Does Digital Infrastructure Improve Urban Economic Resilience? Evidence from the Yangtze River Economic Belt in China

: Under the pressure exerted by COVID-19 and geopolitical conﬂicts, establishing how to enhance urban economic resilience and cope with external risks has become the focus of many studies. This study considers the “Broadband China” program as a quasi-natural experiment and uses panel data from 106 Chinese cities between 2011 and 2020 to explore the inﬂuence of digital infrastructure on urban economic resilience through a difference-in-differences (DID) approach. The results are as follows: (1) Digital infrastructure improves urban economic resilience, and the inﬂuence differs by time and region. (2) Economic vitality, industrial structure upgrading, and industrial structure rationalization either moderate or mediate the impact of the digital infrastructure on economic resilience. Our ﬁndings contribute to a better understanding of how digital infrastructure and economic resilience are related.


Introduction
The current international economic situation is complex and changeable, and the uncertainty caused by new trade protectionism has caused severe economic fluctuations.China's economy is also facing challenges due to reduced international trade and economic recession.The aim of the Sustainable Development Goals set out in the United Nations Agenda 2030 is to build "inclusive, safe, and resilient sustainable cities".As the basic unit of economic activity, the "resilience" of cities in response to uncertain shocks has attracted the attention of many scholars.Urban economic resilience is a crucial indicator for evaluating the urban economy's security, stability, and innovative development [1].Specifically, economic resilience is represented by dynamic resilience with adaptability.When economic development faces external shocks, economic resilience manifests as resistance and resilience to shocks.When the impact persists, economic resilience manifests as adaptability and the regulatory power to deal with environmental changes.After the impact, economic resilience manifests as the innovation and transformational power that promote economic development.Faced with the continuous external shocks and internal risks that cannot be ignored in the current economic development process, the existence of economic resilience is particularly important.Therefore, an in-depth study of the influencing factors and improvement pathways of urban economic resilience are critical for effectively improving China's response to external shocks.
Since resilience was first introduced into urban research, it has shifted from engineering resilience and ecological resilience to evolutionary resilience [2].The concept of engineering resilience points out that resilience can reflect the speed at which a system out of balance due to a disturbance or shock returns to equilibrium.Every impact of the external risks will cause the system itself to start a series of self-healing mechanisms, and related studies focus on the system's resistance to interference [1].Ecological resilience emphasizes that ecosystems have characteristics such as uncertainty [3], and it seems that the system can moderate itself to enter a new state while facing external disturbances.Recently, resilience has been increasingly integrated with theories of adaptive resilience.In the theory of evolutionary economic geography, regional economic resilience refers to the ability of different regions to withstand changes and shocks in competitive markets.This theory focuses on the process of economic adjustment and changes over time [4][5][6].
With the emergence of modern technologies, the global digital economy has experienced rapid promotion.Since China fully implemented the "Broadband China" strategy in 2013, Internet infrastructures, such as the scale of broadband and the level of broadband penetration, have been comprehensively improved.According to the "China Internet Housing Exhibition Status Statistical Report", at the end of 2021, the Internet penetration rate in China was 73.0%.The "Broadband China" policy was released by the Chinese government in 2012, aiming to improve its overall broadband access capabilities.The policy requires that by 2020, the penetration rate of fixed broadband households will reach 70%, and the proportion of administrative villages with broadband access will exceed 98%.To this end, the Chinese government announced model cities with good implementation of the "Broadband China" policy in 2014, 2015, and 2016, respectively.The "Broadband China" policy has significantly improved the urban and rural broadband penetration rate and urban digitalization level, effectively improved the demand support of the urban economy, and guaranteed urban industries' shock-coping capacity.Also, as the material basis for China's digital economy, the Internet has achieved initial coverage in most of the country.After the outbreak of the COVID-19 epidemic, issues related to smart cities and urban resilience have gradually attracted special attention from scholars.Bridging the gap in digital development has gradually become a key issue that needs to be solved to realize the acceleration of cities towards sustainable development [7].
The Yangtze River Economic Belt connects the Eurasia Continental Bridge Corridor and the Yangtze River channel as two horizontal axes, and the coastal Beijing-Harbin Beijing-Guangzhou and Baotou-Kunming channels as three vertical axes.This economic belt has gradually formed a strategic pattern of "two horizontal and three vertical" urbanization, supported by major urban agglomerations and with other areas on the axis as important components.According to the China Statistical Yearbook, it accounts for around 21% of the country's land area and more than 40% of its total GDP.At the same time, it straddles the three major regions of China, with different natural and social conditions.It has become a specialized region for scholars to study China's spatial imbalance and coordinated regional development.Considering administrative region changes and data availability, this study chooses 106 cities as a research sample to examine the influence of digital infrastructure development on urban economic resilience.This article measures urban economic resilience through GDP and its fluctuation level and uses the "Broadband China" policy demonstration city as a dummy variable to conduct a DID test to investigate the relationship between digital infrastructure construction and urban economic resilience.Considering the correlation between urban economic vitality and urban economic resilience, this study uses nighttime light data as an indicator of urban economic vitality to measure the intermediary effect.Since industrial structures are an important part of the urban economic development process, this study uses the industrial rationalization index to measure the rationalization level of the urban industrial structure as a moderating variable.In addition, control variables such as the level of opening of the city to the outside world, the dependence of residents on savings etc., are included.The calculation of specific indicators will be described in detail below.
The remainder of this paper is arranged as follows: Section 2 presents the literature review, while policy context and research assumptions are covered in Section 3. Section 4 presents the methodology and data.Section 5 provides the findings of this study, and the related mechanism effect is explained in Section 6.Finally, Section 7 contains the conclusions and suggestions.

