The Impact of Geographic Factors on Credit Risk: A Study of Chinese Commercial Banks

1 Introduction

Ensuring financial stability and mitigating risks amidst the combined impact of domestic and foreign uncertain factors holds significant importance for China’s long-term economic development, as well as the attainment of transformation and upgrading objectives. With the advent of China’s reform and opening-up policies, the banking industry has assumed a dominant position within the country’s financial system, playing a vital role in resource allocation and macroeconomic regulation. The control of credit risks within commercial banks is a key aspect of upholding financial security, garnering attention from economists and policymakers (Bhattacharya & Chiesa, 1995; Papi et al., 2017; Petersen & Rajan, 2002). In recent years, Chinese commercial banks have undergone a profound and protracted transformation process in terms of industry structure and technological advancements. Regarding industry structure, these banks have set strategic goals aimed at establishing a diversified financial system and expediting market-oriented reforms in the banking sector. Regulatory authorities have gradually eased their control over nonstate-owned banks and new financial institutions, resulting in a growing number of branches established by nonstate-owned commercial banks across various locations. While the operational distance between banks and enterprises has diminished, the functional distance between grassroots bank organizations and their headquarters has increased. Concerning technological advancements, the application of information technology within banks has surged, facilitating the collection and processing of quantitative information such as assets, income, and market share. Consequently, the significance of operational and functional distances between banks and enterprises appears to be weakened. However, information technology does not possess a comparable advantage in gathering and processing qualitative information such as reputation and creditworthiness, thus underscoring the continued importance of geographical factors (Behr & Güttler, 2007; Jiménez et al., 2013; Rajan et al., 2015). Some scholars have posited that information asymmetry constitutes a significant factor contributing to the bank credit risk (Papi et al., 2017).

Due to market incompleteness, banks possess an inherent motivation to establish and maintain close collaboration with enterprises. This facilitates the acquisition and screening of information, thereby addressing the issue of information asymmetry between banks and enterprises (Bhattacharya & Chiesa, 1995). The rapid advancement of information technology has undoubtedly alleviated the constraints imposed by geographical factors on financial activities. However, the impact of information technology primarily extends to the utilization of quantitative information, considering the geographic specificity of information dissemination. Consequently, the dissemination of qualitative information, commonly referred to as soft information, remains subject to the influence of geographical factors (Petersen & Rajan, 2002). To process transactions such as bank withdrawals and financial transfers, banks rely on customers’ hard information. However, when it comes to managing credit risk, banks cannot solely rely on the collection of hard information pertaining to credit targets. The collection and analysis of soft information, including factors such as reputation, creditworthiness, and corporate culture, are crucial.

