Spatial Peer Effect of Enterprises’ Digital Transformation: Empirical Evidence from Spatial Autoregressive Models

: This study uses the spatial autoregressive model for panel data to empirically test the spatial peer effect of enterprises’ digital transformation by using a sample of Chinese listed companies during 2012–2021. We ﬁnd that there is a signiﬁcant spatial peer effect in the digital transformation of Chinese companies, and the level of digital transformation of a company increase with the level of digital transformation of its spatial peer companies. Moreover, heterogeneity analysis shows that the spatial peer effect of digital transformation can be effectively played only under a higher digital environment, higher marketization environment, and state-owned equity nature of companies. The ﬁndings suggest that it should focus on building a benchmark company for digital transformation, vigorously enhance the digital and marketization environment in the region and provide more policy support for the digital transformation of non-state-owned enterprises.


Introduction
With the development and broad application of modern digital technologies such as cloud computing, big data analytics, blockchain, and artificial intelligence, the digital economy has become a significant force driving the economic development of countries around the world [1,2].According to the White Paper on Global Digital Economy released by the China Academy of Information and Communications Technology, the global digital economy will reach 32.6 trillion dollars in 2020, accounting for 43.7 percent of GDP.The digital economy of the United States reached 13.6 trillion dollars, ranking first in the world.China's digital economy is the world's second-largest at 5.4 trillion, but its 9.6 percent growth rate is the world's largest.Given the importance of the digital economy, countries all over the world regard the development of their digital economy and the promotion of digital transformation of enterprises as essential goals of their economic policies.
It is foreseeable that the digital economy will become a required field of competition among countries worldwide and will have a far-reaching impact on the development of companies.Recent literature shows that digital transformation has dramatically improved the performance of companies [3][4][5].The specific paths include reducing information asymmetry costs [6,7], promoting corporate innovation [8,9], and improving the efficiency of management decision-making [4].In addition, digital transformation promotes corporate risk-taking by improving firms' operating flexibility and financing availability [7] but reduces stock price crash risk significantly [2].In the wave of the booming digital economy, as the main body of the micro market economy, companies must actively adapt to the significant changes brought by the digital economy and create new commercial advantages through digital transformation.Therefore, promoting companies to carry out digital transformation actively is an essential topic in current academic research.
A company is not an isolated market subject; it always connects with other companies in the operation process, producing a peer effect among companies.Peer effect refers to the phenomenon that other companies will influence a company's business decisions in the same group, leading to similar decision characteristics [10,11].However, we can define company groups by different characteristics.For example, companies belonging to the same industry can be regarded as a group according to the three-digit SIC industry groups [11,12].This paper mainly focuses on the spatial peer effect of enterprises, that is, whether a company's digital transformation will be affected by the digital transformation of other companies.In terms of technical details, we obtain the longitude and latitude data of each company's office address to construct the spatial weight matrix reflecting the spatial distance of all companies.We use the spatial autoregressive model for panel data [13] to test the spatial peer effect of enterprises' digital transformation.
This paper aims to empirically test the spatial peer effect of enterprises' digital transformation and contributes to the literature in several ways.First, this study proves the spatial peer effect of enterprises' digital transformation.Previous studies mainly analyzed the economic consequences of enterprises' digital transformation but paid little attention to the influencing factors of companies' digital transformation, and did not extend peer effect, a common phenomenon in the research field of companies' behavior decision making, to the study of digital transformation.This study will enrich the literature on enterprises' digital transformation influencing factors.Second, most previous studies on peer effect defined peer group companies as companies in the same industry [11,12], and there was almost no literature to define peer group companies from the perspective of spatial agglomeration.However, the closer the spatial distance of companies, the stronger the degree of mutual influence will be, and the spatial peer effect will be more easily generated.Therefore, the research perspective of this paper has a strong novelty.Third, the spatial autoregressive model for panel data is an essential method of spatial econometrics, which is widely used in the field of the macroeconomy, but seldom used in the microeconomic field of company behavior [14][15][16].In this study, the spatial weight matrix is constructed by obtaining the registered address of listed companies.The spatial autoregressive model is applied to the microeconomy field to expand the model's application scope innovatively.
There are four main findings.First, the digital transformation of Chinese companies shows prominent characteristics of the spatial peer effect.Based on the learning effect and competition effect among companies, the digital transformation level of a company will improve along with the digital transformation level of its neighboring companies.Second, the spatial peer effect of enterprises' digital transformation mainly occurs in the environment of high digital transformation.The generation of the learning effect and competition effect requires a specific environment.The environment of high digital transformation is more conducive to companies' mutual learning and competition, and it is easier to exert spatial peer effect.Third, the spatial peer effect of enterprises' digital transformation mainly occurs in the high marketization environment.The higher the marketization level, the more efficiently the competitive advantages obtained by the digital transformation can be realized into business performance advantages through the market mechanism, thus prompting companies to strengthen learning from each other and produce significant spatial peer effect.Finally, the spatial peer effect of enterprises' digital transformation mainly occurs among state-owned enterprises.The reason is that digital transformation requires extensive internal resource input from companies.Compared with non-state-owned enterprises, state-owned enterprises often get more resources and policy support from the government, and management is more willing to highlight their work performance through digital transformation.
The remainder of this paper is organized as follows.Section 2 makes a theoretical analysis of the mechanism of spatial peer effect of enterprises' digital transformation and puts forward research hypotheses for empirical testing.Section 3 puts forward the spatial autoregression model to test the research hypothesis.It introduces the text analysis method to obtain the measurement of enterprises' digital transformation and, according to the registered address of companies, to obtain the micro-level spatial weight matrix of listed companies and explain the way to access research data.Section 4 reports the estimation results of the spatial autoregressive model using full sample data to verify the spatial peer effect of enterprises' digital transformation.According to the internal and external factors such as the digital environment, marketization environment, and companies' equity nature, we analyze the difference in spatial peer effect of enterprises' digital transformation under different conditions.This section also tests the robustness of the research results from the aspects of sample period, variable measurement, and model estimation methods.Finally, Section 5 concludes the paper with a concise discussion of policy implications.