Urban Economic Resilience
Resilience refers to maintaining a system's organizational structure after certain state variables are perturbed.Subsequently, the concept of resilience was introduced into economics.In the existing literature, there has been extensive research on the definition and influencing factors of economic resilience.In terms of defining the concept of economic resilience, scholars mainly focus on the concept of physical resilience.Reggiani et al. (2002) introduced economic resilience into the spatial economic system, pointing out that resilience is the capacity of an economic system to withstand external shocks without affecting its organizational functions [8].Martin and Sunley (2015) defined economic resilience as resistance, adaptability, and renewal forces based on the perspective of evolutionary resilience [9].
In terms of factors affecting economic resilience, empirical studies mainly focus on industrial diversity and technological innovation.Brown and Greenbaum (2017) pointed out that the role of industrial diversity in economic resilience is not only to disperse risks and resist shocks but also to help cities make structural adjustments [10].The diversified agglomeration of industries can achieve urban economic stability and industrial upgrading through synergy and complementarity, thereby attracting idle financial and human resources between urban networks.It also helps in achieving economies of scale, effectively reducing production costs and improving economic efficiency.In this process, the interweaving of different types of industrial cluster networks has improved urban infrastructure, and supply chain facilities, thereby reducing the operating costs of urban industries.Therefore, limited manpower, material resources, and funds can be concentrated on product and service research and development, promote the pace of industrial structure transformation and upgrading, and then enhance the urban economy's ability to resist shocks [11].At the same time, innovation is a driving force for economic growth, innovation capabilities, and innovation ecosystems.It can realize the optimization of the internal process structure of the enterprise from a micro perspective, thereby improving the enterprise's management level, enhancing the enterprise's innovation ability, environmental adaptability, and resilience, and driving the region to achieve an overall improvement in its level of resilience [12][13][14].

Digital Infrastructure
Digital infrastructure can promote the development of digital technology, thereby affecting the resilience of urban economies.The neoclassical growth theory states that technology is a key factor in economic growth, while the endogenous economic growth theory further internalizes technology as the marginal return increasing the effect of knowledge [15], thereby explaining the important position of technology in economic resilience.The progress of technology and the dissemination of knowledge rely on the support of infrastructure.Based on the above theories, considering the process of China's construction of digital infrastructure, we use the implementation of the "Broadband China" policy as a dummy variable to measure the development of digital infrastructure.
In the digital age, the impact of digital infrastructure construction on urban economic resilience is mainly reflected in the following aspects: First, a good level of digital infrastructure construction can improve decision-making flexibility, control, and support for the decision-making process in urban industrial sectors [16].Second, a sound digital infrastructure is an external driver of social entrepreneurial activities [17].Higher entrepreneurial vitality can improve the efficiency of resource flow and consumption vitality within a city with risk shocks, thereby ensuring the city's ability to cope with uncertain shocks.Third, technological upgrades brought about by the construction of digital infrastructure can improve the location awareness and detection capabilities of cities for external risks, break the blockage of urban dimensions, establish large-scale databases, and enhance the ability of different departments to jointly respond to risk crises [18].In addition, good digital construction can also effectively improve the livability of the city [19], thereby attracting a floating population and active capital and enhancing the economic strength of the city itself.
Using cities in the Yangtze River Delta as a sample, Guo et al. (2023) found that digital infrastructure had the most significant impact on improving economic resilience [20].

Digital Infrastructure and Urban Economic Resilience
As the most active field of economic development, China's digital infrastructure has maintained high growth in the past decade.Therefore, establishing how to effectively stimulate the effect of digital infrastructure on improving economic resilience is an important research topic.This raises the research question of whether the digital infrastructure can contribute to the resilience improvement of the urban economy.
Many scholars have conducted relevant research on the relationship between digitalization and resilience.Nordine et al. ( 2023) have studied the resilience of digitalization to external risk shocks from the perspective of enterprises and found that accelerating the digital transformation of enterprises is crucial for economic recovery and improving the resilience of cities [21].Francesco et al. ( 2023) conducted research by establishing a simulation decision-making framework and found that digitalization can ensure that the urban supply chain has sufficient resilience to deal with risk shocks and maintain a sufficient level of performance [22].Marshall et al. (2023) conducted research on the level of digitalization in rural Australia and found that digitalization can improve the ability of individuals and organizations to effectively respond to and recover from natural disasters [23].However, there is a lack of research that classifies the resilience of different industries and compares it to the economic resilience of the city.
Additionally, only a few scholars have used the DID model to conduct research on digital infrastructure construction and economic resilience.Mao et al. [24] used the DID approach to examine the correlation between digital infrastructure and economic resilience from the perspective of government governance.Guo et al. [20] argued that the construction of network infrastructure has significantly improved economic resilience by promoting industrial structure upgrading and technological innovation.However, previous research mainly uses the index system method to assess urban economic resilience, which makes it hard to overcome the problem of potential causal confusion.Therefore, this study believes that it is quite necessary to examine the influence of digital infrastructure on urban economic resilience by using the non-indicator system method.
Compared with previous studies, the innovation of this paper is mainly reflected in the following points.(1) Integrating digital infrastructure and urban economic resilience into the same research framework and analyzing the theoretical mechanism of digital infrastructure improving urban economic resilience provides a theoretical basis for further research on how to ensure urban economic stability.(2) Different from traditional econometric methods, in this paper we combine the DID model with mechanism testing to explore the mechanism effects in the process of digital infrastructure improving urban economic resilience, which provides a new empirical approach for future research.(3) We divide the Yangtze River Economic Belt into east, central, and west, and this study uses the regional heterogeneity test to analyze the impact of digital infrastructure in different regions on improving urban economic resilience.

Policy Background for Digital Infrastructure
In the past two decades, digital infrastructure construction has been proven to have an influence on economic development.More and more countries have begun to focus on constructing digital infrastructure.Along with the adjustment of the economic structure, the Chinese government has elevated the construction of digital infrastructure to a strategic level and tries to guide enterprises to shift from the traditional model to the digital model [25].The "Broadband China" strategy was first implemented in 2013, and then two other batches of pilot cities were announced from 2014 to 2016 (as in Figure 1), aiming to improve the application level of broadband networks.The cities (clusters) selected as the demonstration sites entered a construction period of about 3 years, with specific construction and development goals in terms of Internet user base, Internet connection speed, and coverage.Since the strategy was implemented, China's digital infrastructure construction has achieved remarkable results.According to the 2021 Communications Industry Statistical Bulletin, by the end of 2021, the number of Internet broadband access ports in China reached 1.02 billion, with an increase of 7.6%.
other batches of pilot cities were announced from 2014 to 2016 (as in Figure 1), aiming to improve the application level of broadband networks.The cities (clusters) selected as the demonstration sites entered a construction period of about 3 years, with specific construction and development goals in terms of Internet user base, Internet connection speed, and coverage.Since the strategy was implemented, China's digital infrastructure construction has achieved remarkable results.According to the 2021 Communications Industry Statistical Bulletin, by the end of 2021, the number of Internet broadband access ports in China reached 1.02 billion, with an increase of 7.6%.
Therefore, this article selected 106 Chinese prefectural cities along the Yangtze River Economic Belt, including 45 treatment cities and 61 control cities.The research area is shown in Figure 1, and cities that joined in the "Broadband China" policy in different years are colored differently.

