing financing constraints as well as reducing the costs of corporate innovation, stimulating innovation vigor and improving regional innovation capacity [36]. Furthermore, the wide application of information and communication technology in smart cities allows digital finance to expand its service to “long-tail” groups and to promote green technology innovation in enterprises in remote areas. Digital finance can evaluate the credit of economic agents based on their behavioral data, reduce transaction costs, and enable investors to screen valuable investment projects more quickly. It will also promote investment in green innovation projects by enhancing liquidity. For example, the carbon finance system uses digital finance to participate in carbon trading activities, which enhances carbon trading liquidity, reduces investment costs, allows more capital to flow to low-carbon projects [37], and enhances green innovation.

Green technology innovation has a U-shaped impact on GTFP. When green technology innovation is low, the rebound effect of technology innovation is more prominent. Efficiency promotion brought about by technology innovation expands the scale of production, increasing demand for energy services and producing more polluting emissions [38]. As shown by Wang (2022), the negative correlation between low-level technological innovation and haze pollution is unremarkable. In contrast, high-level technological innovation significantly reduced pollutant emissions [13]. Furthermore, a lack of capital investment in R&D for green projects in their initial stages also leads some enterprises to choose low-cost and -quality patents; this results in a “patent bubble” phenomenon, wherein the number of patents proliferates but the quality does not improve simultaneously [39,40]. When the scale of digital finance is small, support for green technology innovation is limited, and negative effects, such as rebound effects and patent bubbles, will be more obvious. With the continuous development of digital finance, the substitution effect of green technology innovation will offset the rebound effect. Further easing of financial constraints makes enterprises attach importance to their choice of quality-based green technology, and thus the promotion effect of green technology on GTFP will gradually manifest. From the above analysis, we infer that digital finance can promote green technological innovation, which needs to reach a certain level before it can positively affect GTFP, described as the innovation effect in Figure 1.

2.3.2. Structural Effect

The structural effect describes how digital finance can help to enhance GTFP through upgrading industrial structures. The basic features of digital information technology are high permeability, high additionality, decreasing marginal cost, and external economy [41]. The rapid development of digital technology in smart cities allows digital finance to shift from being factor-driven to being innovation-driven in upgrading the industrial structure [28]. Such a transfer encourages capital flow to new industries represented by new energy and materials, and old industries that consume a lot of energy are therefore gradually eliminated. The intelligent operation and management of smart cities further catalyze financial support for digital finance in the ICT industry, the “demonstration effect” of which helps to reduce structural distortions in other industries [42], and contribute to upgrading the industrial structure.

Industrial structure upgrading has a “U”-shaped impact on GTFP. The contribution of digital finance to GTFP may not be evident during the initial phase of industrial digitization and upgrading. The development of smart cities needs to rely on information technology industries such as artificial intelligence, cloud computing, the Internet of Things, etc. Information industries and data centers’ high energy consumption characteristics will increase carbon emissions [43], especially when energy structures and efficiency still need to be technically improved. With the further upgrading of industrial structure, improved energy efficiency can improve GTFP through reducing undesirable output. Carbon emissions can be reduced directly or through improvements in energy efficiency [44,45]. Therefore, digital finance contributes to upgrading industrial structure, while industrial structure upgrading will have a U-shaped impact on GTFP, described as the structure effect in Figure 1. We propose the following:

Hypothesis 3 (H3). 

Digital finance promotes green technology innovation and industrial structure upgrading in smart cities, both of which have a U-shaped effect on GTFP.

2.3.3. Scale Effect

The scale effect implies that a greater extent of digital finance may promote carbon emissions by scaling up investments, thus reducing GTFP by increasing undesirable outputs. Digital finance has an inverted “U”-shaped effect on the scale of investment. Initially, it provides flexible and diversified financial channels, alleviates corporate financial constraints, broadens credit sources, and promotes corporate investment by improving information transparency. In the long run, the green attributes of digital finance effectively stimulate enterprises’ awareness of environmental protection, driving R&D investment and reducing the scale of non-efficient investment [46]. At the same time, increases in green technology investment reduce the relative proportion of productive investment, thus reducing the negative inhibitory impact of the scale effect. However, the expansion of investment will improve energy consumption and pollution via emissions, which inhibits the enhancement of GTFP [6,12,33,35]. This analysis shows that digital finance has an inverted U-shaped effect on the scale of investment, and that the scale of investment has a suppressive impact on GTFP, described the as scale effect in Figure 1. We propose:

Hypothesis 4 (H4). 

Digital finance has an inverted “U” effect on the scale of investment in smart cities, and such a scale effect will negatively inhibit GTFP.

3. Methodology and Data

3.1. Model Construction

3.1.1. Spatial Econometric Method

The basic assumption of spatial econometrics is spatial dependence, which is determined by the concept of relative space or location [47]. In this case, traditional econometric models suffer from estimation bias without considering the spatial correlation of economic variables [48,49], while spatial econometric models overcome such problems. As mentioned above, digital finance has spillovers on GTFP, so spatial econometric models are appropriate for our research. According to various types of spatial shock, the spatial econometric models include the spatial error model (SEM) and the spatial autoregressive model (SAR). The former examines whether unobserved random shocks are spatially correlated, and the latter examines whether the actions of adjacent regions have impacts on other regions in the wider system [50]. In the spatial analysis process, a spatial correlation test is conducted first. Then, SAR and SEM models are contructed, selecting the optimal model according to LM tests, as shown in the following steps.

(1)

Spatial Autocorrelation Test

A correlation analysis for general data can be conducted using the correlation coefficient method [51]. In contrast, spatially correlated data require the introduction of spatial auto-correlation coefficients to study their spatial distribution characteristics. The global Moran’s I index is commonly used in spatial auto-correlation tests, as shown in Equation (1):

$$I=\frac{\sum _{i=1}^n\sum _{j=1}^n{W}_{ij}\left(x_i-\overline{x}\right)\left(x_j-\overline{x}\right)}{S^2\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}}$$

(1)

In the formula, $S^2=\frac{\sum _{i=1}^n(x_i-\overline{x})}{n}$ is the sample variance, $\overline{x}=\frac{\sum _{i=1}^n{x}_i}{n}$; W_ij is the spatial weight matrix, and x_i and x_j are the observations. Moran’s I ranges from −1 to 1.

$$W_g=\left\{\begin{array}{c}1/d_{ij},\hspace{1em}i\ne j\\ \hspace{1em}0,\hspace{1em}i=j\end{array}\right.$$

(2)

$$W_{t,h,i}=\left\{\begin{array}{c}1/|\overline{V_i}-\overline{V_j}|,i\ne j\\ \hspace{1em}0,\hspace{1em} i=j\end{array}\right.$$

(3)

In this paper, we calculate the spatial weight matrices using four distances. Referring to the calculation of spatial weights by Lin et al. [50], the geography weight matrix W_g is expressed as the reciprocal of the distance between the geographical centers of cities, as shown in Equation (2). The information weight matrix W_i, technology weight matrix W_t, and human capital weight matrix W_h are expressed as reciprocals of the informatization distance, the technology distance, and the human capital distance, respectively, as shown in Equation (3). In the formula, V_i(V_j) denotes the number of internet broadband access households when W_i is calculated, the number of green patent applications per capita when W_t is calculated, and the proportion of people highly educated when W_h is calculated.

