Can urban digitalization significantly improve carbon emission efficiency?Evidence from 282 cities in China

Urban digitalization is a critical focus for economic development and the low carbon transition. Recognizing how urban digitalization influences carbon emissions efficiency (CEE) is of great practical significance to high-quality urban development. Previous studies have lacked a systematic exploration of the internal mechanisms and dynamic effects of urban digitalization on CEE. Based on data from 2011 to 2019 at the municipal level in China, this paper adopts efficiency analysis and entropy value method to measure urban digitalization development and CEE and analyze their spatial–temporal evolution characteristics. Moreover, this paper empirically tests the overall, time, and spatial effects of urban digitalization on CEE, as well as the effect pathways. According to the findings, urban digitalization has a significant stimulative influence on CEE. The promotion effect shows a trend of increasing over time. Urban digitalization has a positive spatial spillover effect on the CEE of surrounding cities, which is conducive to accelerating the integration process of low-carbon development among cities. Urban digitalization improves CEE by raising the level of human and information communications technology capital and optimizing the industrial structures. The above conclusions still hold after robustness and endogenous tests. In addition, compared to cities in the eastern part of China and those with low levels of digitalization, those in the central and western parts of the country, and those with high levels of digitalization show a more significant boost to CEE as a result of urban digitalization. These discoveries have policy design reference value for the region to enhance its urban digitalization development strategy and achieve a transition to green development.


Introduction
Countries around the world are under intense pressure to move closer to carbon neutrality amid the global fight against climate change and related political pressures (Ferreira et al. 2018;Li et al. 2021a, b). Carbon neutrality requires not only the innovation in carbon sink technology but also limits on the total regional carbon emissions. Some measures have been taken to reduce carbon emissions, but China still faces enormous challenges. According to the statistics of the International Energy Agency (IEA 2022), from 2011 to 2021, China's carbon emissions increased by about 2.3 gigatons (Gt), contributing nearly one-third of the world's carbon emissions in recent years and ranking first in the global total carbon emissions (Fig. 1). As a major carbon emitter, China still faces many pressures and challenges to go carbon neutrality. Improving carbon emission efficiency (CEE) is critical to achieving this goal.
Urban digitalization has had a profound impact on CEE. With the deepening integration of digital technologies into economic and social life, China is undergoing a digital transformation from traditional economic and social forms to digital economic forms. Urban digitalization refers to the transformation process of the entity structure of urban development mode driven by digital technology application and data elements, including the digital transformation of economic development, social life, government governance, and other aspects (Vial 2019;Khan et al. 2022a, b, c). In the process, the comprehensive penetration of digital technology Responsible Editor: Eyup Dogan * Siliang Guo GSL200601@126.com 1 in all economic and social activities had an important influence on the entire economic system and social governance. Digitalization provides the impetus for CEE by decentralizing the need for emission-intensive products and optimizing resource management and decision-making processes through system integration (Rubner 2012). However, urban digitalization is built on the basis of electricity, and the development and operation of cloud, blockchain, data centers, and other infrastructures require increasingly energyintensive infrastructure, which may cause more carbon emissions and put pressure on CEE upgrades. In this context, how has urban digitalization in China affected CEE? What is the path and mechanism of this influence? What are the spatial-temporal dynamics of urban digitalization affecting CEE? The discussion on the above issues helps to complement the research content on urban digital transformation and is also of practical significance for achieving carbon neutrality, effectively responding to global climate change and promoting green and low-carbon urban transformation. At present, some literature revolves around the welfare effect of digitalization from the perspective of economic growth (Goldfarb and Tucker 2019), employment and labor income (Acemoglu and Restrepo 2018) and productivity (Dewan and Kraemer 2000). However, research on urban digitalization and carbon emissions is still in its infancy and not only lacks a systematic theoretical framework but also leads to different conclusions. Some research has found that information communications technology (ICT) applications contribute to carbon emission reduction and promoted green and sustainable development. It has been indicated that the spread of the internet can curb CO 2 emission over the long run (Shobande 2021). Increased investment in ICT infrastructure can also have a significant impact on reducing CO 2 emission (Bhujabal et al. 2021). Chen (2021) empirically tested the influence of digitalization on CO 2 emission by using BRICS countries as samples and found that digital technology will significantly reduce carbon emissions. Balogun et al. (2019) also believed that digital technology had a positive impact on sustainable development after conducting case studies of cities on various continents. In addition, the digital transformation of carbon trading markets can accelerate the reduction of carbon intensity, which is also considered an essential path to carbon neutrality. However, some studies prove that the rapid increase of ICT greatly increases the consumption of electricity (Salahuddin and Alam 2015), thus promoting the increase in carbon emissions (Li et al. 2021a, b;Hassan et al. 2022a, b, c). Shvakov and Petrova (2020) conducted an empirical analysis of the top 10 countries in the global competitiveness of digital technology and found that economic digitalization would cause more significant burden on the environment. The inconsistent conclusions of the existing literature may be related to the differences in the sample period and the institutional background. Due to the progress in digital technology, different times and regions may produce systematic differences in carbon reduction effects. In addition, there is still a lack of research to systematically explore the relationship of urban digitalization and CEE. Therefore, this paper aims to reveal the actual relationship and intrinsic mechanism between urban digitalization and CEE and provide a robust empirical basis and policy implications for the CEE enhancement effect of urban digitalization.
The marginal contributions of this paper are as follows: (i) this paper complements previous studies on the effects of CEE. Most current research on CEE impact factors has focused on market policies such as carbon emissions trading and green credits, while research on the impact of digitalization on CEE is relatively lacking. This paper provides in-depth quantitative test evidence on the mechanisms and effects of urban digitalization on CEE, which can provide empirical evidence for the development of carbon neutral strategies in the era of urban digitalization in China and other developing countries. (ii) This paper reveals the impact of urban digitalization on CEE from a more comprehensive perspective. Previous studies have been limited to the analysis of spatial effects. This paper discovers the temporal reinforcement feature and spatial spillover of urban digitalization on CEE. In addition, we analyze heterogeneity in the impact of urban digitalization on CEE, thus providing rich evidence for the ongoing studies. (iii) This paper enriches the study of the environmental impact of urban digitalization. In the past, such studies have mainly focused on highquality economic development, green development, and carbon reduction. In this paper, we provide more empirical evidence from the CEE perspective. In addition, the study identified three different mechanisms, namely, industrial structure, ICT capital, and human capital stock, which can help deepen understanding and recognize the role of the urban digital ecological environment.
The remainder of the paper is organized as follows. "Literature review" presents literature reviews. "Theoretical analysis and research assumptions" puts forward the research hypothesis. "Research design" introduces the measurement model setting and data sources. "Descriptive analysis" presents a descriptive analysis. "Empirical analysis" discusses the empirical results. "Further analysis" further analyzes the mechanism and heterogeneity that urban digitalization affects CEE. "Discussion" offers the discussion. "Policy implications" presents the policy implications. "Conclusions" summarizes the conclusions.