Theorized Mechanisms and Hypotheses
Figure 2 lists the mechanisms of this study, and the two hypotheses are as follows.First, the digital infrastructure enhances the resilience of cities by improving the quality of economic development.The construction of digital infrastructure provides economic development with many advantages, such as processing large-scale data and reducing transaction costs, all of these are favorable to the increase in urban innovation, which strengthens economic resilience.Second, the digital infrastructure enhances the level of economic resilience and maximizes the efficiency of resource allocation.The use of digital technology greatly reduces the temporal and spatial barriers in labor market matching, thereby contributing to the improvement of resource allocation efficiency [26] and urban economic resilience.Finally, digital infrastructure improves the resilience of urban economies by acting on global value chains.Moreover, optimizing resource allocation and promoting technological innovation are essential to improving the division of labor status of urban enterprises in the global value chain, thereby improving urban economic resilience.Thus, we propose Hypothesis 1.Therefore, this article selected 106 Chinese prefectural cities along the Yangtze River Economic Belt, including 45 treatment cities and 61 control cities.The research area is shown in Figure 1, and cities that joined in the "Broadband China" policy in different years are colored differently.

Theorized Mechanisms and Hypotheses
Figure 2 lists the mechanisms of this study, and the two hypotheses are as follows.First, the digital infrastructure enhances the resilience of cities by improving the quality of economic development.The construction of digital infrastructure provides economic development with many advantages, such as processing large-scale data and reducing transaction costs, all of these are favorable to the increase in urban innovation, which strengthens economic resilience.Second, the digital infrastructure enhances the level of economic resilience and maximizes the efficiency of resource allocation.The use of digital technology greatly reduces the temporal and spatial barriers in labor market matching, thereby contributing to the improvement of resource allocation efficiency [26] and urban economic resilience.Finally, digital infrastructure improves the resilience of urban economies by acting on global value chains.Moreover, optimizing resource allocation and promoting technological innovation are essential to improving the division of labor status of urban enterprises in the global value chain, thereby improving urban economic resilience.Thus, we propose Hypothesis 1.In addition to the direct impact of digital infrastructure on economic resilience, is there some other indirect influence?That is, digital infrastructure can affect a particular variable, and this variable plays a role in affecting urban economic resilience, which is the so-called intermediary effect.The construction of digital infrastructure helps promote urban digital vitality, while urban digital vitality can promote the circulation of factor endowments and effectively improve the overall economic strength of the city.Therefore, urban economic vitality is likely to play an intermediary role in the impact of digital infrastructure on economic resilience.This paper identifies urban economic activities based on the radiometric calibration night light data and uses them to symbolize the economic vitality of cities. Elvidge et al. [27] pointed out that light data are suitable for observing human activities and indicate economic activity.
Therefore, how does digital infrastructure play a positive role in promoting urban economic resilience through urban economic vitality?On the one hand, digital infrastructure has positive impacts on the economic vitality of cities.The digital economy can achieve the revitalization of urban economic vitality by reducing information and communication costs, simplifying redundant links, and improving economic activity efficiency [28,29].On the other hand, from the perspective of urban cohesion, Regev and Lihi (2022) studied the strengthening effect of urban vitality on urban cohesion under certain circumstances [30], to improve the city's overall risk impact in the face of uncertain risk shocks.Thus, we propose Hypothesis 2. In addition to the direct impact of digital infrastructure on economic resilience, is there some other indirect influence?That is, digital infrastructure can affect a particular variable, and this variable plays a role in affecting urban economic resilience, which is the so-called intermediary effect.The construction of digital infrastructure helps promote urban digital vitality, while urban digital vitality can promote the circulation of factor endowments and effectively improve the overall economic strength of the city.Therefore, urban economic vitality is likely to play an intermediary role in the impact of digital infrastructure on economic resilience.This paper identifies urban economic activities based on the radiometric calibration night light data and uses them to symbolize the economic vitality of cities. Elvidge et al. [27] pointed out that light data are suitable for observing human activities and indicate economic activity.

Hypothesis 2. Digital infrastructure enhances urban economic resilience through urban economic vitality.
Therefore, how does digital infrastructure play a positive role in promoting urban economic resilience through urban economic vitality?On the one hand, digital infrastructure has positive impacts on the economic vitality of cities.The digital economy can achieve the revitalization of urban economic vitality by reducing information and communication costs, simplifying redundant links, and improving economic activity efficiency [28,29].On the other hand, from the perspective of urban cohesion, Regev and Lihi (2022) studied the strengthening effect of urban vitality on urban cohesion under certain circumstances [30], to improve the city's overall risk impact in the face of uncertain risk shocks.Thus, we propose Hypothesis 2.
Hypothesis 2. Digital infrastructure enhances urban economic resilience through urban economic vitality.

Methodology 4.1.1. DID Approach
In this paper we used the DID approach to examine the effects of digital infrastructure construction on urban economic resilience.The benchmark regression model is as follows: Here, Resilience is the dependent variable, measuring the degree of economic resilience.Digital is the independent variable, which indicates a binary dummy variable according to whether the city participates in the "Broadband China" policy at year t.Control represents different control variables, and λ is its coefficient.Constant terms, the city fixed effect, the year fixed effect, and error terms are represented by α 0 , u i , v t , and ε it , respectively.
An important premise for adopting the DID method is that there is no major difference in the change rate of economic resilience between the treatment group and the control group before policy implementation.Therefore, the development trend of economic resilience for the two groups should remain parallel before the policy.To test the parallel trend hypothesis and avoid multicollinearity problems, we took the year 2014, when the policy started, as the base period and constructed the following model based on the practice of most scholars [31].Considering this, Equation (2) was constructed.By comparing ϕ k , we can conclude whether the parallel trend test has been passed.
Here, "Policy" is a dummy variable.If the city participates the "Broadband China" policy at year t, a value of 1 is assigned, otherwise 0 is.Among them, k < 0, k = 0, and k > 0 indicate the year before, during, and after the policy is implemented, respectively.We mainly focus on the coefficient ϕ k before the policy implementation year (k < 0).If it is not significant when k < 0, this means the parallel trend test is passed.As presented in the equation, when k < 0, the confidence interval contains 0, indicating that the coefficient is not significant.Only when the parallel trend assumption is satisfied can the DID approach be utilized in this study, and the empirical results be reliable.