Commercial banks must tailor credit contracts based on the soft information characteristics of different enterprises. Geographical factors play a significant role in the rootedness of soft information, and the utilization of information technology does not fully exploit its advantages in standardization when collecting and processing soft information. Consequently, the application of information technology may not necessarily mitigate credit risk resulting from information asymmetry [4]. Despite the extensive use of information technology in China’s peer-to-peer lending platforms, financial risks persistently arise. Rajan et al., (2015) highlighted that during the credit securitization process, US banks excessively relied on hard information obtained through modern communication technology, disregarding the collection of soft information. This failure to validate the accuracy of borrower hard information became a critical factor in the US subprime crisis. These instances underscore the significant influence of geographical factors on banks’ effective collection and processing of soft information. In October 2020, the People’s Bank of China sought public opinions on the “Commercial Bank Law of the People’s Republic of China,” which stipulated that local bank requires approval to conduct business across regions. The contribution of this study lies in its examination of the relationship between the spatial organizational structure of Chinese commercial banks and credit risk. It contributes to the existing literature by incorporating geographic factors and information asymmetry into the analysis. The study develops a theoretical model and empirically tests it using microdata from Chinese commercial banks, providing a comprehensive understanding of how the organization of banks influences the collection and processing of soft information, which, in turn, impacts the credit risk. In February 2021, the China Banking and Insurance Regulatory Commission issued a notice to further regulate Internet loan activities of commercial banks, explicitly prohibiting local banks from engaging in Internet loan businesses across regions. Given the ongoing deepening of reforms and evolving organizational structure in China’s banking industry, there is an urgent need for comprehensive research on the impact of geographical factors on the bank credit risk. Prior studies have primarily focused on the bank credit risk from the perspectives of information asymmetry, relational credit, banking market competition, and debt maturity structure (Behr & Güttler, 2007; Jiménez et al., 2013; Liang & Hao, 2019). However, these studies have devoted less attention to the influence of geographical factors. The objective of this study is to examine the relationship between the spatial organizational structure of Chinese commercial banks and credit risk, considering the influence of geographical factors and information asymmetry. Using microdata from Chinese commercial banks, the study aims to develop a theoretical model and empirically test it, providing a comprehensive understanding of how bank organization affects the collection and processing of soft information, which in turn impacts credit risk. This research contributes to the existing literature by incorporating geographical factors and information asymmetry into the analysis of bank credit risk, filling a gap in previous studies that have focused more on other factors. Furthermore, by utilizing specific microdata from the Chinese banking industry, which is undergoing reforms and organizational changes, the study offers empirical evidence and insights that are relevant to this context.

2 Research Objective

This article adopts an adverse selection theoretical framework to examine the association between the spatial arrangement of banking organizations, soft information, and credit risk. The study employs a mediating effect model to empirically investigate this relationship, shedding light on the impact and mechanisms of geographical factors on commercial bank credit risk. The innovative contributions of this article are twofold. First, it offers a unique research perspective by examining the influence of geographic factors on the bank credit risk from the vantage point of soft information. This approach supplements and advances the existing literature on economic geography and commercial bank credit risk. While prior economic geography studies primarily focus on the impact of geographical factors on corporate credit availability or local economic development, they rarely delve into the realm of bank credit risk. Similarly, the existing research on commercial bank credit risk mainly explores the influence of factors such as relationship lending, bank market competition, and debt maturity structure, with limited attention given to the geographic variables of banks. Second, this study employs a mediating effect model to unravel the channels through which geographical factors affect the bank credit risk. While the previous scholarly work has involved qualitative analysis and theoretical deductions concerning the relationship between geographical factors and the bank credit risk, rigorous quantitative methods to explore the causal relationship and underlying mechanisms between the two remain scarce. The study is based on an adverse selection theoretical framework to analyze associations between spatial arrangements, soft information, and credit risk. It aims to empirically test the proposition that geographical factors impact credit risk by influencing soft information production.