(2)

Spatial Econometric Model

The SAR model is shown in Equation (4). GTFP_it and DIFI_it represent the green total factor productivity and digital finance, respectively. The coefficient ρ is the spatial lag coefficient, which measures the impact of GTFP in adjacent regions on local GTFP. W_ij is the spatial weight matrix, X_it represents the control variable, and ε_it is the random disturbance term.

$${GTFP}_{it}=\alpha +\rho {\sum }_{j=1}^N{w}_{ij}{GTFP}_{it}+{\beta }_1{DIFI}_{it}+{\beta }_2{DIFI}_{it}^2+\theta X_{it}+{\epsilon }_{it}$$

(4)

The SEM model is shown as Equations (5) to (6). The coefficient λ is the spatial error coefficient, reflecting the effects of the random disturbance term of GTFP of adjacent regions on local GTFP.

$${GTFP}_{it}=\alpha +{\beta }_1{DIFI}_{it}+{\beta }_2{DIFI}_{it}^2+\theta X_{it}+{\epsilon }_{it}$$

(5)

$${\epsilon }_{it}=\lambda {\sum }_{j=1}^N{w}_{ij}{\epsilon }_{it}+{\sigma }_{it}$$

(6)

3.1.2. Intermediary Effects Model

To further explore how digital finance (DIFI) affects GTFP, we need to investigate its transmission mechanism. The intermediary regression model is a proper method. A basic mediate test contains three steps [52,53,54]. We need to construct non-linear mediating tests to investigate the innovation effects, structure effects, and scale effects. Referring to the non-liner mediation effects practice of Lyu et al. [55], the process of our mediating tests is as follows.

$${GTFP}_{it}={\alpha }_0+{\alpha }_1\times {DIFI}_{it}+{\alpha }_2\times {{DIFI}^2}_{it}+{\alpha }_3\times {Control}_{it}+{\epsilon }_{it}$$

(7)

$${MED}_{it}={\beta }_0+{\beta }_1\times {DIFI}_{it}+{\beta }_2\times {Control}_{it}+{\delta }_{it}$$

(8)

$${GTFP}_{it}={\gamma }_0+{\gamma }_1\times {DIFI}_{it}+{\gamma }_2\times {{DIFI}^2}_{it}+{\gamma }_3\times {MED}_{it}+{\gamma }_4\times {{MED}^2}_{it}+{\gamma }_5\times {Control}_{it}+{\mu }_{it}$$

(9)

$${MED}_{it}={\rho }_0+{\rho }_1\times {DIFI}_{it}+{\rho }_2\times {{DIFI}^2}_{it}+{\rho }_3\times {Control}_{it}+{\delta }_{it}$$

(10)

$${GTFP}_{it}={\theta }_0+{\theta }_1\times {DIFI}_{it}+{\theta }_2\times {{DIFI}^2}_{it}+{\theta }_3\times {MED}_{it}+{\theta }_4\times {Control}_{it}+{\mu }_{it}$$

(11)

Firstly, we test the innovation and structure effects. According to the aforementioned mechanism, digital finance positively improves technology innovation or upgrades industrial structure, both of which have “U”-shaped effects on GTFP, as shown by the top of Figure 2. In the first step, we construct the main effects model shown in Equation (7), which describes the non-linear impact of DIFI on GTFP. The second step tests the linear effects of DIFI on MED. Med is regarded as a dependent variable, and DIFI is used to regress Med, as shown in Equations (8). The third step analyzes the non-linear impact of DIFI on GTFP after controlling the non-linear effects of MED to DIFI. This time MED and MED² are added to Equation (7) as control variables for regression, as shown in Equation (9). If β₁ and γ₃ are remarkable, the mediating effect is obvious. If α₂, β₁, γ₂, and γ₄ are significant, a nonlinear mediating effect exists.

Secondly, we test the scale effect. In our theoretical analysis, digital finance has an inverted “U”-shaped effect on investment scale, while investment scale has a negative effect on GTFP, as shown by the bottom of Figure 2. The first step is the same as the previous. The second step tests the non-linear effects of DIFI on MED. Med is regarded as a dependent variable; DIFI and its square term DIFI² are used to regress Med to test the non-linear effects of DIFI to MED, as shown in Equation (10). The third step analyzes the non-linear impact of DIFI on GTFP after controlling MED, as shown in Equation (11). If ρ₁ and θ₃ are significant simultaneously, the mediating effect is remarkable. A non-linear mediating effect exists if α₂, ρ₂, and θ₂ are significant.

3.2. Variable Selection

3.2.1. Explained Variable

The explanatory variable is GTFP, which is calculated using the SBM directional distance function based on non-desired output [56]. The calculation of traditional all-factor productivity generally adopts the data development analysis method (DEA). However, this method measures efficiency from a radial approach and lacks consideration of non-expected output, so it can not ensure the accuracy of efficiency. Based on the DEA method, the SBM method applies non-radial treatment of the unexpected output variables, considering the relaxation of input–output, as shown in the Formulas (12) and (13). Among them, m is the number of input indicators, and q₁ and q₂ are the number of desired output and non-desired output indicators, respectively. Suppose there are n evaluation units (DUM), the input, desired output, and non-desired output vectors for each evaluation unit are denoted $asxϵR^m$,$y^gϵR^{q_1}$, $y^uϵR^{q_2}$. We define $X=[x_1,x_2,\dots ,x_n]ϵR^{m\times n}$, $Y^g=[y_1^g,y_2^g,\dots ,y_n^g]ϵR^{q_1\times n}$, $Y^u=[y_1^u,y_2^u,\dots ,y_n^u]ϵR^{q_2\times n}$, s⁻, s^g, s^u as slack variables for input, desired output, and non-desired output. λ is a vector of linear combination coefficients of DMU. The results are calculated between [0,1] and show a tendency to decrease with slack. When the results are less than 1, the presence of efficiency losses is indicated.