Robustness Test and the Mediating Effect
In addition, other robustness tests like the instrumental variable (IV), PSM-DID, placebo test, etc., are also conducted in this study.
As mentioned in Hypothesis 2, urban economic vitality is likely to play a role in the process of digital infrastructure affecting urban economic vitality.That is, there may be an influence pathway of "digital infrastructure-urban economic vitality-urban economic resilience".Therefore, to explore the intermediary effects of economic vitality on urban economic resilience, this study selected rationalization as an intermediary variable, and established the following model: Equation ( 3) is used to test the impact of digital infrastructure on intermediary variables.Among them, β 1 measures the impact of digital infrastructure on urban economic vitality, which is the key coefficient of Equation (3).If β 1 is positive and statistically significant, it means that digital infrastructure plays a positive role in promoting urban economic vitality, otherwise it is irrelevant.Equation ( 4) is applied to check whether there was a mediating effect.Of the variables, the coefficient γ 2 is mainly used to reflect the correlation between economic vitality and urban economic resilience.If γ 2 is positive and significant, it indicates the promoting effect of economic vitality on urban economic resilience.If the β 1 in Equation ( 3) and the γ 1 and γ 2 in Equation ( 4) pass the significance test, the correctness of Hypothesis 2 is reflected.

The Moderating Effect
To further explore how industrial structure affects the causality between digital infrastructure and urban economic resilience, the following models were constructed: Here, Mod represents the moderating variables.Based on Equation ( 5), the cross-term of the moderating variables and digital infrastructure was added, and then we constructed Equation (6).If ρ 3 is significant, it indicates the existence of a moderating effect.

Variables
The summary statistics for each of the variables are provided in Table 1 and the economic resilience in 2020 is depicted in Figure 3. Notes: Due to administrative region changes and data availability, 106 cities were selected for this study.
In the above table, resilience is the explained variable, which is used to measure the city's ability to resist risk shocks.The greater the value of resilience, the stronger the city's economic resilience.Digital is an explanatory variable that is used to judge whether the digital infrastructure construction condition of the sample cities have changed.In terms of control variables, save is used to judge the total savings of the urban residents.Excessive savings willingness may inhibit consumption and reduce demand, which is not conducive to economic stability.Size is used to judge the size of the market, and a larger market helps to provide for residents' needs during economic shocks.Open is used to measure the degree of openness of the city's economy to the outside world.An overly open market may reduce the economy's resistance to external risks, which is not conducive to the stability of the city's economy.Finance is used to measure the degree of development of the financial market.A good financial system helps the urban economy repair itself with the help of external capital flows when it encounters a shock.Government is the intensity of government intervention.When this index is high, it means that the degree of market freedom is low, which is not conducive to the self-adjustment of enterprises.Urban represents the level of urbanization, the higher the level, the higher the degree of urban economic development and the stronger its ability to resist risks.The intermediary variable "activity" represents the vitality of the city's economy and can reflect the degree of activity of urban residents and enterprises.The higher the degree, the stronger the self-repair ability of the economy and the stronger its adaptability to shocks.The adjustment variable "Sr" represents the degree of rationalization of the urban industrial structure layout.A healthy and reasonable urban industrial layout is conducive to the internal self-circulation of the urban economy and enhances its ability to isolate external risks.
Urban represents the level of urbanization, the higher the level, the higher the degree of urban economic development and the stronger its ability to resist risks.The intermediary variable "activity" represents the vitality of the city's economy and can reflect the degree of activity of urban residents and enterprises.The higher the degree, the stronger the selfrepair ability of the economy and the stronger its adaptability to shocks.The adjustment variable "Sr" represents the degree of rationalization of the urban industrial structure layout.A healthy and reasonable urban industrial layout is conducive to the internal selfcirculation of the urban economy and enhances its ability to isolate external risks.

Dependent Variable
After the concept of resilience was introduced into the field of economics, it focused on two aspects: the economy's ability to resist external risk shocks and the economy's ability to recover and upgrade after the shock [8,9].Therefore, this paper defines the indicators of economic resilience from two perspectives.On the one hand, it examines whether the urban economy has enough strength to survive the economic shock; on the other hand, it focuses on whether the urban economy can respond to shocks and self-repair from them.In terms of measuring the methods of economic resilience, there are two main methods, namely the single indicator method and the indicator system method.By artificially selecting indicators to build an indicator system, the impact of the difference in indicator dimensions can be removed through the entropy method, but it still cannot eliminate the subjectivity biases of indicator selection.After comprehensive consideration, in this paper we choose the single index method to measure economic resilience.
Since most risk events have a certain degree of contingency, simply selecting an index from a specific aspect of the economy to measure economic strength is likely to lead to distortion [32].Considering the World Bank and the International Monetary Fund usually use GDP as a measure of economic strength, it is one of the appropriate indicators for measuring economic strength [33,34].Therefore, in this paper we intend to use GDP to measure the strength of the urban economy against risks.On the other hand, forcibly

Dependent Variable
After the concept of resilience was introduced into the field of economics, it focused on two aspects: the economy's ability to resist external risk shocks and the economy's ability to recover and upgrade after the shock [8,9].Therefore, this paper defines the indicators of economic resilience from two perspectives.On the one hand, it examines whether the urban economy has enough strength to survive the economic shock; on the other hand, it focuses on whether the urban economy can respond to shocks and self-repair from them.In terms of measuring the methods of economic resilience, there are two main methods, namely the single indicator method and the indicator system method.By artificially selecting indicators to build an indicator system, the impact of the difference in indicator dimensions can be removed through the entropy method, but it still cannot eliminate the subjectivity biases of indicator selection.After comprehensive consideration, in this paper we choose the single index method to measure economic resilience.
Since most risk events have a certain degree of contingency, simply selecting an index from a specific aspect of the economy to measure economic strength is likely to lead to distortion [32].Considering the World Bank and the International Monetary Fund usually use GDP as a measure of economic strength, it is one of the appropriate indicators for measuring economic strength [33,34].Therefore, in this paper we intend to use GDP to measure the strength of the urban economy against risks.On the other hand, forcibly stabilizing economic fluctuations, such as by injecting cheap credit into the banking system, often leads to more catastrophic collapses [35].In fact, it is like small tears and strains in muscles, which can be strengthened through self-repair [36].The negative impact of risks on the economy is also an opportunity for the economy to achieve self-repair and upgrade in the process of self-evolution [37].Therefore, GDP volatility is not always a negative indicator.The recession rate of the GDP can effectively reflect the urban economy's response to risk shocks, while the growth rate of the urban economy can reflect its self-upgrading ability.In this study, the absolute value of the GDP fluctuation level is used to measure the city's response ability to economic risk.Furthermore, considering that there are unit and numerical differences between GDP and GDP volatility, this study standardizes them to eliminate the impact of their magnitudes and units on measurement.
Therefore, the resilience of urban economies is measured by comparing changes in economic output and their economic strength [8].Combining the measurement method by Feng et al. (2023) [38] and the above theoretical analysis, we set the following model: Here, Resilience is the explanatory variable.GDP is the normalized GDP based on 2010 and after excluding price factors, while ∆gdpv is the normalized value of the absolute change in China's GDP growth rate.The larger the value, the higher the resilience of the urban economy.