Theoretical Analysis and Testable Hypotheses
In the era of the digital economy, only by complying with the development trend of the digital economy and realizing their digital transformation can companies remain invincible in the market competition.Digital transformation has become the number one strategic choice for many companies.Digital transformation means not only the application of digital technology but also the overall optimization of business processes through the application of digital technology and the establishment of an organizational thinking mode adapted to digital technology [17].The application of companies' digital technology includes the application of underlying technology and the application of technology practice.The application of underlying technology refers to the basic digital technology on which enterprises' digital transformation depends, mainly including artificial intelligence, blockchain, cloud computing, big data, etc. Companies can realize the digital upgrade of hardware infrastructure by embedding these underlying technologies into production and operation activities, essential technical support, and basic organizational structure.The application of technology practice is the deep integration of the underlying technology with the core market business, internal and external value chain, and management mode transformation, focusing on specific digital business scenarios, such as mobile payment, digital finance, and industrial Internet [18].With the advancement of digital transformation, the value chain of companies will be reshaped, create excess returns for companies far beyond their competitors, and set an example for surrounding companies to benefit from digital transformation, forming the spatial peer effect of digital transformation.
Spatial distance determines whether the enterprises' digital transformation can produce a spatial peer effect.Although we regard the company as a whole research object, all business decisions are made and executed by the employees, and the individual behavior tendency of the employees determines the behavior characteristics of the company.When a company implements digital transformation, it will increase the investment in hardware and software, and its organizational structure will also change.Employees have a direct and profound experience of this.As social people, employees are bound to have various intersections with individuals from different companies in work and life so that employees will communicate with each other about the digital transformation happening in the company.Individual employees always have a limited radius of action.According to probability, two people close to each other are always more likely to have a work/life interaction than two people far away.Therefore, based on the distance difference between individuals, the degree of mutual influence between employees will also decrease with the increased distance.As the basic theory of spatial econometrics suggests, although things are generally related, things closer in space are more closely related than things farther away [19].Furthermore, when we increase the research perspective from the employee to the company level, the generation logic of company behavior is based on the individual behavior of employees.The mutual influence degree of enterprises' digital transformation will also decrease with the increased distance between enterprises.Specifically, the distance-based spatial peer effect of enterprises' digital transformation is mainly reflected in the learning and competition effect.
First, there is a learning effect between firms.There is no fixed model for digital transformation.Most companies introduce digital technology based on their business and strategic development needs in a spontaneous state [6].Different companies' business types and strategic planning are not the same, and the underlying technology application and technology practice application in the early stage of digital transformation is also different.
At this time, due to the high information acquisition cost leading to information asymmetry and other problems, companies are often faced with more significant uncertainty in the decision-making process of digital transformation [20,21].By observing and learning about the digital transformation decisions of neighboring companies, companies can significantly reduce their decision-making cost and uncertainty risk [4].For example, some medical companies may take the lead in applying artificial intelligence to intelligent imaging diagnosis and treatment.Some financial companies may take the lead in applying big data mining technology to financial data analysis and product development.Leading companies will set an example for digital transformation, and neighboring companies will also imitate the digital transformation strategies of leading companies and improve their digital transformation level [22].
Whether the learning effect is rational can be divided into two types: effective learning and blind learning [23].Effective learning means that companies make digital transformation decisions consistent with those of peer companies through rational analysis of internal and external primary conditions after observing the improvement of production efficiency brought by the digital transformation of spatial peer companies [24,25].Blind learning refers to a company that, after observing the digital transformation of its peer company, carries on the digital project irrationally due to herd mentality and imitates the digital transformation decision of its peer company.Whether effective or blind learning, the generation of learning effect inevitably depends on the spatial distance between peer companies.Only when the peer company's spatial distance is close will communication and exchange between the company's employees be possible, and the learning effect can be realized.However, when the spatial distance of peer companies is far away, the probability and convenience of communication between employees are significantly reduced, and the demonstration role of leading companies in digital transformation is challenging.The learning effect is difficult to occur.
Second, there is a competitive effect between firms.In essence, the spatial peer effect of enterprises' digital transformation reflects the convergence of companies' production factor input mix, the logic behind it lies in the competition relationship between companies in the product market.In the fierce market competition environment, to maintain the market share and improve the market share of products, companies often pay close attention to the strategic trends of competitors and maintain their industrial status by imitating the economic decisions of competitors [26].By implementing digital transformation, leading companies can effectively reduce the degree of internal and external information asymmetry [6,7], optimize the decision-making process, and improve the input and output of innovation [27,28].It finally improves competitiveness in the product market by taking the lead in digital transformation.At this time, for companies that have not carried out digital transformation, if they turn a blind eye to the progress of the digital transformation of their peers, they will only lose out in the market competition.The management with a higher sense of crisis will inevitably increase the investment in the enterprises' digital transformation based on the needs of product market competition.Moreover, under the background of the current era of the booming digital economy, the wide application of digital technology has been deeply rooted in people's hearts.Due to limited financial and human resources restrictions, some companies may fail to take the lead in digital transformation.When they see peer companies already have some progress on digital transformation, they will develop a sense of urgency.As a result, companies that fail to carry out digital transformation due to internal resources must start the digital transformation process.Based on the learning effect and competition effect, the digital transformation of enterprises will show the characteristics of the spatial peer effect.The following hypothesis is proposed.