Literature review
The existing literature involving CEE is mainly related to its definition, measuremen, and influencing factors. In terms of definition, different scholars have defined CEE from different angles. Previous studies generally used single indicators such as carbon emissions per unit GDP , carbon emissions per unit of energy consumption (Hassan et al. 2022a, b, c), and carbon index (Mielnik and Goldemberg 1999). These individual indicators are straightforward, but not comprehensive. To systematically analyze CEE, scholars proposed to define CEE as the maximum economic output and minimum carbon emissions that under constant multi-factor inputs such as capital, labor, and energy (Li and Cheng 2020). In terms of measurement methods, the stochastic frontier method (SFA) and data envelopment analysis (DEA) are used to measure CEE. Because the SFA method requires the boundary to adopt a specific frontier function, an improper function form may lead to an error estimation result. Unlike the SFA method, the DEA method does not require any specification of frontier function and can deal with multiple input and output indexes simultaneously (Charnes et al. 1978). Therefore, some improved DEA models have been widely used to measure CEE, for example, super-SBM model , non-radial DDF model (Yao et al. 2015), and non-radial DEA model (Kang et al. 2018), etc. In terms of influencing factors, scholars found that the main reasons for the changes in CEE include many factors such as industrial structure, energy utilization structure, level of science and technology investment, and government intervention (Narayan et al. 2016;Wang et al. 2021;Zhou et al. 2010).
The rapid development of digital technology has attracted the attention of many scholars on digitalization. The early research on digitalization was more information oriented, and most of them focused on a single ICT investment (Brynjolfsson and Hitt 2000). Digitalization refers to the use of information and intelligent means, focusing on the key areas and core links of urban operation, and promoting the overall transformation of the economy, society, and urban governance (Li et al. 2018a, b). Tr and Clpa (2020) pointed out that digitalization is a deep integration process of digital technology and economic society. With the popularization of digitalization in the field of economics, research on the digital economy has attracted much attention. The research contents mainly involve the conceptual and theoretical connotation of digital economy (Zhang 2019) and the law of economic development with the digital economy as the background (Dyatlov 2018;Khan et al. 2019). In recent years, digitalization research has gradually been refined, and the focus has shifted to industry and enterprise digitalization research. Many scholars (Li et al. 2018a, b) focused on enterprise, industry, organization, and other levels and analyzed the changes caused by digital technology from the perspective. For example, Chen et al. (2020) believed that enterprise digitalization is a strategic behavior to improve enterprise competitiveness and realize profit increment by utilizing digital technology to realize enterprise digitalization. Zheng and Wang (2022) perceived that the application of artificial intelligence significantly moved up the global value chain of Chinese manufacturing enterprises.
At present, research on the role of digitalization is mainly carried out from two aspects: the socioeconomic effects and the environmental effects. With the rapid development of digitalization, its economic and social effects have been widely concerned. Scholars focus on the positive utility of digitalization in terms of economic aggregate increase (Jiang and Sun 2020), industrial structure upgrading (Liu et al. 2022), innovation efficiency improvement (Han et al. 2019), production efficiency improvement (Guo and Luo 2016), optimization of the economic geographical pattern , and high-quality economic development (Zhao et al. 2020). In the meantime, the environmental improvement effects of digitalization are also a focus of academic attention. Some scholars believe that digitalization reduces carbon emissions by increasing the efficiency of environmental regulation through the application of digital technologies in various fields (Khan et al. 2022a, b, c;Shigeno et al. 2022). Relying on digital technology, we can set up a green digital platform for communication between the government, enterprises, and the public and guarantee the quality of ecological environment (Yang et al. 2020a). Meanwhile, network information has become an important driving force in promoting environmental pollution control. For example, the informal environmental regulations generated by search volume data about pollution on online platforms (Li et al. 2017) and the online haze public opinion can improve urban air quality. In addition, the information transmitted by digital media can guide the public to form green environmental protection concepts and thus alleviate urban pollution. Some scholars have also concerned the influence of digitalization on environmental quality. For example, the e-commerce industry in the digital economy (Yang et al. 2020b), as an environmentally friendly industry, can squeeze the living space for industries with high pollution and emission and promote high-quality urban development through the extrusion effect.
To sum up, the existing research offers some helpful information and inspiration for exploring the environmental effects of urban digitalization. However, previous studies have primarily analyzed the impact of digital technology or digital economy on resource utilization efficiency and the environment. Few studies have examined the comprehensive effect of urban digitalization on economic growth and carbon emissions. CEE can represent the combined effects of economy and environment. Therefore, it is a valuable topic to clarify the impact of urban digitalization on CEE. At the same time, few existing studies on the effects of urban digitalization have paid attention to its temporal and spatial evolution characteristics. We certainly know that it is difficult to understand genuine relationships and the laws of change without breaking through the perspective of time and space. In addition, the existing literature mainly discusses urban digitalization and CEE from static and result-level qualitative theories and ignores the valuable empirical tests and the exploration of the internal mechanisms. Therefore, it is challenging to provide experience and guidance for exerting the environmental welfare effect of urban digitalization.