Independent Variable
This paper generated a "Digital" dummy variable.That is, if a city was established as a pilot city in year t, the value was 1 for year t and beyond, otherwise it was 0. Due to administrative region changes and data availability, a total of 106 cities were included for analysis in this study, with 45 cities as the treatment group and 61 cities as the control group.

Other Variables
The literature has proven that urban economic resilience is affected by economic vitality and industrial structure [39].Therefore, in this study we chose the vitality of the economy as a mediating variable and the rationalization of industrial structure as a moderating variable.The economic vitality was measured according to radiometric calibration night light data.The measurement method was the average of the brightness values on each pixel in the area, and the data source was Harvard Dataverse.The industrial structure rationalization was measured through a rationalization index [40].The ratio of the output value in the tertiary industry to that of the secondary industry was used to calculate the industrial structure upgrade.In addition, considering factors that may affect economic resilience, some other variables were chosen: the per capita savings of urban residents (Save), measured by the year-end deposit balance of financial institutions over the urban population; the size of the urban market (Size), measured by the retail sales of consumer goods over GDP; the dependence on foreign capital (Open), measured by the amount of urban FDI over GDP; financial market activity (Finance), measured by the deposits and loans of financial institutions over GDP; the ability of the government to distribute resources (Government), measured by government expenditure over GDP; the level of urban infrastructure (Infrastructure), measured by highway mileage over urban area; and the urbanization process (Urban), measured by the urban population over the total population.

Data Source
The China City Statistical Yearbook, the China Urban Construction Statistical Yearbook, the China Statistical Yearbook for Regional Economy, and the Statistical Bulletin on National Economic and Social Development were used as sources of the data.In addition, the interpolation method was applied when missing values were present.

Parallel Trend Test
The main purpose of the parallel trend test is to verify a key assumption in the difference-in-differences (DID) method.That is, the treatment group and the control group are parallel in time trends before treatment, which is an important premise for using the DID method.Thus, a parallel trend test was constructed based on Equation (2).Since ϕ k is −0.035 and not significant, it indicates that the research sample passes the parallel trend test.Furthermore, the range of dotted lines in the line chart reflects the significance of ϕ k .When the dashed line intersects the x-axis, ϕ k is not significant, which indicates no significant relationship between digital infrastructure and economic resilience.When the dashed line does not intersect the x-axis and is located above it, ϕ k is significant, and there is a significant and positive relationship between them.According to Figure 4, there was no discernible difference between the groups before the policy in terms of economic resilience.After the implementation of the policy, significant differences could be observed, indicating that the research sample passed the parallel trend test.In addition, the effect of digital infrastructure construction on urban economic resilience was most significant in the two years after the policy was applied.
the interpolation method was applied when missing values were present.

Parallel Trend Test
The main purpose of the parallel trend test is to verify a key assumption in the difference-in-differences (DID) method.That is, the treatment group and the control group are parallel in time trends before treatment, which is an important premise for using the DID method.Thus, a parallel trend test was constructed based on Equation (2).Since φk is −0.035 and not significant, it indicates that the research sample passes the parallel trend test.Furthermore, the range of dotted lines in the line chart reflects the significance of φk.When the dashed line intersects the x-axis, φk is not significant, which indicates no significant relationship between digital infrastructure and economic resilience.When the dashed line does not intersect the x-axis and is located above it, φk is significant, and there is a significant and positive relationship between them.According to Figure 4, there was no discernible difference between the groups before the policy in terms of economic resilience.After the implementation of the policy, significant differences could be observed, indicating that the research sample passed the parallel trend test.In addition, the effect of digital infrastructure construction on urban economic resilience was most significant in the two years after the policy was applied.To make the parallel trend test more convincing, this study conducted an econometric regression to analyze the trend before the implementation policy for the treated group, and the analysis results are shown in Table 2.During the econometric regression, the main purpose of constructing interaction terms is to explore whether there are significant differences in urban economic resilience between the two groups before policy implementation.As shown in Table 2, the coefficient of the interaction term (treatment#before-2015) is 0 and not statistically significant, which means that there is no significant difference between the treatment group and control group in economic resilience before policy implementation.This can be interpreted as the two groups of samples being parallel in trend, and with no significant difference before the policy implementation [41].
Additionally, in this paper we also take urban economic resilience as the explained variable and use regression to test whether the treatment group and the control group To make the parallel trend test more convincing, this study conducted an econometric regression to analyze the trend before the implementation policy for the treated group, and the analysis results are shown in Table 2.During the econometric regression, the main purpose of constructing interaction terms is to explore whether there are significant differences in urban economic resilience between the two groups before policy implementation.As shown in Table 2, the coefficient of the interaction term (treatment#before-2015) is 0 and not statistically significant, which means that there is no significant difference between the treatment group and control group in economic resilience before policy implementation.This can be interpreted as the two groups of samples being parallel in trend, and with no significant difference before the policy implementation [41].Additionally, in this paper we also take urban economic resilience as the explained variable and use regression to test whether the treatment group and the control group have parallel trends before the "Broadband China" policy is implemented, and the results are shown in Figure 5.In Figure 5, we can see that before the policy took effect in 2015, the treatment group and the control group were almost parallel in the trend of urban economic resilience, which once again proves that the research sample in this study has passed the parallel trend test.
Sustainability 2023, 15, x FOR PEER REVIEW 12 of 21 have parallel trends before the "Broadband China" policy is implemented, and the results are shown in Figure 5.In Figure 5, we can see that before the policy took effect in 2015, the treatment group and the control group were almost parallel in the trend of urban economic resilience, which once again proves that the research sample in this study has passed the parallel trend test.