Hypothesis 1 (H1).
Enterprises' digital transformation has spatial peer effect.The level of digital transformation of a company increases with the level of digital transformation of its spatial peer companies.
The spatial peer effect of enterprises' digital transformation is affected by their external environment.When a company observes that its peers are implementing digital transformation, whether it is based on the learning effect or competition effect, the company's coping strategy depends to a large extent on the intensity of the digital atmosphere in the external environment.China has a vast geographical area, and there is a massive gap in the level of digital development in different regions.For example, Beijing, Shanghai, Zhejiang, and Guangdong provinces are home to many digital technology companies.The local governments also promote the development of the digital economy as a priority development strategy in this region [2,7].However, the economic development level of China's central and western provinces is relatively low.The local governments' policies aim to promote regional economic development and undertake backward production capacity transferred from the eastern coastal areas [29,30].Digital transformation is difficult to enter the sight of companies and governments of China's central and western provinces.
In a higher digital atmosphere, the company's management has a deeper understanding of the importance of digital technology applications.The employees will also discuss the application of digital technology in life and work communication more often.The company's response to peer companies' digital transformation will become more sensitive, and the spatial peer effect of digital transformation will be easier to play.On the contrary, in the weak digital atmosphere, the management does not understand the possible benefits of digital transformation, and the employees lack due recognition of digital technology.Even if the peer companies implement the digital transformation process, the surrounding companies will not produce the learning effect and competition effect, which will not produce the spatial peer effect of digital transformation.The following hypothesis is proposed.

Hypothesis 2 (H2).
Enterprises' digital transformation has spatial peer effect only in a higher digital environment.
Another important external environment for Chinese companies is the level of marketization in their regions.Since the reform and opening, China has adopted a socialist market economy and given full play to the fundamental role of the market mechanism in resource allocation.However, the market reform process in different regions is inconsistent, resulting in differences in marketization levels among regions [31,32].China's marketoriented reform process can be evaluated from five dimensions: the relationship between the government and the market, the development of a non-state-owned economy, the development of product markets, the development of factor markets, the development of market intermediary organizations, and the legal environment [33].The spatial peer effect of enterprises' digital transformation in different marketization environments will differ.The fundamental reason companies are willing to invest financial and human resources in digital transformation lies in the expectation that the application of digital technology can bring about changes in production technology and operation mode and improve the market competitiveness of companies.However, whether the expected effect of enterprises' digital transformation can be realized depends not only on the company's input intensity but also on the timely and effective market feedback provided by the external market.
When companies are in a high level of marketization environment, leading companies can get positive feedback from the market by taking the lead in digital transformation, including comprehensive responses from the government, upstream and downstream supply chains, and consumers [34,35].As the surrounding companies witness the leading companies gaining benefits from digital transformation, they will be more eager to catch up with their competitors and maintain their market position by learning and imitating the digital process of the leading companies.Therefore, producing the spatial peer effect of enterprises' digital transformation is easier.On the contrary, when the marketization level of companies is low, leading companies invest many costs for digital transformation.However, it is not easy to obtain positive market feedback.It cannot set a role model for the surrounding peer companies, which will not produce the spatial peer effect of digital transformation.The effective operation of the market mechanism is an important external factor for the spatial peer effect of enterprises' digital transformation.Therefore, the market feedback obtained by leading companies taking the lead in digital transformation is different under different marketization environment conditions.Only in a higher marketization environment can the company's digital transformation generate a spatial peer effect through the exertion of the learning and competitive effects.The following hypothesis is proposed.