Urban digitalization and CEE
Urban digitalization had a profound impact on CEE from many aspects, as digital technologies are widely applied. First, from the macro governance perspective, governments can use digital technologies to identify energy market trends and price trends and thus control total energy supply (Bhattacharya 2015). At the same time, by improving the information transparency and accessibility of the carbon trading market, digital technology not only helps to break the market monopoly and administrative monopoly and establishes an effective market competition order (Yang et al. 2020a;Khan et al. 2022a, b, c) but also promotes the digitalization and information reform of the market supervision and the rational allocation of carbon quota. Thus, regional CEE can be effectively improved (Gu et al. 2020). Second, from the perspective of companies, digital technology can not only optimize the end treatment technology of enterprise CO 2 emission but also achieve real-time acquisition and analysis of energy information through accurate control of energy flow data and guide the efficient allocation of energy factors (Huang et al. 2019). The support of digital finance reduces the budget constraint of companies and alleviate resource misallocation (Michalopoulos et al. 2015), enabling enterprises to realize more research and development investment through capital allocation, guiding the goal of clean industrial transformation and green development, thus improving energy utilization efficiency and promoting the improvement of CEE. In addition, from the perspective of energy conservation, digitalization breaks regional boundaries, breaks through time constraints, speeds up the flow and production of factors (Shigeno et al. 2022), and saves energy consumption due to spatial and temporal factors in production and life, thus reducing energy consumption and improving CEE. Therefore, we express hypothesis 1 as follows: H1. Urban digitalization contributes to increasing CEE.

Urban digitalization, industrial structure, and CEE
Urban digitalization can optimize the industrial structure. First, with the advance of urban digitalization, the role of digital economy in national economic growth has been widely recognized (Ma et al. 2022). Relying on modern and emerging science and technology, the digital economy has built smart education, enabled smart life, promoted industrial intelligence, and continuously optimized and adjusted the internal structure of the first, second, and third industries to improve the industrial structure rationalization. Second, relying on the characteristics of high permeability and strong diffusion, digital technology can break the boundary between industries and promote integration between related industries (Ren et al. 2021). New fields and formats of digitalization have been created on the basis of industrial integration, which is conducive to promoting advanced industrial structures. Third, the digital network platform formed by urban digitalization can promote cross-industry and cross-field resource sharing through scale effects and competition effects (Zuo et al. 2020), optimize traditional industrial production modes, supply chain, and value chain, and further improve operational efficiency of industrial organization, thus enhancing the industrial structure (Liu et al. 2022). The optimization of industrial structure through digitalization is beneficial to increase CEE. Urban digitalization transfers the factors of production from the inefficient sector to the efficient sectors by optimizing industrial structure. The reasonable allocation of production efficiency changes the path dependence and use efficiency of the economy on resources (Liu and Jin 2019;Hassan et al. 2022a, b, c) and improves the resource allocation efficiency thus improving regional CEE (Khan et al. 2021;Shao et al. 2022). Therefore, we express hypothesis 2 as follows: H2. Urban digitalization increases CEE by optimizing the industrial structure.

Urban digitalization, ICT capital, and CEE
First, urban digitalization increases the level of ICT capital accumulation. Digital infrastructure is a core element for deepening urban digitalization, and its development level determines the potential of digital development (Shi et al. 2018). Therefore, the digital infrastructure construction of urban digitalization will directly drive a large amount of ICT capital investment and promote capital flow, thus improving the accumulation level of urban ICT capital (Goldfarb and Tucker 2019).
Second, ICT capital accumulation plays a positive role in improving CEE. On the one hand, ICT capital improves green production efficiency, the speed of renewal of green machinery, and equipment and the flexibility of manufacturing by promoting the efficiency of green technology innovation (Zhang and Wei 2019;Li et al. 2019), thereby decreasing the energy consumption intensity of companies. On the other hand, the digital infrastructure formed by ICT investment can effectively reduce the configuration and use of the information asymmetry and make various production factors including energy, which leads to configuring the domain and the link to the highest efficiency, thus optimizing the structure of enterprises, improve enterprise resource allocation efficiency of production and improving the energy unit of economic output and eventually improving the CEE. After decades of development, ICT has become widely used in the national economy. ICT capital helps reduce energy consumption and CO 2 emissions in applied industries such as transport, construction, online learning, and healthcare and plays a crucial role in improving energy efficiency in other sectors. With the help of big data and machine learning, traditional industries can draw more efficient production solutions through data collection and analysis and promote the continuous reduction of carbon emissions per unit product (Gelenbe and Caseau 2015). We therefore believe that ICT investment has reached a relatively mature stage, where ICT contributes more to reducing carbon emissions than it generates. Therefore, we express hypothesis 3 as follows: H3. Urban digitalization increases CEE by accelerating the accumulation of ICT capital.

Urban digitalization, human capital, and CEE
Urban digitalization improves the breadth and depth of human capital accumulation. Human capital in this paper refers to the educated population, not the companytrained employees. On the one hand, data has become an essential factor of production in the digital age (Balogun et al. 2019), and the emergence of a large number of new digital industries puts forward specific requirements for human capital. In the context of urban digitalization, many knowledge-skill intensive tasks require talents with digital knowledge, information network, and communication technology skills (He 2021). To cope with the new environment and forms of business, individuals with different human capital improve their educational level through "learning through work" or "re-education." On the other hand, urban digitalization enables digital technology to penetrate production, life, and other aspects. It promotes people to improve their comprehensive ability and accomplishment through continuous learning so as to keep pace with the times (Qi et al. 2020;Tufail et al. 2022). Specifically, the development of urban digitalization deeply affects the labor market model and the employment model of workers (Dyatlov 2018;Chen et al. 2022) to encourage people to improve their working ability and business level through various training and online learning and reduce the possibility of being replaced. At the same time, human capital accumulation is beneficial for enhancing CEE. According to endogenous growth theory, human capital can stimulate economic growth. By accelerating the allocation and transformation of production factors, human capital can enhance economic benefits and green production levels, thus having a substantial impact on CEE. Human capital can help absorb foreign clean technologies and provide technical support to save production and reduce carbon emissions, thereby improving CEE. Whether advanced alien clean technologies and production methods can be effectively disseminated and used locally is closely related to whether local human capital can adapt to the alien technologies. The more human capital accumulated, the stronger the absorption capacity of alien technologies, and the easier it will be for local enterprises to adopt higher environmental standards and engage in green production, which will help improve the local CEE. Thus, hypothesis 4 is formulated as follows: H4. Urban digitalization increases CEE by accelerating the accumulation of human capital. Figure 2 shows the theoretical analysis framework of this paper.