Benchmark Regression Results
Table 3 shows the results of the DID analysis.From columns (1) to ( 6), the coefficient of Digital is consistently significant at the 1% level, which shows that the development of digital infrastructure improves urban economic resilience.Hypothesis 1 is valid.Column (1) is the result of OLS regression, and column ( 2) is the result after adding the control variables.Subsequently, the individual variable was controlled, and the results are shown

Benchmark Regression Results
Table 3 shows the results of the DID analysis.From columns (1) to ( 6), the coefficient of Digital is consistently significant at the 1% level, which shows that the development of digital infrastructure improves urban economic resilience.Hypothesis 1 is valid.Column ( 1) is the result of OLS regression, and column ( 2) is the result after adding the control variables.Subsequently, the individual variable was controlled, and the results are shown in columns ( 3) and ( 4), respectively.Columns ( 5) and ( 6) show the regression results with both city and time fixation.According to column ( 6), the coefficient of Digital is 0.062 and statistically significant at the 1% level.This means those cities affected by the construction of digital infrastructure will display a higher ability to withstand, adapt, and recover when facing external uncertainty shocks.In addition, the coefficients of Save and Open are negative, indicating that the dependence of cities on foreign investment and residents' dependence on savings have a negative impact on the resilience of the urban economy.Therefore, to achieve the goal of improving economic resilience, policymakers should analyze the impact of residents' savings on the urban economy and ensure the city has a high level of self-circulation to accelerate the construction of digital infrastructure.Otherwise, once the external economic environment fluctuates, the risk will spread quickly to the interior of the city.

Spatio-Temporal Heterogeneity Test
Considering that the geographical location may lead to large differences in the environmental, economic, and social characteristics of the sample cities, this may affect urban economic resilience.Therefore, by dividing the sample into different regions, it is much easier to capture the heterogeneity between different regions.In this study, the sample was divided into eastern, central, and western regions according to the Chinese Bureau of Statistics in 2019, and regression tests were carried out separately.
According to Table 4, the effects in all three regions are positive and significant at the 1% level.The strongest impact is in the eastern region, followed by in western and central regions.In the eastern region, compared with cities that did not join the policy, economic resilience for cities that joined increased by 13.7%.In addition, the increase in economic resilience in the central and western regions reached 2.5% and 3.4%, respectively.The impact of digital infrastructure construction on resilient economic growth in the eastern region is more significant than in other regions.Endogeneity refers to the existence of correlations between variables, which may lead to bias in regression estimates.In empirical research, the problem of endogeneity often arises because the causal relationship between variables may be bidirectional.By using the lagged terms of explanatory variables as instrumental variables, this study tries to eliminate endogeneity issues and thereby more accurately estimate causal relationships.Therefore, this study performed lagging first-order and second-order regression of the explanatory variables (Digital) as tool variables to test their robustness.Therefore, the explanatory variables (Digital) were treated laggingly, and regression was performed under the conditions of controlling for individuals and time, and the results are in Table 5.The coefficients of the lagging first-order variable (L1.Digital) and lagging second-order variable (L2.Digital) were 0.058 and 0.056, respectively, and significant at the 1% level.This indicates the positive effect of the construction of digital infrastructure on economic resilience.

PSM-DID Estimation
The PSM-DID combines the methods of propensity score matching (PSM) and DID, with the purpose of improving the accuracy of causal inferences.Considering that the initial differences between the treatment group and the control group may lead to biased estimates, we use the PSM-DID method in this article to eliminate the impact of the initial differences.First, the similarity of the samples needs to be calculated.This study uses the propensity score as the matching basis, that is, calculating the linear propensity index and grouping the sample similarity.Secondly, a proper matching method is chosen.As the most used matching method, the nearest neighbor matching method can screen out the individual value in the control group with the smallest difference in propensity score from the treatment group, and it is used for the PSM-DID test.
This study performs PSM on the data to reduce selection bias between the treatment and control groups, and then regression is performed on the matched data to estimate the accurate effect.To test whether the control variables have an impact on the analysis results, this study uses methods of not adding and adding control variables (the same as in Table 3) to conduct analysis on the premise that the samples have been rematched, and the test results are shown in Figure 6.In Table 6, column (1) presents the result without control variables, while column (2) with control variables.The results were positive and significant, indicating that digital infrastructure improves economic resilience.
the test results are shown in Figure 6.In Table 6, column (1) presents the result without control variables, while column (2) with control variables.The results were positive and significant, indicating that digital infrastructure improves economic resilience.

Placebo Test
The purpose of the placebo test is to prevent the treatment group and the control group from being affected by other related variables.Therefore, in this study we conduct a placebo test, replace the treatment group in the sample, and apply the newly generated pseudo-treatment group and the control group to the test again.If the regression result after regrouping is insignificant, it can be explained that the regression result changed when the sub-sample was changed.Therefore, the original regression result is not due to coincidence, which can demonstrate the robustness of the regression result.
There were 61 cities in the control group, and we randomly selected 45 cities from 106 cities as the "pseudo treatment group".As these 45 cities were pilot cities for the "Broadband China" policy and the other cities were the control group, we generated a "pseudo policy dummy variable" (interaction term) for regression.Interactions were randomly selected 500 times to check if the coefficients differed from the baseline estimation.
In the 500 samples, 100% of the regression results were on the left side of the baseline regression coefficient.Subsequently, this study plotted the results of 500 sampling regressions.Considering that the difference between K density and P value will reduce the interpretation of the image, the K density line was removed and redrawn, as shown in Fig- ure 7b.As can be seen in Figure 7a, the random integration coefficient deviates from the true value, and it is clear from Figure 7b that the kernel density atlas of the observed values is spread around 0. Overall, the coefficients are mostly concentrated near zero, with most estimates having p-values greater than 0.1, indicating that our estimation results are