$$\rho =\mathit{min}\left[\frac{1-\frac{1}{m}\sum _{i=1}^m\frac{s_i^{-}}{x_{i0}}}{1+\frac{1}{q_1+q_2}\left(\sum _{i=1}^{q_1}\frac{s_t^g}{y_{t0}^g}+\sum _{i=1}^{q_2}\frac{s_t^u}{y_{t0}^u}\right)}\right]$$

(12)

$$s.t.x_0=X\lambda +s^{-}{y}_0^g=y^g\lambda -s^g{y}_0^u=y^u\lambda +s^u\lambda ,s^{-},s^g,s^u\ge 0$$

(13)

The input factors include capital stock (unit: 10,000 yuan), labor (unit: ten thousand people), energy (unit: ten thousand kwh), and technology expenditure (unit: 10,000 yuan). Capital stock is estimated using the method of Zhang et al. [57]. Labor input is expressed as the number of employees in each city. Energy input is described by society-wide electricity consumption. Technology is reflected by public expenditure on science and technology. The desired output (Y) is presented by the regional GDP of cities (unit: billion yuan), and undesired outputs (U) include industrial SO₂ emissions (unit: ton), industrial dust emissions (unit: ton), and industrial waste-water emissions (unit: ten thousand tons).

3.2.2. Core Explanatory Variable

Digital finance (DIFI) is derived from the Digital Finance Research Center of Peking University. The index comprehensively summarizes the connotation and characteristics of digital finance, considering horizontal and vertical comparisons of digital development, and reflects the diversified characteristics of digital financial services. It includes the total index and three sub-indices of the breadth of coverage (Cov), depth of use (Use), and level of digitization (Dig). Cov represents the comprehensive coverage of digital finance to users. Use denotes the actual use of digital financial services, which is the total number of digital financial services used by customers. Dig comprehensively considers the convenience, cost, and creditability of digital financial services. The value of DIFI is better reflected through better convenience, lower cost, and higher creditability [58].

3.2.3. Control Variables

Local economic growth (Pgdp) is calculated using the logarithm of GDP per capita (10,000 yuan). Rapid economic development may have a negative impact on the environment; however, with a changing mode of economic growth and the gradual establishment of a resource-saving society [59], economic development will have a positive relationship with GTFP.

Government intervention (Gov) is measured using the ratio of government fiscal expenditure to total local GDP. Government intervention can solve market failure problems, act as a reasonable guide for industrial structure transformation, and eliminate backward production capacities, thus promoting GTFP [60].

The degree of openness (Fdi) is measured using the ratio of foreign direct investment to local GDP. Fdi brings advanced management experience and production technology spillover, contributing to energy savings and emission reduction. However, it can also seize the market shares of local enterprises and inhibit local motivation for technological development [61]. Therefore, the effect of FDI on GTFP is uncertain.

Urbanization (Urban) is measured using the ratio of resident urban employees to the total urban population. The process of urban expansion will increase the emission of pollutants. Thus, Urban is negatively correlated with GTFP [62].

Science expenditure (Science) is expressed as the proportion of local science and technology expenditure to government fiscal expenditure. The support of the government in science and technology helps to meet the financial demand for corporate innovation, and contributes to improving production technology [63]. Science can positively improve GTFP.

Infrastructure (Trans) is calculated using the ratio of highway mileage to the area of a city (km/km²). Transportation investment can significantly improve low-carbon economic growth, which manifests by enhancing both the benefits and efficiency [64]. Therefore, it has a positive relationship with GTFP.

3.2.4. Mediating Variables

The mediating variables include those describing the innovation effect, structural effect, and scale effect. The innovation effect is a green technological innovation (Tech) which is measured using the logarithm of the number of green patents. The structural effect is expressed by the industrial structure (Is), which is the share of the tertiary sector in GDP. The scale effect is denoted by the scale of productive investment (Invest), which is the ratio of the scale of fixed asset investment to GDP.

3.2.5. Heterogeneity Variables

In addition, human capital, the level of informatization, urbanization, and marketization of financial resource allocation all affect the relationship between DIFI and GTFP. We will test heterogeneity based on these groups. Human capital (Human) is presented by the degree of the advanced labor market, which is the ratio of the number of students enrolled in universities to the number of employee in each city [65]. The level of informatization (Inter) is the ratio of households accessing internet, within the city’s population. The marketization of financial resource allocation (Market) is expressed as the proportion of loans to non-state enterprises, which is estimated according to the method of Zhang and Jin [66].

3.3. Data Source and Description

We selected three batches of pilot smart cities (prefecture-level cities) announced successively in January 2013, August 2013, and April 2015, excluding those with incomplete data. Finally, we chose the panel data of 100 pilot smart cities from 2011–2019 as the sample for the study.

Table 1. Variable definitions and summary descriptions.

Variable	Meaning	Obs	Mean	Std.Dev.	Min	Max
GTFP	Green total factor productivity	900	0.55	0.182	0.213	1
DIFI	Digital finance	900	1.662	0.653	0.213	2.959
Cov	Coverage breadth of digital finance	900	1.573	0.633	0.019	2.972
Use	Usage depth of digital finance	900	1.618	0.678	0.125	3.115
Dig	Digitization level of inclusive finance	900	2.024	0.822	0.036	4.379
Pgdp	Local economic growth	900	1.516	0.707	−0.748	3.446
Gov	Government intervention	900	0.203	0.118	0.009	0.675
Fdi	Degree of openness	900	0.016	0.016	0	0.132
Urban	Urbanization	900	0.561	0.149	0.214	1
Science	Degree of science expenditure	900	0.019	0.021	0	0.191
Trans	Infrastructure	900	1.084	0.525	0.078	2.430
Tech	Green technology innovation	900	4.354	1.606	0	8.652
Is	Industrial structure	900	0.411	0.102	0.101	0.741
Invest	Investment scale	900	0.84	0.296	0.249	1.945

details the names, definitions and descriptive characteristics of the main variables. Among them, GTFP figures were obtained from the China City Statistical Yearbook, China Statistical Yearbook, and China Urban Construction Statistical Yearbook. DIFI, Cov, Use, and Dig are from the Peking University Digital Financial Inclusion Index of China (PKU-DFIIC). Tech was obtained from the website of the State Intellectual Property Office. Market is derived from the China Statistical Yearbook, China Compendium of Statistics 1949–2008, Almanac of China’s Finance and Banking, and China Industry Statistical Yearbook. Other variables are from the China City Statistical Yearbook, provincial and municipal statistical yearbooks.

4. Empirical Analysis

4.1. Spatial Autocorrelation Analysis

Table 2. Moran’s I index of digital finance and green total factor productivity.