Explained variable: carbon emission efficiency (CEE)
In this paper, the super-efficiency SBM (SE-SBM) model considering undesired output is adopted to calculate CEE. The SBM model can solve the slack problem by adding unexpected output variables and modifying the slack variables. However, the SBM model produces a situation where multiple decision units have an efficiency value of 1, which makes it challenging to compare the decision units, leading to a bias in the final decision. However, the SE-SBM model is less affected by environmental factors and breaks through the traditional value upper limit of 1. Especially when all DMUs reach the efficiency bound, it can reorder the efficiency values of the DMUs to achieve DEA effectiveness. (Ning et al. 2021). Therefore, this paper uses MATLAB software programming to measure and study the CEE value of the city and constructs the SE-SBM model as follows : In formulas (1) and (2), s g represents the expected output is insufficient. s − represents too much investment. s b represents too much undesired output. λ represents the weight vector. m represents the quantity of input factors. p 1 and p 2 represent the quantity of expected output factors and the quantity of undesirable output factors, respectively. k is the evaluated unit.
The SE-SBM model to calculate CEE involves input and output indicators. According to pertinent literature (Ma et al. 2015), this paper mainly selected capital stock, workforce and energy as the input. In this paper, GDP was chosen as the desired output and carbon dioxide emissions as the undesirable output.

Core explanatory variable: urban digitalization index (CDI)
At present, the digitalization level is mainly measured at the provincial level, and there are two measurement methods as follows. One is the single-indicator approach. This method uses a certain indicator, such as digital infrastructure, digital economy application, and digital industry development, to construct the index system and calculate the digital economy index (Yang and Jiang 2021). Another method is to use the digital financial inclusion index or the digital economy index published by Tencent Research Institute directly to reflect the digital economy development (Zhang et al. 2021). Comprehensively considering various dimensions of urban digitalization, we constructed the urban digitalization indicators from five aspects: digital infrastructure, digital industry, digital technology, digital applications, and digital finance. We used the entropy method to calculate the value of the comprehensive digitalization index.

Mediating variables
• Industrial structure (IS): in this paper, we drew on relevant studies (Gan et al. 2011;Yu et al. 2020) and used the ratio of the output value of the tertiary industry to the output value of the secondary industry to represent the changing in industrial structure. • ICT capital stock (ICT): in this paper, we used ICT fixed capital stock as a proxy for ICT capital. We measured the ICT capital of each city through two steps by referring to the digital economic accounting framework of China Academy of Information and Communication Technology (CAICT) and related literature (Ceccobelli et al. 2012). First, the ICT capital of each province in the study area was measured based on the perpetual inventory method. Second, the ICT capital stock of each city was calculated as the product of the proportion of ICT capital in the physical capital stock of each province and the physical capital stock of each city under the province. • Human capital stock (HUM): in this paper, we used the length of education method to represent the level of human capital referring to the research results of Li et al. (2018a, b). The corresponding duration of education for primary school, junior high school, senior high school, and junior college and above was set at 6, 9, 12, and 16 years, and the proportion of the labor force in each province with different levels of education was taken as the weight. We first calculated the average number of years of education for each province's workforce. The number of employees in each city at the end of the year was then multiplied by the average educational years of the workforce in the province where the city is located to obtain the human capital stock of the city's workforce.

Control variables
In this paper, we referenced previous literature Zhou and Luo 2021) and control for the four variables of population density (POPD), government intervention (GOV), science and education level (AO), and energy consumption (EI) that may affect carbon emission performance. Table 1 shows the definition of the variables in this paper.

Samples and data
In this paper, we selected 282 cities with observed values from 2011 to 2019 as a sample for empirical research.
The reason for this is twofold. On the one hand, consider that urban digitalization has only taken off in recent years. On the other hand, to ensure the continuity and validity of the data, we excluded the cities with administrative division adjustments and large numbers of missing data during the study period. Among the sample cities, the eastern region includes Beijing, Tianjin, and cities in the province of Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan provinces. The rest of the cities belong to the central and western regions. The variable data mentioned above are from China Urban Statistical Yearbook (2012-2020), China Regional Statistical Yearbook (2012-2020), statistical yearbook, and statistical bulletin of all provinces and cities. The digital financial inclusion index comes from the Index System and Index Compilation of Digital Financial Inclusion published by the Internet Finance Research Center of Peking University (Guo et al. 2020a). Some missing values are filled by linear interpolation method and adjacency annual significance. In addition, to reduce sample fluctuations, this paper takes a logarithmic treatment for all non-ratio indexes. The descriptive statistics of each variable are shown in Table 2. The maximum value of the variance inflation factor (VIF) of all variables in this paper is 1.95, which is less than the threshold value of 10. Therefore, the problem of multicollinearity between variables is excluded.