Placebo Test
The purpose of the placebo test is to prevent the treatment group and the control group from being affected by other related variables.Therefore, in this study we conduct a placebo test, replace the treatment group in the sample, and apply the newly generated pseudo-treatment group and the control group to the test again.If the regression result after regrouping is insignificant, it can be explained that the regression result changed when the sub-sample was changed.Therefore, the original regression result is not due to coincidence, which can demonstrate the robustness of the regression result.
There were 61 cities in the control group, and we randomly selected 45 cities from 106 cities as the "pseudo treatment group".As these 45 cities were pilot cities for the "Broadband China" policy and the other cities were the control group, we generated a "pseudo policy dummy variable" (interaction term) for regression.Interactions were randomly selected 500 times to check if the coefficients differed from the baseline estimation.In the 500 samples, 100% of the regression results were on the left side of the baseline regression coefficient.Subsequently, this study plotted the results of 500 sampling regressions.Considering that the difference between K density and P value will reduce the interpretation of the image, the K density line was removed and redrawn, as shown in Figure 7b.As can be seen in Figure 7a, the random integration coefficient deviates from the true value, and it is clear from Figure 7b that the kernel density atlas of the observed values is spread around 0. Overall, the coefficients are mostly concentrated near zero, with most estimates having p-values greater than 0.1, indicating that our estimation results are unlikely to be obtained by chance and less likely to be influenced by other policies or random factors.This indicates that the regression result passed the placebo test.
unlikely to be obtained by chance and less likely to be influenced by other policies or random factors.This indicates that the regression result passed the placebo test.

Other Robustness Tests
In this study, we also conduct other robustness checks, namely, the replacement of dependent and independent variables, the removal of outliers, and the adjustment of the samples.First, the purpose of replacing the explained variables and explanatory variables is to evaluate the robustness of the results to determine whether the analysis results are affected by the choice of a specific calculation method.Secondly, the purpose of shrinking the tail is to remove the impact of extreme values on the empirical results.The existence of extreme values can have an adverse effect on statistical analysis, leading to increased bias and variance in parameter estimates.By shrinking the tail, the impact of extreme values on the analysis results can be reduced.Finally, this study adjusts the sample year to ensure that the regression results are not just due to the specific impact of a certain year.
The results of the additional robustness tests are shown in Table 7.To prevent the calculation method of the dependent variable from causing incidences in the results, we replaced the calculation method of the dependent variable (Resilience) in Equation ( 8) to test whether the previous empirical results have universality.Y represents the annual GDP value, i represents the city, and r represents the country.The regression results are shown in columns (1) and (2) of Table 7.
Additionally, this study replaced the calculation method of the explanatory variable (Digital).We selected the number of Internet broadband access interfaces, the number of telephone users, the number of mobile phone users, the number of employees in telecommunications-related industries, and the telecom service income and used them to calculate a new Digital through the entropy method [42].The regression without and with control variables was conducted separately, and the results are in columns (3) and (4).
Considering the extreme values in the data, to reduce the impact of data anomalies, in this study we conduct quantile processing on the explanatory variables and tail shrinking, thereby allowing the data at less than 1% and more than 99% to be replaced by the data at 1% and 99%.Column (5) displays the analysis results.Finally, considering that cities joined the "Broadband China" policy every year after 2014, the effect was reflected in each of the three years of 2015, 2016, and 2017.To test whether there was a high

Other Robustness Tests
In this study, we also conduct other robustness checks, namely, the replacement of dependent and independent variables, the removal of outliers, and the adjustment of the samples.First, the purpose of replacing the explained variables and explanatory variables is to evaluate the robustness of the results to determine whether the analysis results are affected by the choice of a specific calculation method.Secondly, the purpose of shrinking the tail is to remove the impact of extreme values on the empirical results.The existence of extreme values can have an adverse effect on statistical analysis, leading to increased bias and variance in parameter estimates.By shrinking the tail, the impact of extreme values on the analysis results can be reduced.Finally, this study adjusts the sample year to ensure that the regression results are not just due to the specific impact of a certain year.
The results of the additional robustness tests are shown in Table 7.To prevent the calculation method of the dependent variable from causing incidences in the results, we replaced the calculation method of the dependent variable (Resilience) in Equation ( 8) to test whether the previous empirical results have universality.Y represents the annual GDP value, i represents the city, and r represents the country.The regression results are shown in columns (1) and (2) of Table 7.Additionally, this study replaced the calculation method of the explanatory variable (Digital).We selected the number of Internet broadband access interfaces, the num-ber of telephone users, the number of mobile phone users, the number of employees in telecommunications-related industries, and the telecom service income and used them to calculate a new Digital through the entropy method [42].The regression without and with control variables was conducted separately, and the results are in columns (3) and (4).
Considering the extreme values in the data, to reduce the impact of data anomalies, in this study we conduct quantile processing on the explanatory variables and tail shrinking, thereby allowing the data at less than 1% and more than 99% to be replaced by the data at 1% and 99%.Column (5) displays the analysis results.Finally, considering that cities joined the "Broadband China" policy every year after 2014, the effect was reflected in each of the three years of 2015, 2016, and 2017.To test whether there was a high proportion of variables in a certain year, which leads to the results caused by coincidence not matching the actual situation, a sample from 2015 to 2017 was reduced from the whole sample to test whether the effect was still significant, and the results are presented in columns ( 6) to (8).

Mechanism Verification 6.1. Mediating Effect of Urban Economic Vitality
Columns (1) to (3) in Table 8 show the mediating effect of urban economic dynamism through the stepwise regression coefficient test.Among them, the regression results of column (1) in Table 8 are consistent with those in column (6) of Table 3. Column (2) displays the impact of digital infrastructure on urban economic vitality, and column (3) shows the mediating effect of urban economic vitality.To confirm the mediating effect of urban economic vitality on the digital infrastructure affecting economic resilience, this study uses the Sobel and bootstrap tests, and both prove that urban economic vitality (Activity) is an effective mediating variable.That is, the stronger the city's economic vitality, the more the construction of digital infrastructure will boost urban economic resilience.According to column (2), the coefficient of Digital is 0.673 and significant at the 1% level.It shows that with a 1% increment in the level of digital infrastructure construction, the economic vitality of the city will increase by 0.673%.Similarly, according to column (3), the coefficient of Activity is 0.014 and significant at the 1% level.This indicates that whenever the level of urban economic vitality increases by 1%, urban economic resilience will increase by 0.014%.Therefore, H2 is supported.According to columns (2) and (3), the mediating effect of urban economic vitality on the relationship between digital infrastructure and urban economic resilience accounts for approximately 15% of the overall impact.
There is some research that provides an explanation for this effect.Previous research shows that digital infrastructure affects the economic vitality of cities by boosting the vitality of urban innovation [9], thereby enhancing urban economic resilience.On the one hand, the digital economy promotes urban economic resilience through mechanisms that affect the activity of urban entrepreneurship.On the other hand, the digital economy promotes the resilience of urban economies through mechanisms that affect urban innovation.The widespread application of the Internet accelerates the dissemination of knowledge in the entire economic field, thereby accelerating urban innovation.