Year	DIFI (Wg)		DIFI (Wi)		DIFI (Wt)		DIFI (Wh)		GTFP (Wg)
	Moran Index	z-Value	Moran Index	z-Value	Moran Index	z-Value	Moran Index	z-Value	Moran Index	z-Value
2011	0.201 ***	4.213	0.112 ***	2.433	0.345 ***	6.904	0.257 ***	4.548	0.054 *	1.292
2012	0.201 ***	4.207	0.090 **	1.991	0.369 ***	7.356	0.277 ***	4.901	0.078 **	1.783
2013	0.214 ***	4.468	0.090 **	2.003	0.325 ***	6.511	0.284 ***	5.012	0.090 **	2.022
2014	0.199 ***	4.169	0.058 *	1.363	0.332 ***	6.634	0.317 ***	5.575	0.055 *	1.325
2015	0.205 ***	4.290	0.075 **	1.693	0.358 ***	7.159	0.296 ***	5.226	0.105 ***	2.322
2016	0.222 ***	4.625	0.110 ***	2.393	0.375 ***	7.491	0.284 ***	5.017	0.124 ***	2.731
2017	0.245 ***	5.093	0.145 ***	3.093	0.383 ***	7.646	0.302 ***	5.325	0.101 ***	2.313
2018	0.320 ***	6.601	0.167 ***	3.526	0.359 ***	7.185	0.252 ***	4.476	0.103 **	2.300
2019	0.325 ***	6.678	0.167 ***	3.521	0.366 ***	7.310	0.252 ***	4.468	0.096 **	2.134

Note: *, **, *** indicate significant at the 10%, 5%, and 1% levels, respectively.

shows the results of the Moran’s I index for digital finance under the four weight matrices from 2011–2019, all of which are significantly positively correlated. The significance under W_g and W_t is higher than the others. Thus, we chose the two weight matrices with the strongest spatial correlation, W_g and W_t, for benchmark regression, and the other two for robustness tests. Spatial dependence is determined by a notion of relative space [47]. Geographic distance is the most intuitive indicator for determining economic relationships in the study of spatial economics [36]. As mentioned above, the reduction in the geographical distance reduces information asymmetry, thus facilitating the flow of factors between cities and increasing spatial connection. High levels of digital constructions in smart cities facilitate the diffusion of technology, thus increasing spatial dependence on the technological dimension. The Moran’s I indices of GTFP under W_g weight are also significantly positive, and show an overall increasing trend, indicating that GTFP in smart cities has significant spatial clustering characters. Therefore, it is necessary to consider the influence of spatial factors and construct a spatial panel model.

4.2. Spatial Model Selection

LM and robustness tests are used to select spatial models, according to the spatial econometric model selection process [67]. As shown in

Table 3. Results of LM tests.

LM Test	Wg	Wh	Wi	Wt
Moran’s I	12.455 ***	2.968 ***	3.431 ***	2.791 ***
LM Spatial error	146.461 ***	7.730 ***	10.571 ***	6.924 ***
Robust LM Spatial error	10.578 ***	9.721 ***	1.182	3.380 *
LM Spatial lag	136.581 ***	3.714 *	9.394 ***	4.553 **
Robust LM Spatial lag	0.699	5.706 **	0.006	1.009

Note: *, **, *** indicate significant at the 10%, 5%, and 1% levels, respectively.

, the LM test was constructed for selecting the appropriate spatial econometric model. We can see that the results of LM Spatial error and LM Spatial lag are both significant for the W_g weight matrix. Then, it is necessary to calculate the Robust LM-Error and Robust LM-Lag statistics based on the robust Lagrange multiplier test to further determine the more suitable model, i.e., SAR or SEM. We can see that the result of robust LM Spatial error is also significant at the 1% level, while the result of Robust LM Spatial lag is not. Therefore, we choose the spatial error model (SEM). The results for the W_t weight matrix are similar to W_g. LM tests and their robustness tests show that the SEM model outperforms the SAR model.

4.3. Analysis of Spatial Econometric Models

4.3.1. Results of Benchmark Regression

Table 4. Estimation results of SEM models.

	Wg				Wt
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
DIFI	−0.2591 ***				−0.2055 ***
	(0.0448)				(0.0347)
DIFI2	0.0578 ***				0.0414 ***
	(0.0141)				(0.0110)
Cov		−0.3046 ***				−0.2407 ***
		(0.0391)				(0.0315)
Cov2		0.0724 ***				0.0522 ***
		(0.0126)				(0.0103)
Use			−0.1795 ***				−0.1695 ***
			(0.0351)				(0.0321)
Use2			0.0333 ***				0.0306 ***
			(0.0108)				(0.0098)
Dig				−0.0970 ***				−0.0932 ***
				(0.0277)				(0.0259)
Dig2				0.0141 *				0.0135 *
				(0.0077)				(0.0072)
Pgdp	0.1157 ***	0.1204 ***	0.1127 ***	0.1063 ***	0.1219 ***	0.1273 ***	0.1157 ***	0.1100 ***
	(0.0185)	(0.0185)	(0.0184)	(0.0184)	(0.0184)	(0.0185)	(0.0183)	(0.0184)
Gov	0.0132 *	0.0112	0.0180 **	0.0197 **	0.0205 ***	0.0183 **	0.0231 ***	0.0261 ***
	(0.0078)	(0.0076)	(0.0079)	(0.0079)	(0.0077)	(0.0077)	(0.0078)	(0.0077)
Fdi	−1.1293 **	−1.0063 **	−1.2282 ***	−1.2325 ***	−1.0987 **	−0.9514 **	−1.1863 **	−1.1822 **
	(0.4596)	(0.4536)	(0.4652)	(0.4672)	(0.4644)	(0.4612)	(0.4660)	(0.4658)
Urban	−0.2763 ***	−0.2340 ***	−0.2854 ***	−0.3462 ***	−0.3053 ***	−0.2790 ***	−0.2977 ***	−0.3671 ***
	(0.0841)	(0.0840)	(0.0846)	(0.0853)	(0.0841)	(0.0840)	(0.0846)	(0.0853)
Science	0.2809 **	0.2500 **	0.2920 **	0.3271 ***	0.1839	0.1561	0.2068 *	0.2140 *
	(0.1139)	(0.1120)	(0.1169)	(0.1173)	(0.1146)	(0.1135)	(0.1155)	(0.1160)
Trans	−0.0005	0.0048	0.0025	−0.0142	0.0022	0.0039	0.0056	−0.0100
	(0.0217)	(0.0215)	(0.0219)	(0.0220)	(0.0216)	(0.0214)	(0.0218)	(0.0219)
λ	0.3159 ***	0.3560 ***	0.2195 ***	0.2780 ***	0.1556 **	0.1479 **	0.1368 **	0.2002 ***
	(0.0718)	(0.0672)	(0.0659)	(0.0643)	(0.0640)	(0.0627)	(0.0627)	(0.0621)
_cons	0.7843 ***	0.7718 ***	0.7319 ***	0.7338 ***	0.7504 ***	0.7433 ***	0.7224 ***	0.7297 ***
	(0.0539)	(0.0501)	(0.0509)	(0.0516)	(0.0514)	(0.0492)	(0.0501)	(0.0512)
N	900	900	900	900	900	900	900	900
Overall-R2	0.1674	0.1775	0.1592	0.1384	0.1709	0.1813	0.1597	0.1384
Within-R2	0.1605	0.1745	0.1567	0.1253	0.1665	0.1810	0.1579	0.1273
Between-R2	0.1747	0.1850	0.1612	0.1474	0.1744	0.1828	0.1610	0.1460