Hypothesis 3 (H3).
Enterprises' digital transformation has spatial peer effect only in a higher marketization environment.
An essential feature of the ownership structure of Chinese companies is the existence of many state-owned enterprises.There are significant differences between state-owned and non-state-owned enterprises regarding resource constraints, decision-making logic, and other aspects that impact spatial peer effect in the enterprises' digital transformation.Digital transformation requires the introduction of blockchain, artificial intelligence, big data, and other digital technologies, with a large amount of hardware and software input as the support and requires companies to have relatively sufficient financial and human resources.Comparatively speaking, the budget constraint of state-owned enterprises is much lower than that of non-state-owned enterprises.When non-state-owned enterprises make digital transformation decisions, they often face the problems of insufficient capital, difficulty obtaining bank loans, and high loan interest rates.It will hinder the digitalization process of non-state-owned enterprises.However, it is easier for state-owned enterprises to obtain low-interest rate loans from banks, and it is also easier for them to obtain government financial subsidies and preferential tax policies.Therefore, state-owned enterprises can obtain more resources for their digital transformation decisions [7,32,36].
From the perspective of decision logic, whether state-owned or non-state-owned enterprises, the motivation for digital transformation is more from the internal needs of companies in the face of market competition.However, compared with non-state-owned enterprises, the digital transformation of state-owned enterprises has more external impetus from the government.Based on the critical position of the digital economy in developing the national economy, governments at all levels in China are vigorously promoting the digital development level of their regions.In addition to formulating strategic planning for guidance, state-owned enterprises are also the focus of local governments.The State-Owned Assets Supervision and Administration Commission (SASAC hereafter) is a crucial department of governments and the equity holders of state-owned enterprises at all levels.The strategic economic decisions of local governments can be transmitted to state-owned enterprises at all levels through the equity control chain of SASAC.It can urge state-owned enterprises to actively implement the government's strategic decisions [37].At the same time, the supervision of the Communist Party to the management of companies [38,39] and the governance of the Party committee of companies [40] also play a positive role in the response of state-owned enterprises to the government's digital economy development strategy.In areas with a high proportion of state-owned enterprises, the large state-owned enterprises could crowd out smaller enterprises and private sector developments.In this condition, the higher marketization environment is challenging to promote the generation of the spatial peer effect of digital transformation.However, state-owned enterprises with sufficient digital transformation resource supply and pressure from the government will still be highly motivated to start the digital transformation.Therefore, based on the sufficient resource guarantee and external impetus of state-owned enterprises, this paper puts forward the following hypothesis.

Hypothesis 4 (H4).
Enterprises' digital transformation has spatial peer effect only under the condition of state-owned shareholding nature.

Variable Definitions
Companies do not publish direct measurement indicators of digital transformation.The existing literature on measuring enterprises' digital transformation usually includes the following three indirect methods: Dummy variables are constructed according to whether the company has carried out digital transformation [4]; Five-point Likert scale or semistructured interviews are used to evaluate the digitalization level of companies [21,41]; Through the text analysis method, the digital-related text information is extracted from the company annual report to construct the digital transformation index [5,7,18,42].Comparatively speaking, text analysis is the most used measurement method of digital transformation in the literature, and we also use this method to construct the measurement index of digital transformation.The specific steps are as follows: First, download the annual reports of Shanghai and Shenzhen A-share listed companies from 2010 to 2021 and convert them into TXT files.
Second, build a dictionary reflecting the characteristics of enterprises' digital transformation.The structure of the digital transformation vocabulary map includes the keywords of the application of underlying technology and the application of technology practice.For example, the former include artificial intelligence, machine learning, deep learning, face recognition, cloud computing, blockchain, and other underlying technology keywords that companies rely on for digital transformation.In contrast, the latter include keywords that digital technologies such as mobile payment, industrial Internet of Things, digital finance, smart healthcare, and other digital technologies are applied in company business practice [5,18].
Third, the management discussion and analysis (MD&A) is intercepted from the annual report of listed companies.The number of digital transformation feature words occurrences in this module is counted and summed up.The reason why MD&A is chosen as the text analysis object instead of the full text of the company's annual report is that MD&A is the discussion and analysis of the management on the past business conditions and future business plans, which can better reflect the strategic implementation and guidance of the enterprise's digital transformation.
Fourth, the frequency of digital transformation feature words obtained by the analysis was divided by the total length of the MD&A text and then multiplied by 10,000 to obtain Digital as the explained variable.The larger the value of this indicator, the higher the enterprise's digital transformation level.
The explanatory variable is the spatial lag term of enterprises' digital transformation W•Digital, where W is the spatial weight matrix.The steps to obtain the spatial weight matrix are as follows: 1.
Obtain the detailed longitude and latitude coordinate data of the registered address of listed companies.It should be noted that the registered address of a listed company is often its primary office location, where the company's most core employees and management are gathered.Companies will establish new branches and subsidiaries elsewhere as their business grows.However, their management is often dispatched by the parent company, and the corporate culture also follows the parent company, so their digital transformation will also be affected by the parent company.Since we need to use the address information of listed companies to measure the spatial distance between different companies, it is obviously more reasonable to use the registered address of the parent company than the addresses of other branches.