Static panel model
In this paper, based on the above theoretical analysis, we developed a general panel-referenced regression model and empirically tested the relationship between urban digitalization and CEE. The results of the Hausman test showed a Hausman value of 46.34, which is significant at the 1% level, indicating that the model rejects the null hypothesis of random effects. Therefore, it is suitable for choosing fixed effect models for benchmark regression analysis. The model is set as follows: where i is the city, and t is the period. μ i and σ t represent individual effect and time effect, respectively. ε it represents random perturbation term.
It should be noted that the estimation of the parameters of the empirical model is biased because the level of urban digitalization development may be mutually causal with CEE and there are potential omitted variables. In view of the potential endogeneity problem, the instrumental variable regression method was used to fully identify the net effect of urban digitalization on CEE. The 2SLS model based on instrumental variables is as follows:

Mediating effect model
In this paper, we used the three-step mediating effect model to analyze the influencing mechanism of urban digitalization on CEE step by step (Wen and Ye 2014). (3) In addition, we further adopted the bootstrap sampling method for testing the mediation effect to ensure the accuracy of the results. The three-step model is as follows.
First, regression estimation is made based on the impact of CDI on CEE.
Second, the regression estimation is carried out with the impact of CDI on the intermediary variable M.
Third, regression estimation is carried out with the impact of CDI and M on CEE.

Time effect model
The temporal dynamic effect of urban digitalization development on CEE refers to whether current urban digitalization will have an impact on CEE in future periods. This paper conducts lag processing on core explanatory variables based on model (1) and uses L to represent the number of lag periods to verify the time effect. The time effect model constructed in this paper is as follows.

Spatial effect model
In this paper, we have developed an econometric model of the impact of digitalization on CEE from a spatial perspective. Specifically, we selected the spatial autoregressive model (SAR) and the spatial error model (SEM) for empirical analysis. Meanwhile, we used the spatial Durbin model (SDM) for robustness tests. The models are shown in Eqs. (10) and (11). where i is the city, and t is the period. W i̇J is the weight matrix of spatial panels. ρ and γ are spatial autoregressive and spatial autocorrelation coefficients, respectively. X represents explanatory variables, including core explanatory variables and other control variables. ε it is a spatial error autocorrelation term, and ζ it is a random interference term. When ρ is not zero and γ and θ are zero, the model is SAR. When ρ and ρ are zero and θ is not zero, the model is SEM. When ρ and γ are not zero and θ is zero, the model is SDM.
In this paper, we constructed three spatial weight matrices to reflect the spatial correlation characteristics of CEE. The first is the spatial adjacency weight matrix W 1 .
The value of W 1 is 1 or 0 according to whether two cities are adjacent or not. The second is the geographical distance weight matrix defined as follows: . d ij represents the straight-line distance between city i and city j, which can be obtained according to the longitude and latitude of the two cities. The third is the economic distance weight matrix, which is defined W i̇J = 1 |GDp i −GDp j | , where GDp i and GDp j are the mean per capita GDP of city i and city j ( i ≠ j), respectively (Feng et al. 2019).

Temporal and spatial evolution characteristics
Temporal evolution characteristics Figure 3 shows the time changing trends of CDI and CEE in China. In this paper, we selected variable values for 2013, 2015, 2017, and 2019 to draw kernel density curves. Figure 1a is the nuclear density diagram of CEE. It became clear that the center of the curve gradually shifted to the right over time, demonstrating that the sample city CEE gradually increased, and the growth rate slowed down at later times. In terms of shape, the kernel density curve changed from "tall and thin" type to "short and fat" type, indicating that the overall gap between urban CEE gradually expands. From the fluctuation of the tails on both sides of the kernel density curve, the right tail was significantly longer than the left one each year, and the trailing period (10) on the right side lengthens with time, indicating that some low-efficiency cities show low-value agglomeration, the number of cities in high-value regions was lower than that in low-value regions, and the ratio of cities with higher efficiency value was lower. Figure 3b is the nuclear density diagram of CDI. The peak of the wave moved to the right-side year by year, and the peak height gradually decreased, indicating that the digitalization level has improved to varying degrees in each city. The development digitalization in different cities were increasing divergent, with the pattern gradually shifting from convergence to dispersion. The curve had an apparent right trailing characteristic, which gradually aggravated with time, indicating that some low digitalization cities exhibit low-value agglomeration. While the proportion of cities with high digitalization levels is lower than that of cities with low digitalization levels, the proportion of cities with high digitalization levels is lower. Figure 4 shows the spatial distribution of CEE in 2011 and 2019. The spatial differentiation of sample urban CEE from 2011 to 2019 was evident, demonstrating a gradual decreasing state from the eastern coastal area to the northwest inland area. Since 2011, the CEE of Beijing, Shenzhen, Guangzhou, Shanghai, Qingdao, Wuhan, and Changsha has increased significantly, among which Shenzhen has increased the most from 0.484 to 1.117, and the average annual increase is 14.53%. However, Jinchang, Wuzhong, Xining, Fuzhou, Lu'an, and Ganzhou had a relatively small increase in CEE. Jinchang had the smallest increase, from 0.226 to 0.257, and the average annual increase is 1.52%. By 2019, Shenzhen, Guangzhou, and Beijing were the core of the sample cities in China, and Shanghai and Qingdao were the highvalue sub-core. The CEE gradually decreased outwards, and cities in the North-East, Midlands, and North-West had comparatively low CEE. From 2011 to 2019, the number of effective cities with a CEE greater than 1 increased from 12 to 20. In terms of specific distribution, most effective cities are in the eastern region, such as Dalian, Qingdao, Yantai, Quanzhou, and Shenzhen, have CEE greater than 1, indicating that these regions have fast economic development, optimization of energy and industrial structure, continuous improvement of clean technologies, and continuous strengthening of environmental protection. Figure 5 shows the spatial distribution of CDI in 2011 and 2019. The level of urban digitalization showed an increasing distribution from west to east. Over time, the digital development pattern had changed from "multi-point" sporadic distribution with individual cities as the core to a "group" agglomeration pattern. In 2011, the level of digitalization varied significantly between cities. The digitalization showed the feature of "multi-point" sporadic distribution, forming the digitalization development pattern in the Beijing-Tianjin-Hebei region, Chengdu-Chongqing urban agglomeration, Yangtze River Delta, and Guangdong-Hong Kong-Macao urban agglomeration as the core. In 2019, the overall development level of digitalization had improved significantly, and the pattern of digitalization development showed a cluster pattern of digital growth poles and core cities in each region spreading to surrounding cities. On the one hand, this is because core cities influence neighboring cities through the spillover effect of digitalization. On the other hand, the diffusion of digital resources from core cities improves the pattern and structure of urban development, which is the result of the optimal allocation of digital elements.