Note: *, **, *** indicate significant at the 10%, 5%, and 1% levels, respectively. Standard errors are reported in parentheses. Estimated by commands of spatial econometric models [68]. The following tables are the same.

presents spatial regression results under W_g and W_t. The spatial spillover coefficients λ are significantly positive in all models, indicating that digital finance can affect the GTFP of both local cities and their adjacent cities. As shown in columns (1) and (5) of Table 4, the coefficients of DIFI are significantly negative, and the coefficients of DIFI² are significantly positive, indicating that the impact of digital finance on GTFP is “U”-shaped. The development of digital finance will enhance GTFP only when it reaches a certain level. The turning points under the geography and technology weight matrices are 2.2413 and 2.4819, respectively. Only after crossing the turning point can digital finance positively promote GTFP, thus contributing to green and sustainable economic development. Otherwise, it will inhibit the improvement of GTFP and not be conducive to sustainable growth. By contrast, the average level of digital finance in smart cities is 1.662, which is to the left of the inflection point. Taking the geography weight matrix as an example, when digital finance increases by 35% from the mean value of 1.662 to the inflection point of 2.2413, the GTFP will decrease by 7%. When digital finance exceeds the inflection point and increases by 35% to the value of 3.0258, GTFP will increase by 12%. In the early stage, capital idling caused by imperfect digital finance [5] and the high energy consumption of digital infrastructures [44] may inhibit GTFP. The coordination between digital technology and finance will continue to increase when the development of digital finance achieves a certain level. Then, its ability to optimize and restructure traditional production factors such as capital and labor will continue to increase, which further stimulates its resource allocation and green attribution, and promotes GTFP.

The regression results of most control variables are consistent with our analysis. The coefficients of Pgdp, Gov, and Science are significantly positive in most models. Urban is negatively related to GTFP. The coefficient of FDI is significantly negative, indicating that foreign investment has a specific crowding-out effect on the local market, thereby discouraging firms’ innovation enthusiasm, and is not conducive to GTFP. The coefficient of Trans is not significant, and further strengthening of the positive role of infrastructure on GTFP is needed.

The regression results of the coverage, usage, and digitization dimensions are shown in columns (2)–(4) and (6)–(8) in Table 4. The coefficients of their primary terms are significantly negative, while those of their quadratic terms are significantly positive, also showing “U”-shaped characters. The coverage dimension improves GTFP most among the three sub-dimensions, and the digitization dimension the least, which is similar to the findings of Yu et al. [16]. We can see from the above analysis that DIFI and its sub-dimensions have a “U”-shaped relationship with GTFP under significant spillovers. Hypotheses H1 and H2 are thusly verified.

4.3.2. Endogeneity and Robustness Tests

We perform 2SLS regression with the use of instrumental variables to avoid the bias caused by endogeneity. The first instrument variable is the lag in digital finance (L.DIFI). For the second one (Dis_Dif), we multiply the geographical distance from each smart city to Hangzhou by the average value of national DIFI (except for the city), constructing a time-varying instrumental variable [6]. The results of endogeneity tests are shown in columns (1)–(4) of

Table 5. Endogeneity and robustness tests.

	IV = L.DIF		IV = DIS_DIF		Model I	Model II
	First Stage	Second Stage	First Stage	Second Stage
	DIFI	GTFP	DIFI	GTFP	EC	GTFP
	(1)	(2)	(3)	(4)	(5)	(6)
Iv	0.517 ***
	(0.0182)
L.DIFI			0.836 ***
			(0.00753)
DIFI		−0.268 ***		−0.214 ***	−0.2737 **	−0.2654 ***
		(0.0666)		(0.0632)	(0.1079)	(0.0809)
DIFI2		0.0602 ***		0.0411 **	0.0959 ***	0.0573 ***
		(0.0196)		(0.0177)	(0.0311)	(0.0220)
Pgdp	0.834 ***	0.133 ***	0.0394 **	0.130 ***	0.0159	0.1187 ***
	(0.0578)	(0.0289)	(0.0199)	(0.0279)	(0.0189)	(0.0381)
Gov	0.0369 **	0.0142	0.00451	0.0236 **	−0.0060	0.0942 ***
	(0.0185)	(0.00861)	(0.00801)	(0.0116)	(0.0201)	(0.0315)
Fdi	−2.493 **	−0.811	0.152	−1.073 *	0.6051	−1.6059 **
	(1.224)	(0.565)	(0.395)	(0.562)	(0.6151)	(0.8139)
Urban	2.678 ***	−0.370 ***	0.0967	−0.496 ***	−0.1392 *	−0.1705
	(0.280)	(0.130)	(0.0973)	(0.135)	(0.0812)	(0.1628)
Science	0.510 *	0.152	0.0823	0.150	0.0312	0.2578 **
	(0.276)	(0.121)	(0.0844)	(0.118)	(0.2106)	(0.1037)
Trans	0.492 ***	−0.0120	0.0227	0.0113	−0.0152	0.0359
	(0.0921)	(0.0407)	(0.0293)	(0.0409)	(0.0190)	(0.0329)
ρ					0.6509 ***
					(0.0378)
λ						0.1696
						(0.1269)
Constant	−2.634 ***		0.352 ***		0.5941 ***	0.6466 ***
	(0.142)		(0.0569)		(0.1125)	(0.1122)
Kleibergen-Paap rk LM		185.197 ***		453.686 ***
Cragg-Donald Wald F		205.198		906.551
N	900	900	800	800	800	264
R2	0.839	0.159	0.980	0.156
Overall-R2					0.1260	0.2295
Within-R2					0.1290	0.1441
Between-R2					0.0872	0.2894

Note: *, **, *** indicate significant at the 10%, 5%, and 1% levels, respectively. Standard errors are reported in parentheses. Columns (1) to (4) describe the results of endogeneity tests. Columns (5) to (6) are results of the robustness tests. Model I replaces the explained variable, and model II replaces the samples. According to the LM tests, model I selects the SAR model, and model II selects the SEM model. W_g is taken as the spatial weight matrix.