2.
According to the listed companies' longitude and latitude coordinate data, we calculate the straight ground distance between the two pairs and use the inverse of the distance as their spatial distance weight.

3.
All companies' spatial distance weight data are arranged into a symmetric matrix.
For example, assuming that there are n listed companies in the sample, the space straight-line distance between listed company i and listed company j calculated by longi-tude and latitude coordinate data is r ij .The space weight coefficient of i and j is w ij = 1/r ij , and the space weight matrix can be defined as follows: The diagonal elements in Table 1 are w 11 = • • • = w nn = 0.After the row standardization of the above matrix, the matrix obtained is the spatial weight matrix-the closer the spatial distance between companies, the greater the weight, and vice versa.Therefore, the spatial weight matrix can reflect the influence of spatial peer companies on digital transformation.The closer the spatial distance is, the stronger the mutual influence is, while the farther the spatial distance is, the weaker the mutual influence is.We get the spatial lag term W•Digital of the enterprises' digital transformation by multiplying the spatial weight matrix W by the explained variable Digital.The key explanatory variable W•Digital reflects the overall digital transformation level of all the spatial peers of a company weighted by the spatial distance weight.To control the influence of other factors on the enterprises' digital transformation, we added the control variables as follows: Ln_Asset and Lev, which control the essential financial characteristics of companies; Roa and Growth, which reflect the growth ability of companies; Independence and Duality, which reflect the corporate governance structure; and Ln_Age reflects the companies' establishment years.All variables are defined as shown in Table 1.

Model Design
We construct the following spatial autoregressive model for panel data to verify the spatial peer effect of enterprises' digital transformation.
In Equation (2), γ is the characteristic that the individual does not change with time, and the generation process of the disturbance term µ is µ = ρW • µ + ε, ε ∼ N 0, σ 2 I n .We use the fixed-effects regression estimator to estimate the spatial panel data model to obtain consistent estimation results.Based on the research purpose, this paper mainly focuses on the parameter estimation results of λ.If the coefficient of λ is significantly positive, it indicates that there are spatial peer effects in the enterprises' digital transformation, and the leading companies taking the lead in digital transformation can drive the surrounding peer companies to carry out digital transformation also.If the coefficient of λ is significantly negative, it indicates a reverse spatial peer effect in the enterprises' digital transformation, and the leading companies taking the lead in digital transformation will hinder the digital transformation of surrounding peer companies.If the coefficient of λ fails to pass the significance test, it indicates that there is no spatial peer effect in the enterprises' digital transformation, and the digital transformation of leading companies will not affect the surrounding peer companies.

Data
We used the data of A-share listed companies in Shanghai and Shenzhen.The data of Digital were obtained using Python to analyze the text of the MD&A section of annual reports from listed companies.The data of other variables were obtained from the China Stock Market and Accounting Research (CSMAR) database.According to the previous research, we deleted the sample of finance companies and winsorized the continuous variables at the 1% level in both distribution tails.As for the sample period selection, the spatial autoregressive models for panel data required a strongly balanced panel, and all variables of each research sample were required to have observational data in all sample periods.China's capital market is in its infancy, and the number of early listed companies is negligible.The sample period span of different lengths will significantly impact the sample size.We used the period from 2012 to 2021 as the sample period and obtained 14,020 research samples as the largest sample size.

Summary Statistics
Table 2 presents the summary statistics of the main variables.The average value of Digital is 3.62, indicating that in the annual reports of Chinese listed companies, there are 3.62 keywords of digital transformation in every 10,000 words of MD&A.However, the median Digital is only 0.42, indicating that the digital transformation of China's listed companies is generally low, and more than half of them are below the overall average.The summary statistics results of other variables are also consistent with the reality of Chinese companies, and the individual differences among companies are significant.