Spatial correlation analysis
Global spatial autocorrelation Table 3 shows the calculation of the spatial autocorrelation coefficients per year using Moran's I method under the geographical distance matrix. All the global Moran's I for CEE and CDI from 2011 to 2019 were greater than 0, and most passed the significance test at the level of 1%, indicating that CEE and urban digitalization have a significant positive spatial correlation. In other words, the spatial distribution of the two appears similar to the agglomeration phenomenon. From a trend point of view, the global Moran's I of CEE showed a fluctuating upward trend from 2011 to 2019, indicating that the degree of agglomeration of urban CEE has intensified. The Moran's I of the CDI from 2011 to 2019 presented a relatively stable state, but also some fluctuations, indicating that the degree of urban digitalization development agglomeration is relatively stable.
Local spatial autocorrelation Figure 6 shows the Moran scatter diagrams in 2011 and 2019, respectively. CEE was mainly distributed in "low-low" (L-L) and "high-high" (H-H) quadrants in Chinese cities, and a small amount in "high-low" (H-L) quadrants. Most cities in China showed "high-high" and "lowlow" clustering states, indicating that cities with higher (lower) CEE levels are surrounded by other cities with

Empirical analysis
Baseline regression analysis Table 4 shows the baseline regression results for urban digitalization on CEE. The coefficient of urban digitalization was significantly positive at the 1% level with or without control variables, indicating that urban digitalization improvements can significantly increase CEE. Hypothesis 1 is verified. At the same time, by gradually adding control variables, we found that the estimated coefficient of urban digitalization after adding control variables was larger than that without adding time, which proves that the increase of control variables strengthens the influence of urban digitalization on CEE. The performance of the control variables varies. Population density (POPD) was significant positive. The growth of population density will generate positive agglomerative externalities, bringing agglomerative economic benefits such as labor pool and knowledge spillover, and contribute to the advancement of CEE. Science and technology expenditure (AO) can significantly inhibit the improvement of CEE. The above results may be because government spending on science and technology and education does not provide enough support for cleaner technology research and development activities or does not effectively promote green technology in industrial production, but leads to market efficiency loss and resource allocation distortion, which hinders the improvement of CEE. The coefficients of government intervention (GOV) and energy consumption intensity (EI) were not significant, indicating that these two variables cannot effectively inhibit the improvement of CEE. The possible reason is that, from the perspective of government intervention, the more the government spends, the more it invests in environmental protection and pollution control. The better the construction of local environmental regulation mechanisms, the more effectively the government can control carbon emissions. However, excessive government intervention in the market will lead to excessive investment by enterprises, which will lead to resource shortages and the decline of CEE. The regression coefficients of CDI were all significantly positive, and their values gradually increased with the current period, the first lag period, and the second lag period, indicating that the urban digital construction in the current period has an increasing promoting effect on CEE in the current year, the second year, and the third year in the future. The reason for this phenomenon is that human capital accumulation, material capital accumulation, and industrial structure changing all require a certain process in the path of urban digitalization affecting CEE. Therefore, the impact of urban digitalization on CEE through human capital, ICT capital and industrial structure is weakest in the current period. Over time, the capital accumulation promoted by urban digitalization gradually increased, which had an impact on production efficiency, and the industrial structure was gradually optimized. Thus, the promoting effect on CEE is steadily enhanced. Table 6 reports the regression results on the spatial impact of urban digitalization on CEE. First, both SAR and SEM model with different weight matrices, at least one of the spatial autoregressive coefficient rho and the spatial correlation coefficient lambda, which reflects the spatial autocorrelation, pass the significance test, indicating that the CEE of each city and its neighboring cities have a positive spatial correlation. If the neighboring cities improve CEE through capital accumulation and industrial structure adjustment, spatial spillover effects and neighborhood imitation behavior tend to have a driving effect on the improvement of CEE. The urban digitalization coefficient was significantly positive for the three different weights, which shows that urban  Table 7 shows the results of the decomposition of spatial impact of urban digitalization on CEE. The results of the spatial spillover effect decomposition showed that both direct effect and indirect effect coefficients are significantly positive, indicating the presence of spatial spillover effects and that local digital development can significantly improve the CEE of neighboring areas.  Specifically, under the geographical distance weighting matrix, the direct effect of urban digitalization on the CEE was 0.159, which was significant at the 10% confidence level, indicating that the improvement in the level of urban digitalization has a significant positive effect on the CEE in this region. The indirect effect of urban digitalization on CEE was 0.012, which was significant at the 10% level, demonstrating that improvements in urban digitalization are significantly positive in geographically close areas. Nevertheless, the direct effect was larger than the indirect effect, which means that the spatial spillover effect of urban digitalization on CEE is relatively weak. Under the weighted matrix of economic distance, the direct and indirect effects of urban digitalization on CEE were 0.201 and 0.627, respectively, which were significant at the 10% level, indicating that the improvement in urban digitalization levels is significantly positive in both local and economically distant neighboring areas. At the same time, the indirect effect was larger than the direct effect, which means that the impact of urban digitalization on CEE has a solid spatial spillover effect.

Robustness test
The endogenous test In this paper, we adopted two methods to alleviate the possible endogeneity problems. First, we constructed a dynamic panel data model by introducing dependent variables with one-stage lags and used the two-stage SYS-GMM estimation to deal with possible endogeneity. Second, the 2SLS estimation method was used for regression with instrumental variables. Referring to the studies of relevant scholars (Bartik 2009), the tool variable "Bartik Instrument" is constructed. That is, the product of the lagging first order of CDI and the first order difference of CDI (CDI t − 1 × ∆CDI t − 1 ). Column (1) in Table 8 shows the results of SYS-GMM. According to AR (1) and AR (2), the random disturbance term had first-order sequence autocorrelation but no secondorder sequence autocorrelation. The results of Sargan test showed that there was no over-identification bias of instrumental variables in the estimation results, indicating that the estimation results are valid. In summary, the selection of the two-stage SYS-GMM in the dynamic panel model is adequate to alleviate the possible endogeneity.
Columns (2) and (3) in Table 8 show the 2SLS regression results after using instrumental variables. Column (2) shows that the coefficient of the instrumental variable is significantly positive, the significance of the non-discernable test (K-LM test) is significant at 1% level, and the significance of the weak instrumental variable (Wald F test) is lower than 10%, indicating that the selection of instrumental variable is reasonable. After taking endogeneity into account, the coefficient of CDI in the second stage regression results in a significantly positive value at the 1% level, confirming the robustness of the previous regression results.