. After using instrument variables, DIFI also shows a “U”-shaped relationship with GTFP. Therefore, the conclusion is the same when we consider endogenous influence.

A series of robust tests are conducted in this article. Firstly, the explanatory variables are replaced. We decompose GTFP into technical efficiency (EC) and technical progress (ET), using the Malmquist–Luenberger index method, and replacing GTFP with technical efficiency (EC) for the regressions, as shown in column (5) of Table 5. Secondly, we limited the sample to the first 33 pilot smart cities. The results are shown in column (6) of Table 5. Thirdly, we use the spatial weight matrix of information (W_i) and human capital (W_h) for re-estimates, as shown in

Table 6. Robustness tests.

	Wi				Wh
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
DIFI	−0.2035 ***				−0.1962 ***
	(0.0342)				(0.0343)
DIFI2	0.0408 ***				0.0383 ***
	(0.0109)				(0.0108)
Cov		−0.2442 ***				−0.2224 ***
		(0.0316)				(0.0307)
Cov2		0.0535 ***				0.0458 ***
		(0.0104)				(0.0100)
Use			−0.1645 ***				−0.1689 ***
			(0.0309)				(0.0331)
Use2			0.0288 ***				0.0306 ***
			(0.0094)				(0.0101)
Dig				−0.0893 ***				−0.0990 ***
				(0.0253)				(0.0268)
Dig2				0.0124 *				0.0155 **
				(0.0071)				(0.0074)
Pgdp	0.1246 ***	0.1296 ***	0.1182 ***	0.1127 ***	0.1201 ***	0.1267 ***	0.1132 ***	0.1071 ***
	(0.0184)	(0.0185)	(0.0183)	(0.0184)	(0.0183)	(0.0184)	(0.0182)	(0.0182)
Gov	0.0206 ***	0.0184 **	0.0233 ***	0.0266 ***	0.0159 **	0.0151 **	0.0175 **	0.0197 **
	(0.0078)	(0.0077)	(0.0078)	(0.0078)	(0.0077)	(0.0077)	(0.0078)	(0.0077)
Fdi	−1.1566 **	−1.0012 **	−1.2462 ***	−1.2617 ***	−1.3192 ***	−1.1763 **	−1.3790 ***	−1.4443 ***
	(0.4641)	(0.4602)	(0.4662)	(0.4677)	(0.4627)	(0.4623)	(0.4628)	(0.4656)
Urban	−0.3227 ***	−0.2942 ***	−0.3133 ***	−0.3922 ***	−0.2926 ***	−0.2689 ***	−0.2845 ***	−0.3489 ***
	(0.0839)	(0.0836)	(0.0844)	(0.0850)	(0.0841)	(0.0837)	(0.0841)	(0.0847)
Science	0.1845	0.1540	0.2108 *	0.2166 *	0.1397	0.1270	0.1482	0.1551
	(0.1147)	(0.1135)	(0.1157)	(0.1162)	(0.1144)	(0.1135)	(0.1155)	(0.1154)
Trans	0.0006	0.0029	0.0043	−0.0129	0.0083	0.0087	0.0118	−0.0021
	(0.0216)	(0.0213)	(0.0218)	(0.0219)	(0.0215)	(0.0214)	(0.0218)	(0.0218)
λ	0.1290 *	0.1489 **	0.0805	0.1635 **	0.2054 ***	0.1750 ***	0.2148 ***	0.2606 ***
	(0.0675)	(0.0654)	(0.0651)	(0.0643)	(0.0529)	(0.0529)	(0.0526)	(0.0532)
_cons	0.7573 ***	0.7521 ***	0.7268 ***	0.7415 ***	0.7396 ***	0.7286 ***	0.7173 ***	0.7252 ***
	(0.0513)	(0.0490)	(0.0496)	(0.0508)	(0.0515)	(0.0492)	(0.0506)	(0.0513)
N	900	900	900	900	900	900	900	900
Overall-R2	0.1702	0.1809	0.1590	0.1361	0.1712	0.1816	0.1596	0.1386
Within-R2	0.1668	0.1809	0.1582	0.1284	0.1661	0.1810	0.1569	0.1242
Between-R2	0.1727	0.1819	0.1595	0.1417	0.1750	0.1827	0.1615	0.1485

Note: *, **, *** indicate significant at the 10%, 5%, and 1% levels, respectively. Standard errors are reported in parentheses. W_g is taken as the spatial weight matrix.

. We can see in all the robustness tests that the coefficients of DIFI are significantly negative, and those of DIFI² are significantly positive. Therefore, the conclusion is robust.

4.3.3. Mediating Analysis

The testing of mediating effects is performed with SEM models using the geography weight matrix, as shown in

Table 7. Mediating effect tests.