Baseline Estimation Results Using the Full Sample
Table 3 reports the baseline estimation results using the full sample data from 2012 to 2021.According to Table 3, the key explanatory variable W•Digital coefficients are all positive at the significance level of 1% in Columns (1) to (3).W•Digital reflects a companion of digital transformation all the space peer companies after spatial weight matrix weighted.The significantly positive coefficient shows that based on the digital transformation of enterprises in space showing the learning effect and competition effect, a company's level of digital transformation increases with the level of its spatial peer companies.Digital transformation of enterprises has a significant spatial peer effect.Hypothesis H1 proposed in this paper is valid.For control variables, the coefficients of Ln_Asset, Roa, and Growth are all significantly positive in Columns (2) and (3), indicating that the larger the asset scale, the stronger the profit level and the higher the growth level of a company, the more willing it is to carry out digital transformation and the more financial resources it will invest in the process of digital transformation.However, the coefficient of Lev is significantly negative in Column (2), indicating that a higher asset-liability ratio means that the company's capital is reduced, and the resources available for digital transformation are reduced accordingly.The coefficient of Ln_Age is significantly negative in Column (2), indicating that the more extended established companies are, the less willing they will be to carry out digital transformation due to inertia of thinking and solidifying business model.

Additional Analysis 4.3.1. Grouping Estimation Analysis Based on Digital Transformation Level
The spatial peer effect of enterprises' digital transformation depends on the mutual communication between employees in their work and life as the micro-mechanism.When the digital environment of companies is different, the spatial peer effect will also be affected.Different regions in China have different levels of digital transformation.According to the registered addresses of listed companies, we statistically obtained the average digital transformation level of listed companies in each province.We used it as a measurable indicator of digital transformation at the provincial level.The regions with higher digital transformation levels than the median are considered high digital environments.In contrast, the regions with lower digital transformation levels are considered low digital environments.The coefficients of W•Digital in Columns (1) to ( 3) are all significantly positive at the 1% level.When a company is in a relatively high digital environment, employees' daily work and life are immersed in a solid digital atmosphere so that the company has a clearer understanding of the advantages of digital transformation.When companies witness the surrounding peer companies actively carrying out digital transformation, their awareness of the risks of digital transformation will also increase.Then, more human and financial resources will be invested in digital transformation so that digital transformation shows a pronounced spatial peer effect.However, the coefficients of W•Digital in Columns ( 4) to (6) do not pass the significance test.When in a low digital environment, the company lacks recognition of digitalization itself.Even if the surrounding companies are carrying out digital transformation, they will not decide on digital transformation, and the spatial peer effect of digital transformation will not occur.Hypothesis H2 proposed in this paper is valid.
It should be noted that the coefficients of W•Digital in Table 4 are much smaller than those in Table 3, and they are not in the same order of magnitude.The main reason is that the variable W•Digital reflects the digital transformation level of all other companies spatially related to one company after being weighted by the spatial distance weight.In Table 3, all samples are used for model estimation, but Table 4 uses sub-samples for model estimation.W•Digital has more digital transformation information of its peer companies reflected in Table 3 than in Table 4, so it will also show a larger coefficient in the estimation results.The sample size and geographical location of the samples included in different models are different, and the digital transformation information content of partner companies included in W•Digital is also very different.Therefore, it is not appropriate to compare the size of the W•Digital coefficients under different samples.Based on the research purpose of this paper to verify that there is a spatial peer effect in enterprises' digital transformation, we pay more attention to the sign of the W•Digital coefficient and its significance level.

Grouping Estimation Analysis Based on Marketization Level
China's market-oriented reform is still in progress, and the level of marketization varies significantly in different regions.In different market environments, the timeliness and effectiveness of digital transformation for enterprises to obtain market feedback are entirely different.We use China's provincial-level marketization index [33] to classify provinces.The regions with higher marketization indexes than the median are considered a high marketization environment.In contrast, the regions with lower marketization indexes are considered a low digital environment.Table 5 reports the model estimation results based on different market environment sub-samples.   1 for variable definitions.The T statistic is enclosed in brackets."***", "**", and "*" denote significance at the 1%, 5%, and 10% levels, respectively.Columns (1) to (3) use the subsample of a high marketization environment, and Columns ( 4) to ( 6) use the subsample of a low marketization environment and covers the period from 2012 to 2021.
The coefficients of the W•Digital in Columns (1) to (3) are all significantly positive at the 1% level.It shows that when companies are in a high marketization environment, leading companies can obtain timely and effective market feedback and reap more commercial benefits by taking the lead in digital transformation.This is an example for neighboring companies to guide them to digital transformation.However, the coefficients of the W•Digital in Columns (4) to (6) are not through the test of significance, which shows that when the company was in a low marketization environment, the digital transformation of leading companies failed to get the market feedback.The surrounding companies will not follow the digital work of leading companies, and it is challenging to play the spatial peer effect of digital transformation.Hypothesis H3 proposed in this paper is valid.