Substitution of key variables
Considering that some variable selection may have an uncertain impact on the estimation results, this paper conducted a robustness test by substituting key variables. First, replace the explained variable. The ratio of real GDP to CO 2 emission (CEGDP) was taken as another way to measure the efficiency of CO 2 emission, and the expected sign was positive. The results are shown in column (1) of Table 9. The coefficient for urban digitalization development was significantly positive at the 5% level, which is consistent with the above regression results. Second, replace the core  Zhao et al. (2020), the urban digitalization index (CDI2) was reconstructed by using principal component analysis to assign weights to digitalization indexes. The test results are shown in column (2) of Table 9. The results proved that the coefficient of CDI2 was still significantly positive at the 1% level, proving that the conclusions of this paper are reliable.

Change of methods
In this paper, we used different methods such as mixed OLS, random effects, differential GMM, and SDM for fitting the regression to improve the robustness of the results. The regression results (Table 10) demonstrated that whether the model of OLS, random effect, differential GMM, or SDM, the results all confirmed that urban digitalization contributes to improving CEE. The results are consistent with the previous empirical conclusions, proving that changing the empirical analysis method does not change the fundamental conclusions of the research.

Further analysis
Mediating effect analysis Table 11 shows the mediating effect test results. Among them, columns (1) and (2) display the mediation path test results of human capital accumulation. The results of the second step (column 1) test show that the impact of urban digitalization on the intermediary variable LnHUM is significantly positive, and the third step (column 2) test shows that the intermediary variable positively influence CEE. The coefficient signs of θ 1 and α 2 are the same as those of α 1 , indicating that human capital accumulation plays a significant part in mediating the effect of urban digitalization on CEE. Columns (3) and (4) display the mediation path test results of ICT capital accumulation. After the introduction of the intermediary variable in the model, the coefficient signs of θ 1 and α 2 are the same as those of α 1 , indicating that ICT capital accumulation also plays a significant part in mediating the impact of urban digitalization on CEE. With the continuous in-depth implementation of urban digitalization and the continuous improvement of digital infrastructure, ICT capital accumulation level and quality are continuously improved, thus promoting the growth of urban CEE. Columns (5) and (6) display the mediation path test results of industrial structure. After the introduction of the intermediary variable in the model, the coefficient signs of θ 1 and α 2 are the same as those of α 1 , indicating that the upgrading effect of industrial structure also plays a significant part in mediating the impact of urban digitalization on CEE.
The test results of this paper also show that the indirect effect of human capital is 0.132, the indirect effect of ICT capital is 0.707, and the indirect effect of industrial structure is 0.020. All three are significant, and the three mediating effects caused by urban digitalization account for 46.71% of the total effect, which proves that the three mediating effects explored in this paper are significant. Human capital accumulation, ICT capital accumulation and industrial structure are all effective ways for urban digitalization to influence CEE. In this paper, we further used the Bootstrap method to verify the mediating effect of the above variables and thus improve the accuracy and credibility of the mediating effect results. Table 12 reports the results of the Bootstrap test (500 samples). The results showed that the coefficients of the three mediating variables were significantly positive at the levels of 10%, 1%, and 1%, respectively, indicating that human capital accumulation, ICT capital accumulation, and industrial structure upgrading play a mediating role in the impact of urban digitalization on CEE. Table 13 shows the results of the heterogeneity analysis. In this paper, we divided CEE into groups according to the median of geographic location and digital development level, and adopted a double fixed effect model for heterogeneity analysis. The results in columns (1) and (2) proved that the urban digitalization in eastern and central China produced a significant positive influence on CEE. Still, the promoting effect was stronger in central and western China than in eastern China, suggesting that the central and western regions have a more vital late-comer advantage in meeting carbon reduction targets. The reason for this result may be that the central and western regions tend to have slower economic development, higher dependence on traditional resources, and lower energy utilization efficiency compared to the eastern regions. While the development of urban digitalization, along with the application and popularization of digital technologies, can help keep market players better informed about the changing laws of the energy market, thus improving energy factor allocation efficiency.

Heterogeneity test
The results in columns (3) and (4) showed that urban digitalization produces a positive promotion influence to CEE in cities with a high level of digitalization but not in cities with a low level of digitalization. The reason for this result may be that areas with higher levels of urban digitalization have a more obvious advantage in digital infrastructure and digital industry development. Moreover, due to the concentration of a large number of digital innovation talent and innovation capital, these regions can better play the role of digital empowerment under various advantages, and the effect of green emission reduction is noticeable. In areas where urban digitalization is still in its initial stage, there is a lack of digital talent, relatively backward digital infrastructure construction and still low integration and development with industry. The increase in resource consumption in the primary stage of urban digitalization and the effect of digital empowerment cancel each other, resulting in a negligible boost to the CEE from digitalization in this region.