	MED = Tech		MED = Is		MED = Invest
	(1)	(2)	(3)	(4)	(5)	(6)
	Tech	GTFP	Is	GTFP	Invest	GTFP
DIFI	0.7757 ***	−0.1566 ***	0.0863 ***	−0.2199 ***	0.3691 ***	−0.2281 ***
	(0.0530)	(0.0412)	(0.0060)	(0.0422)	(0.0651)	(0.0463)
DIFI2		0.0283 **		0.0513 ***	−0.0722 ***	0.0519 ***
		(0.0132)		(0.0132)	(0.0198)	(0.0145)
MED		−0.0955 ***		−1.1840 ***		−0.0843 ***
		(0.0163)		(0.3100)		(0.0226)
MED2		0.0095 ***		1.1698 ***
		(0.0019)		(0.3352)
Pgdp	0.2564 ***	0.1124 ***	−0.0160 **	0.1110 ***	−0.0920 ***	0.1064 ***
	(0.0945)	(0.0186)	(0.0072)	(0.0185)	(0.0295)	(0.0185)
Gov	−0.0163	0.0111	−0.0011	0.0133 *	0.0009	0.0134 *
	(0.0297)	(0.0076)	(0.0023)	(0.0077)	(0.0099)	(0.0077)
Fdi	1.0738	−1.3472 ***	0.0280	−1.0849 **	1.9252 ***	−0.9664 **
	(1.9596)	(0.4576)	(0.1526)	(0.4578)	(0.6417)	(0.4580)
Urban	1.0480 **	−0.2634 ***	0.0160	−0.2843 ***	−0.2015	−0.2915 ***
	(0.4302)	(0.0831)	(0.0327)	(0.0840)	(0.1342)	(0.0835)
Science	0.0098	0.1880	−0.0487	0.2698 **	−0.1565	0.2732 **
	(0.4432)	(0.1145)	(0.0343)	(0.1135)	(0.1477)	(0.1127)
Trans	0.6822 ***	0.0151	−0.0098	−0.0020	0.0332	0.0015
	(0.1268)	(0.0222)	(0.0095)	(0.0218)	(0.0381)	(0.0215)
λ	0.4849 ***	0.2553 ***	0.6819 ***	0.2873 ***	0.5747 ***	0.3298 ***
	(0.0523)	(0.0691)	(0.0391)	(0.0703)	(0.0500)	(0.0711)
_cons	1.3356 ***	0.9061 ***	0.2945 ***	1.0294 ***	0.6609 ***	0.8416 ***
	(0.2734)	(0.0557)	(0.0215)	(0.0828)	(0.0908)	(0.0561)
N	900	900	900	900	900	900
Overall-R2	0.4281	0.1873	0.3083	0.1696	0.1012	0.1794
Within-R2	0.6605	0.2044	0.6374	0.1817	0.2741	0.1700
Between-R2	0.4028	0.1758	0.2043	0.1618	0.0463	0.1879

Note: *, **, and *** indicate significant the level of 10%, 5%, and 1%, respectively. Standard errors are reported in parentheses. W_g is taken as the spatial weight matrix.

. When the mediating variable is technological innovation (Tech) or industrial structure (Is), the test is conducted according to Equations (7)–(9). The results of Equation (8) are shown in columns (1) and (3) of Table 7, and the coefficients of DIFI are both significantly positive. The results of Equation (9) are shown in columns (2) and (4) of Table 7. The coefficients of MED and MED², DIFI and DIFI² indicate that the effects of Tech and Is on GTFP show “U”-shaped characters. As mentioned earlier, the rebound effect of technological progress initially inhibits the improvement of GTFP. When technological innovation reaches a certain level, energy-intensive raw materials are continuously replaced by clean ones; then, the undesired output is reduced and GTFP is improved. Meanwhile, the smart operation and management of smart cities are based on the construction of information cloud platforms, and the digitization of industries is important for upgrading industrial structure in such cities. The initial layout of the digital industry requires a large number of resources. When industrial structures are upgraded to higher levels, they can enhance GTFP by contributing to enterprises’ low-carbon transformation. Therefore, the mechanism is such that DIFI promotes Tech and Is, and these two channels have “U”-shaped effects on GTFP. Hypothesis H3 is thusly verified.

The mediating test of investment (Invest) is conducted according to Equations (7), (10) and (11). The regression results of Formula (10) are shown in Column (5) of Table 7, and in Column (6), the results of Equation (11). These indicate that DIFI has an inverted “U”-shaped effect on Invest, and the expansion of Invest negatively affects GTFP. As we mentioned, DIFI improves Invest by easing financial restraints, which increases resource consumption and inhibits GTFP. Further development of DIFI can reduce corporate speculation and make companies more focused on improving investment efficiency [69], thus decreasing the scale of non-efficient productive investment, alongside improving GTFP. Therefore, DIFI has a “U”-shaped influence on GTFP through the intermediary effect of Invest. This result is consistent with Hypothesis H4.

4.3.4. Heterogeneity Analysis

Heterogeneity analyses are conducted in terms of human capital, the informatization, urbanization, and financial marketization of different smart cities. We divide low-value and high-value groups according to the medians of the above factors from 2011–2019. The results of heterogeneous tests based on human capital are shown in columns (1)–(2) of

Table 8. Results of heterogeneity analysis.

	Human		Inter		Urban		Market
	High	Low	High	Low	High	Low	High	Low
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
DIFI	−0.1496 ***	−0.2326 ***	−0.1583 ***	−0.1838 ***	−0.2356 ***	−0.1678 ***	−0.3182 ***	−0.1684 ***
	(0.0504)	(0.0509)	(0.0510)	(0.0526)	(0.0557)	(0.0545)	(0.0548)	(0.0537)
DIFI2	0.0334 **	0.0373 **	0.0335 **	0.0263	0.0488 ***	0.0279	0.0796 ***	0.0277
	(0.0156)	(0.0164)	(0.0154)	(0.0178)	(0.0167)	(0.0187)	(0.0170)	(0.0172)
Pgdp	0.1136 ***	0.1436 ***	0.0874 ***	0.1487 ***	0.1950 ***	0.0888 ***	0.0638 **	0.1568 ***
	(0.0268)	(0.0254)	(0.0285)	(0.0261)	(0.0290)	(0.0253)	(0.0266)	(0.0256)
Gov	0.0122	0.0145	0.0133	0.0085	0.0334 **	0.0023	0.0147	0.0075
	(0.0112)	(0.0103)	(0.0155)	(0.0091)	(0.0131)	(0.0099)	(0.0106)	(0.0115)
Fdi	−0.1549	−2.7606 ***	−1.1218 **	−1.3270	−1.3331 *	−0.8255	−0.9736	−1.1563
	(0.5868)	(0.7417)	(0.5531)	(0.8101)	(0.7264)	(0.6132)	(0.6126)	(0.7030)
Urban	−0.2430 *	−0.2885 ***	−0.0613	−0.4413 ***	−0.3850 ***	−0.3046 **	0.0207	−0.5245 ***
	(0.1259)	(0.1116)	(0.1236)	(0.1151)	(0.1392)	(0.1534)	(0.1253)	(0.1116)
Science	0.2607 **	−1.4552 ***	0.2439 **	−1.6845 ***	0.2667 **	−1.3317 ***	−0.1183	0.3319 ***
	(0.1149)	(0.5248)	(0.1128)	(0.5069)	(0.1068)	(0.5097)	(0.4486)	(0.1196)
Trans	−0.0278	0.0524 *	0.0502	−0.0046	0.0057	0.0057	0.0179	−0.0096
	(0.0319)	(0.0296)	(0.0350)	(0.0259)	(0.0328)	(0.0294)	(0.0310)	(0.0293)
$\mathsf{\lambda }$	0.1667 *	0.2524 ***	0.2274 ***	0.1761 **	0.3230 ***	0.1454 *	0.2429 ***	0.2283 ***
	(0.0882)	(0.0778)	(0.0850)	(0.0671)	(0.0776)	(0.0881)	(0.0804)	(0.0833)
_cons	0.6636 ***	0.7726 ***	0.5539 ***	0.8404 ***	0.6897 ***	0.7797 ***	0.7003 ***	0.8198 ***
	(0.0744)	(0.0724)	(0.0795)	(0.0830)	(0.1065)	(0.0756)	(0.0772)	(0.0701)
N	450	450	450	450	450	450	387	513
Overall-R2	0.1082	0.2558	0.1276	0.3055	0.2927	0.1741	0.1640	0.2415
Within-R2	0.0734	0.3234	0.0635	0.3114	0.1378	0.2180	0.1642	0.1969
Between-R2	0.1247	0.1895	0.1588	0.2995	0.3744	0.1346	0.1887	0.2732

Note: *, **, ***, are respectively significant at the 10%, 5% and 1%. Standard errors are reported in parentheses. W_g is taken as the spatial weight matrix.