Grouping Estimation Analysis Based on Ownership
China has many listed companies controlled by the state.Companies with different ownership natures face different resource constraints in the digital transformation process, and their willingness to digital transformation is also different.According to the ownership differences of the controlling shareholders of listed companies, we divide the whole sample into two subsamples: state-owned and non-state-owned enterprises.Table 6 reports the model estimation results based on different subsamples of equity nature.The coefficients of W•Digital in Columns (1) to (3) are all significantly positive at the 1% level, indicating that digital transformation has a significant spatial peer effect among state-owned enterprises.Although the coefficient of W•Digital in Column ( 5) is significantly positive at the 1% level, this Column model does not control for industry and year effect.In Column (6), where all control variables are added and industry and year effects are controlled, the coefficient of W•Digital does not pass the significance test.There are no spatial peer effects in digital transformation among non-state-owned enterprises.It is imperative to control the model's industry and year effects to obtain unbiased estimation results.Hypothesis H4 is verified.

State-Owned Enterprises
Non-State-Owned Enterprises Since the spatial autoregressive models must use strongly balanced panel data for model estimation, a total of 14,020 observations from 1402 companies during 2012-2021 were used as the research sample to obtain the maximum sample size.We further changed the sample period span, and the number of cross-sections and the total number of samples obtained each year also changed significantly to test the robustness of the research conclusion under different sample conditions.When we use 2011-2021 as the sample period, a total of 13,079 observations of 1189 companies are obtained, and the model estimation results are shown in Columns (1) to (3) in Table 7.When we use 2013-2021 as the sample period, a total of 13,779 observations of 1531 companies are obtained.The model estimation results are in Columns ( 4) to (6) in Table 7. Due to the data requirements of the strong balance panel, the variation of the sample period span will have a significant impact on the number of companies entering the study sample each year.The W•Digital coefficients of Columns (1) to (6) in Table 7 are all significantly positive at the 1% level, indicating that although the change of the sample span makes the sample of companies observed each year considerably change, it does not affect the robustness of the research conclusion of this paper.Namely, the spatial peer effect exists in the Digital transformation of enterprises.The W•∆Digital coefficients of Columns (1) to (3) in Table 8 are all significantly positive at the 1% level, indicating that spatial peer effect also exists in the incremental digital transformation level of Chinese listed companies.The incremental level of digital transformation of a company will increase with the improvement of spatial peer companies, which further verifies the robustness of the research conclusions.In the previous model, the fixed effects estimation results are consistent regardless of whether the individual effect γ is correlated with explanatory variables, so the estimation results in Tables 3-8 are unbiased.However, when the individual effect γ is uncorrelated with explanatory variables, using the random effect will lead to less variance estimation results than the fixed effect, so we further use the random effect for robustness testing.As shown in Table 9, the coefficients of all W•Digital in columns (1) to (3) are significantly positive at the 1% level, indicating that the spatial peer effect of digital transformation of Chinese listed companies will not change due to the difference in estimation methods.

Robustness Test by Using First-Order Lag Terms of Control Variables
Model Equation (2) may have endogeneity problems.For example, a company's financial performance will affect its digital transformation process, but the digital transformation will also affect its financial performance.In addition, other control variables may also have similar problems.To further alleviate the possible endogeneity concerns of the research conclusions, we used the first-order lag terms of the control variables for re-regression.The reason is that last year's financial performance will affect this year's digital transformation, but this year's digital transformation will not affect last year's financial performance.The same principle applies to other control variables."***", "**", and "*" denote significance at the 1%, 5%, and 10% levels, respectively.The dataset is the strongly balanced panel data of Chinese listed companies and covers the period from 2013 to 2021.