Moderating Effect of Industry Structure
To avoid the collinearity problem, in this study we regress the digital infrastructure (Digital), industrial structure upgrading (Su), and industrial structure rationalization (Sr) by employing the method of centralized multiplication to generate the cross-terms (C_Digital * C_Sr and C_Digital * C_Su).Based on Equations ( 5) and ( 6) and combined with the analysis results in columns ( 4) and ( 5) of Table 8, when the urban industrial structure layout tends to be more rationalized, economic resilience is more affected by the positive promotion of digital infrastructure.The coefficient of the cross-term (C_Digital * C_Sr) is significantly positive at the 1% level.At the same time, according to columns ( 6) and (7) in Table 8, industrial structure upgrading also has a significant positive effect on the resilience of the urban economy.The moderating effects of Su and Sr are 2.95% and 24.9%, respectively.
From the perspective of industrial structure upgrading, the market and industrial development always face various externalities and asymmetry, resulting in overcapacity or excessive fluctuations [43].And the resilience of a city is built on its components.The adjustment of industrial structures help urban economic entities develop defense capabilities, respond flexibly to unforeseen changes and crises, and put forward new solutions in the face of unprecedented situations [44].Regulating the rationalization of the industrial structure is conducive to reducing the friction of unreasonable changes in the industrial structure and accelerating the optimal allocation of resources among industries, thereby improving the resilience of the urban economy.
Also, the optimization of the industrial structure can open new pathways for improving the efficiency of green development.On the one hand, at the theoretical level, breakthroughs in digital technology and innovative concepts can provide an opportunity for late-developing countries to optimize industrial pathways and achieve industrial upgrading.On the other hand, from a practical point of view, relying on intelligent industrialization innovation and intelligent industrial transformation can provide support for China to enhance its ability to resist external shocks and improve economic resilience.Therefore, studying the industrial structure upgrading mechanism and formulating reasonable industrial policies are strategic requirements for boosting urban economic resilience.

Discussion
Digital infrastructure construction is an effective pathway for improving urban economic resilience, which can enhance its ability to resist uncertainty.Based on panel data for 106 cities during the period of 2011-2020 in the Yangtze River Economic Delta, in this study we investigated the impact of digital infrastructure on economic resilience.At the same time, we conducted mediating effect and moderating effect analyses to examine the influencing mechanisms between digital infrastructure and economic resilience.
The conclusions are as follows: First, digital infrastructure significantly improves urban economic resilience.This still holds after controlling for individual-time fixed effects and after conducting robustness checks.In addition, the study also found that a city's dependence on openings has a negative impact on its economic resilience.
Second, urban economic vitality has a mediating effect on the impact of digital infrastructure on urban economic resilience.And this intermediary effect is a partial intermediary effect, which accounts for approximately 15% of the overall impact.In other words, approximately 15% of the impact of digital infrastructure on urban economic resilience is achieved by improving urban economic vitality.
Third, the impact of digital infrastructure on urban economic resilience is affected by industrial structure upgrading and rationalization, which have a significant moderating effect.The more advanced the industrial structure is, the more reasonable the industrial layout will be, and the more obvious the impact of digital infrastructure is in promoting the resilience of urban economics.In relation to this, our new finding is of the moderating effect of industrial structural structure upgrading and industrial structure rationalization on the impact of digital infrastructure on economic resilience.
In summary, the construction of digital infrastructure has a strong impact on urban economic resilience, and is an effective way to improve economic resilience.On this basis, the government should focus on stimulating economic vitality and giving the urban economy sufficient vitality through reasonable policy guidance.In addition, policymakers should also pay attention to the coordination of industrial structures, ensure the healthy development of the urban industrial layout, and effectively play the regulatory role of the industrial structure.

Policy Implications
Based on the empirical results, we have the following suggestions for the construction of digital infrastructure: First, policymakers should focus on promoting the construction of urban digital facilities and strengthening support for the digital economy.It should be noted that the government should pay attention to stimulating investment and avoiding damage to the vitality of the urban economy caused by excessive savings.In addition, the urban economy should be prevented from forming high external dependence to maintain its ability to resist the damage caused by the economic chain reaction.
Second, due to the differences in economic development among regions, digital infrastructure constructions of equal magnitude may have different effects.Since there exist obvious differences in the public services and infrastructure within the regions of the Yangtze River Economic Belt, the government should first guide the construction of digital infrastructure in the eastern region, giving full attention to its leading role in the central and western regions.Through the construction of a big data interconnection platform, experience learning and resource mutual assistance will be realized, and the coordinated development of the central and western regions will be driven forward.Then, the government can take this as an example to promote the development of other regions in all aspects, to balance the development differences between regions.
Third, policymakers should pay attention to the intermediary effects of economic vitality and the moderating effects of industrial structure, such as enhancing urban economic vitality by increasing support for urban innovation and entrepreneurship.At the same time, the government should be aware of the upgrading of the industrial structure and promote the agglomeration of high-tech enterprises to drive the development of the tertiary industry.Additionally, the local factor endowment and characteristic advantages should be considered to avoid the fierce competition brought about by the convergence of industrial structures.

Sustainability 2023 , 21 Hypothesis 1 .
15, x FOR PEER REVIEW 6 of Digital infrastructure enhances economic resilience in China.

Table 2 .
Parallel trend test results before policy implementation.

Table 2 .
Parallel trend test results before policy implementation.

Table 3 .
Results of benchmark regression.
Notes: All columns are presented with year and city fixed effects.**, and *** are 5%, and 1% significance levels, respectively.

Table 4 .
Results of spatial heterogeneity analysis.

Table 5 .
Test results of tool variables.

Table 6 .
Results of PSM-DID estimation.

Table 6 .
Results of PSM-DID estimation.

Table 7 .
Other robustness test results.