. The coefficients of DIFI are both significantly negative, and those of DIFI² are significantly positive. DIFI and GTFP show a “U”-shaped relationship in both groups, and are more prominent in the low group. The turning point of DIFI is 3.1180 and 2.2395 for the low and high-level groups, respectively. Improvements in human capital can reduce energy consumption through innovation effects, and can offset the negative effects at the early stage. Spatial penetration of DIFI increases with the development of digital technology, which is conducive to accelerating innovation in low-human capital cities during the process of learning by doing. Therefore, the inhibitory effects are weaker in high-human capital groups, and the positive effects are more obvious in low-human capital groups.

The results of heterogeneous tests for informatization, urbanization, and financial marketization are shown in columns (3)–(8) of Table 8. We can see a significant U-shaped impact in the high-level group. The turning points of DIFI for high level informatization, urbanization, and financial marketization groups are 2.3627, 2.414, and 1.9987, respectively. These indicate that DIFI in high-value groups first prevents and then promotes GTFP. However, DIFI in low-value groups has significant inhibitory effects on GTFP before crossing the inflection points, but no significant positive promotion after crossing them. Smart cities with a high level of informatization provide hardware support for digital financial services in smart productions. Highly urbanized smart cities have a higher level of digital infrastructure condition for DIFI. Factors flow more adequately in smart cities with higher financial marketization, thus reducing transaction costs, waste of resources, and energy consumption. All the above make DIFI in the high group contribute more significantly to GTFP.

5. Conclusions and Suggestions

5.1. Main Conclusions

This paper theoretically examines the “U”-shaped impact of digital finance on GTFP and its spillovers in smart cities, as well as analyzing its mechanisms from the three perspectives of innovation effect, structural effect, and scale effect. Based on panel data from China’s 100 cities selected as pilot smart cities between 2011 and 2019, we use spatial models to illustrate the “U”-shaped impact, the mechanisms, and heterogeneous characteristics, with intrinsic and stable tests. Our conclusions are as follows.

(1) Digital finance and GTFP in smart cities show a significant “U”-type relationship with spillovers. Digital finance can promote GTFP when achieving a certain level; otherwise, it will inhibit the enhancement of GTFP. Among the three sub-dimensions, the U-shaped impact of the coverage dimension is the most significant, and the digitization dimension is the weakest. Digital finance spillovers impact GTFP through four aspects: geography, information, technology, and human capital, among which the geography and technology spillovers are the most significant.

(2) Digital finance has a “U”-shaped effect on GTFP through innovation, structural and scale effects. It promotes green technology innovation and upgrades industrial structure, and both mediating channels have a “U”-shaped impact on GTFP. Furthermore, digital finance has an inverted “U”-shaped impact on the investment scale, the expansion of which inhibits the growth of GTFP.

(3) The impacts of digital finance on GTFP are heterogeneous. The “U”-shaped impacts are significant in both groups divided by human capital, and are more prominent in the lower group. In smart cities with high information, urbanization and financial marketization, digital finance has significant “U”-shaped impacts on GTFP. In smart cities with low levels of these factors, digital finance has significant inhibitory effects on GTFP before crossing the inflection points, and no significant promotion effects after crossing them.

5.2. Policy Implications

First, it is necessary to improve digital finance according to the timing and local conditions of different smart cities. For those cities in which digital finance has not reached the inflection point, interconnection and information sharing should be strengthened to reduce the information asymmetry of digital investment and financing platforms to avoid misallocating financial resources. Cities that have crossed the inflection points should fully use digital technologies to expand the digitization of financial services.

Second, spillover effects should be leveraged to realize linkage improvement in GTFP. Inter-regional cooperation should be promoted among smart cities to fully release the spatial spillover dividends in the sharing of technology, transmission of information, and exchange of talents. At the same time, the multi-polar and networked development of smart cities should be promoted, so that the radiation effects can be dispersed through multiple urban pole nuclei.

Third, digital finance nonlinearly affects GTFP through innovation, structure, and scale effects, which should be made full use of for green and sustainable development. It is necessary to reduce information asymmetry in green technology financing, and optimize the green technology innovation industry chain. We should take advantage of the high level of digitalization and informatization construction in smart cities, empower industrial structure upgrading with industrial digitalization and informatization, strengthen the coordination of industrial chains, and promote the intelligent development of various industries. The expansion of the scale of investment will inhibit the improvement of GTFP. Clean production should be comprehensively promoted, and the demonstration role of green factories should be brought into play to create a green production system, and to reduce energy consumption in the production process.

Fourth, a differentiated development strategy of digital finance should be adopted based on the heterogeneity of its “U”-shaped effects. Significantly promoting GTFP through digital finance is challenging in smart cities with low informatization, urbanization and financial marketization. Therefore, breaking through these bottlenecks has become an urgent task, needed to promote the interconnection of information platforms to realize the intelligence of urban life and the greening of the ecological environment. It is also necessary to continuously improve the smart financial system and effectively integrate digital and financial elements by using the spatial penetration of digital finance to reduce financial friction.

5.3. Research Limitations and Future Research

This study is subject to some limitations that could be improved in the future. Firstly, the selected data could be improved. We used the panel data of smart cities for analysis; this may be extended to include enterprise data. More firm-level research needs to be conducted for the improvement of data availability. Secondly, the empirical methodology could be progressed. Spatial econometric models can test for the existence of spillovers, but are limited in describing spatially linked networks. A social network analysis may be used in the next step to explore the spatial association networks of GTFP in smart cities. This form of analysis analyzes different cities’ positions and roles in the network to provide a more accurate picture of spillover effects. Thirdly, the influence of environmental policies can be further considered. Changes in inflection points and differences in the mediation mechanism of non-linear impacts under different degrees of environmental regulation require more research.