Discussion
This paper provides empirical evidence that urban digitalization is conducive to CEE improvement. This conclusion supports the view that digitalization is "positive" for reducing carbon emissions (Sareen and Haarstad 2021;Xu et al. 2022). Over the long term, the improvement of the urban digitalization level will contribute to CEE by accelerating capital accumulation and optimizing industrial structure. The specific contents are as follows. First, this paper confirms that urban digitalization has a positive influence on CEE. This conclusion remains robust after considering endogeneity, changing dependent variables and estimation methods. This finding further proves the view by some scholars that urban digitalization has deep influence on the ecological environment (Balogun et al. 2019;Su et al. 2021;Mn and Stab 2020). Moreover, there is regional heterogeneity in this effect; that is, the degree of digitalization promotion is lower in areas with better digitalization and higher in areas with poor digitalization. In addition, the impact of urban digitalization on CEE is more pronounced in central and western cities than in eastern cities.  Second, urban digitalization has a significant positive time effect and a spatial spillover effect on CEE. From a perspective of time, the marginal effect of urban digitalization on CEE increases over time. From the standpoint of space, the digitalization of the local city helps to improve the CEE of the neighboring area. This conclusion is consistent with the related research conclusion that there are spatial spillover effects of digitalization on the environment (Li et al. 2021a, b). It is worth noting that considering the geographic distance matrix, the direct impact of urban digitalization on CEE is much larger than the indirect impact. On the contrary, the indirect effect of urban digitalization on CEE is significantly higher than the direct effect under the economic distance weight matrix. This finding deepens the existing literature on spatiotemporal dynamic effects. The above conclusions also provide a broader space for post-study on the spatial-temporal dynamic effects of urban digitalization.
Third, urban digitalization can improve CEE by increasing the human capital accumulation, ICT capital accumulation and industrial structure optimization. All three mechanisms have a partial mediator effect. These findings support existing research (Guo et al. 2020b;Hu et al. 2021) that recognizes the traditional effect of digitalization on human capital accumulation and the upgrading of industrial structure. The difference, however, is that the existing studies do not further discuss the mechanistic implications. In this paper, we take this as a breakthrough point to further explore and prove the mediating mechanism effect of human capital and ICT capital accumulation.
There are some limitations to this paper that provide important avenues for future research. First, this paper measures the level of urban digitalization development based on digital infrastructure, digital economy, digital technology and digital inclusive finance. On the one hand, there are still some shortcomings in the measurement of urban digitalization due to the availability of data. On the other hand, there is a periodicity in the development of urban digitalization, which may have different effects on CEE. In the beginning of urban digitalization, it mainly focuses on infrastructure coverage, while in the later stages, it mainly involves integration and penetration of technology. Subsequent studies can expand and improve on this based on data richness and periodicity of urban digitalization. Second, this paper analyzes the mechanisms of urban digitalization affecting CEE. However, this paper only focuses on three mechanisms, and the effect of urban digitalization on CEE may also be realized by other path mechanisms. The specific mechanistic effects of urban digitalization on CEE need to be explored more extensively in follow-up studies.

Policy implications
(1) Promote CEE with urban digitalization. Urban digitalization development has effectively improved CEE, so we should continue to accelerate urban digitalization and accelerate the development of new digital infrastructure. The government should improve the level of digitalization in the city's economy, society, people's livelihoods, and urban governance and use digitalization to optimize the efficiency of utilization of urban resources. The negative externalities of carbon emissions can be addressed through digital environmental tools to facilitate the implementation of carbon peak and carbon neutrality.
(2) Break down digital barriers and information 'silos' and construct the sharing pattern of ecological environmental data resources within and between regions. In the process of fostering urban digitalization development, cooperation and assistance among cities at different levels of action should be strengthened, and exchanges on digitalization and environmental protection should be encouraged. With the help of a convenient and efficient digital platform, technical cooperation and trade can be carried out to facilitate the exchange of knowledge and technology.
(3) When coordinating and designing relevant carbon reduction policies, relevant government departments need to recognize the main path and source of the impact of urban digitalization on CEE. Seize opportunities for digital transformation and change, and promote industrial structure optimization and upgrading with the help of the digital economy. Attach importance to the cultivation of digital talent and the accumulation of human capital. Formulate and improve ICT investment policies to accelerate the spread of the ICT capital. In addition, different cities should reflect on the dilemma of promoting carbon reduction through digitalization, accurately identify intermediary channels, maximize the environmental impact of urban digitalization development, and enhance the effectiveness of reducing carbon emissions.
(4) Different regions should combine their own conditions to form a unique digitalization development strategy. The eastern and central regions should strengthen technological exchanges, appropriately guide the advanced enterprises and talents in the eastern region to provide targeted support to the central and western regions, adopt digital technology to predict regional carbon emissions, improve the carbon trading market, and adjust the industrial structure and energy utilization technology. Adjusting the pace of digitalization in different regions, breaking down the industry barriers and geographic restrictions on new models and new business forms, so as to improve the differences and synergies in the governance of the digital economy in different regions.

Conclusions
China has set development goals for carbon peak and carbon neutrality in response to global climate change.
Researching the CEE and its promotion mechanism in China under urban digitalization is of great significance to realize urban sustainable development and achieve the "double carbon" goal. It is necessary to form a long-term mechanism to reduce carbon emissions with the help of urban digitalization. In this paper, we use balanced panel data of 282 Chinese cities from 2011 to 2019 as research samples and adopts different empirical methods to test the influence relationship, space-time effect and action path of urban digitalization on CEE. The main conclusions are as follows: (1) During the sample investigation period, urban digitalization can significantly promote the improvement of CEE, and the research conclusion still holds after endogeneity problem treatment and a series of robustness tests. The internal influence mechanism shows that the intermediary channels for urban digitalization to realize CEE upgrading include not only increasing ICT capital accumulation, but also promoting industrial structure upgrading and enhancing human capital accumulation.
(2) The test of spatial-temporal dynamic effects shows that the marginal effect of urban digitalization on CEE increases over time, and there is a significant spatial spillover effect, which is helpful in improving the CEE of neighboring areas.
(3) Heterogeneity analysis shows that urban digitalization has a significant promoting effect on CEE in cities with high digitalization levels. In contrast, this effect is not significant in cities with low levels of digitalization. Urban digitalization can significantly improve the CEE of cities in the East and Midwest, but the CEE enhancement effect of cities in the Midwest is greater than that of cities in the East.
Availability of data and materials All data generated or analyzed during this study are not included in this submission but can be made available upon reasonable request.