Conclusions
At present, the digital economy is booming, and the wide application of digital technology has become an important driving force for social and economic progress.Although more and more companies have taken the step of digital transformation, many still have doubts about the prospect of digital technology applications.They are hesitant to proceed with the digital transformation process.The governments and academia are very concerned about how to promote enterprises' digital transformation.This paper attempts to theoretically and empirically analyze the spatial interaction effect of enterprises' digital transformation from the micro perspective of company spatial interaction, that is, how a company's digital transformation is affected by its spatial peers.It is helpful to analyze the spatial distance between companies to explore the micro-influence factors of enterprises' digital transformation.The critical theoretical significance of this paper includes incorporating the spatial peer effect among companies into the influencing factors of enterprises' digital transformation and incorporating the spatial autoregressive model, which is widely used in macroeconomic research, into the research of listed companies at the micro level.The research perspective and research method of this paper are highly innovative.
Our research shows that the generation mechanism of the spatial peer effect of enterprises' digital transformation lies in that leading companies take the lead in digital transformation, which can set an example for the surrounding peer companies and trigger mutual learning and competition between companies.It can encourage the surrounding peer companies to make digital strategic decisions and devote more resources to digital transformation.We use a sample of Chinese A-share listed companies in Shanghai and Shenzhen to construct a spatial weight matrix by calculating the spatial distance between companies through the latitude and longitude information of their registered addresses and then use the spatial autoregressive model to empirically test the spatial peer effect of enterprises' digital transformation.The research results show a significant spatial peer effect in the digital transformation of Chinese companies, and the level of digital transformation of a company increases with the level of digital transformation of its spatial peer companies.Moreover, heterogeneity analysis shows that the spatial peer effect of digital transformation can be effectively played only under a higher digital environment, higher marketization environment, and state-owned equity nature of companies.
Our results have several implications.First, focus on building a benchmark company for digital transformation.Based on the critical role of digital transformation in developing enterprises and the national economy, governments of various countries should pay attention to leading digital companies as role models when formulating incentive policies for digital transformation.Encourage digital transformation benchmarking companies to summarize their experience and vigorously publicize the business model changes brought by digital transformation to the production and operation of companies.So that more space peer companies can realize the importance of digital transformation through the learning effect and competition effect and make the spatial peer effect of digital transformation can be exerted in an enormous spatial scope.Second, vigorously enhance the environment for digitalization and marketization in the region.As the main body of micro-activities, all companies' decisions will be affected by the environment in which they are located.All regions should vigorously improve the overall level of digitalization, including the popularization and application of digital infrastructures such as digital networks, 5G communication technology, and industrial robots in the local area, to create a thriving atmosphere for the development of the digital economy.At the same time, local governments at all levels should also strengthen the construction of legal systems, play the fundamental role of market mechanisms in resource allocation, and enable leading digital companies to obtain market feedback promptly and effectively.Third, companies should choose the external environment conducive to their digital transformation.Digitization is the primary trend of current world economic development.Based on the spatial peer effect of digital transformation, companies should actively establish offices in areas with a high digital environment so that employees can be exposed to more digital living and working environments.Fourth, non-state-owned enterprises should actively seek policy support for digital transformation.Due to financial constraints, there is no spatial peer effect of digital transformation among non-state-owned enterprises.To cope with the difficulties of digital transformation, non-state-owned enterprises should actively use the bond market, banks, and other financing channels to ease the financial tension.Companies should also establish effective internal control and equity governance mechanisms to make business decisions conducive to long-term development.

Table 3 .
Baseline estimation results using the full sample.
We use the fixed-effects regression estimator to estimate the spatial panel data model.See Table1for variable definitions.The T statistic is enclosed in brackets."***" and "**" denote significance at the 1% and 5% levels, respectively.The dataset is the strongly balanced panel data of Chinese listed companies and covers the period from 2012 to 2021.
Table 4 reports the model estimation results based on different subsamples of digital environments.

Table 4 .
Grouping estimation results based on different digital environments.
(6)use the fixed-effects regression estimator to estimate the spatial panel data model.See Table1for variable definitions.The T statistic is enclosed in brackets."***","**",and "*" denote significance at the 1%, 5%, and 10% levels, respectively.Columns (1) to (3) use the subsample of a high digital transition environment, and Columns (4) to(6)use the subsample of a low digital transition environment and covers the period from 2012 to 2021.

Table 5 .
Grouping estimation results based on marketization level.
We use the fixed-effects regression estimator to estimate the spatial panel data model.See Table

Table 6 .
Grouping estimation results based on ownership.

Table 8 .
Estimation results by using change model.We use the fixed-effects regression estimator to estimate the spatial panel data model.Variables are obtained by taking the first-order difference according to the variables in Table1.The T statistic is enclosed in brackets."***" and "**" denote significance at the 1% and 5% levels, respectively.The dataset is the strongly balanced panel data of Chinese listed companies and covers the period from 2012 to 2021.
4.4.3.Robustness Test by Using a Random-Effects Estimator Table 10 reports the estimation results in which Columns (1) to (2) are estimated with fixed effects, and Columns (3) to (4) are estimated with random effects.According to Table 10, the key explanatory variable W•Digital coefficients are still positive at the significance level of 1% in Columns (1) to (4).The conclusions of this paper are still robust.

Table 9 .
Estimation results by using generalized least-squares random-effects estimator.We use the generalized least-squares random-effects estimator to estimate the spatial panel data model.See Table1for variable definitions.The T statistic is enclosed in brackets."***" and "**" denote significance at the 1% and 5% levels, respectively.The dataset is the strongly balanced panel data of Chinese listed companies and covers the period from 2012 to 2021.

Table 10 .
Estimation results by using first-order lag terms of control variables.
We use the fixed-effects regression estimator in Columns (1) to (2) and use the generalized least-squares randomeffects estimator in Columns (3) to (4).See Table1for variable definitions.The T statistic is enclosed in brackets.