The presence of information asymmetry, both between banks and borrowers and within commercial banks themselves, poses challenges to the efficient allocation of credit resources. Asymmetric information stands as a significant contributor to the bank credit risk (Papi et al., 2017). In light of market incompleteness, commercial banks possess an inherent motivation to establish and maintain close collaboration with enterprises. This facilitates the acquisition and screening of information, thereby overcoming the issue of information asymmetry between banks and enterprises (Bhattacharya & Chiesa, 1995). In recent years, the relaxation of government regulations and the rapid advancement of information and communication technology have expanded the geographical scope of business operations within China’s commercial banking sector. Consequently, the geographical layout of the banking industry has undergone varying degrees of transformation across different countries, leading to changes in the relationships between banks and enterprises, as well as between different levels within banks. The theoretical community has increasingly recognized the role of geographical factors in credit activities. The process of information collection and processing by banks involves information exchange between the bank’s operational departments and borrowers, as well as information exchange among different levels within the bank (operational departments and decision-making departments). Existing literature primarily examines the relationships between geographical factors, bank-enterprise interactions, and bank credit operations from these two perspectives. Since the 1990s, there has been a relaxation of banking regulations by European and American regulatory agencies, resulting in a deepening of cross-regional operations for banks. This has led to a continuous expansion in the number of branch offices and business outlets for commercial banks and an increase in the geographical distance between banks and enterprises. As a result, the academic community has increasingly recognized the significance of the geospatial relationship between banks and enterprises in credit activities. Financial activities are intertwined with specific natural and cultural geographical contexts. Hence, geographical factors can influence the collection, dissemination, and interpretation of information, particularly soft information, by banks toward enterprises, consequently impacting credit activities (Alessandrini, 2009; Behr & Güttler, 2007; Bhattacharya & Chiesa, 1995; Jiménez et al., 2013; Liang & Hao, 2019; Papi et al., 2017; Petersen & Rajan, 2002; Rajan et al., 2015). The advancements in communication technology have diminished the geographical limitations on credit activities between banks and enterprises. However, Liberti and Petersen (2019), Petersen (2002), and Petersen and Rajan (2002) argue that modern communication technology has primarily expanded the utilization of hard information, while it lacks advantages in collecting and processing soft information that is challenging to standardize. The collection of soft information regarding companies still necessitates frequent and dependable face-to-face interactions between parties involved in the transactions. Furthermore, the scope of information covered by hard information is limited, and factors like geographical distance inherently influence the objectivity of hard information, including credit ratings, throughout the information collection process. Several empirical studies have examined the association between geographic distance and soft information. Agarwal and Hauswald (2010) discovered that a shorter geographic distance between borrowers and lenders facilitates banks in gathering customer soft information, leading to fairer credit ratings. Bartoli et al. (2013) revealed that information technology and geographic factors exhibit a complementary relationship rather than a substitutive one. Consequently, the academic community has directed attention toward understanding the impact of this complementary relationship on the spatial arrangement of commercial banks and enterprises. Bogdan (2016) and Zhishan et al. (2014) investigated the spatial distribution of business outlets for state-owned and joint-stock banks in China. Their research established that bank branches are frequently situated in economically developed and politically advanced regions, enabling commercial banks to access richer financial information and secure better customer resources. What influence does the advantage of acquiring soft information due to proximity between banks and enterprises have on both parties? Agarwal and Hauswald (2010) and Petersen and Rajan (2002) empirically demonstrated, based on the US data, that closer geographic proximity between banks and enterprises corresponds to higher credit availability for enterprises and lower credit interest rates. Alessandrini (2009) observed a negative relationship between the bank branch density and the sensitivity of enterprise cash flow. Bellucci et al. (2015) found that greater geographic intimacy between banks and enterprises leads to reduced requirements for corporate loan collateral. Bai et al. (2022), utilizing microdata from China’s manufacturing industry, discovered that local financial development reduces the geographic distance between banks and enterprises, promoting productivity growth in local enterprises. Furthermore, the establishment of regional financial centers positively impacts productivity growth in both the city and the surrounding areas. Conversely, a greater geographic distance between commercial banks and enterprises may impede the collection of soft information, thereby exacerbating the credit risk.

The expansion of commercial banks’ business operations has led to an increasing number of bank branches operating in various locations. Consequently, the academic community has begun to focus on the impact of the spatial distribution structure of bank hierarchical organizations on credit activities. Soft information has a distinct regional nature, making it challenging for high-level decision-making departments in banks to directly interact with borrowers in remote areas. Consequently, grassroots operational departments of banks are better positioned to acquire soft information. The collection and processing of soft information by banks can result in information asymmetry between grassroots operational departments and higher-level decision-making departments (Papi et al., 2017), leading to several issues. Alessandrini (2009) argued that greater physical and cultural distance between bank headquarters and its branches increases the cost of transmitting soft information within the bank, exacerbating information asymmetry between the two. This not only gives rise to conflicts of interest but also allows branch offices to potentially abuse their authority for personal gain. Stein (2002) analyzed the situation from the perspective of incentive mechanisms and found that due to the nonstandard nature of soft information, greater geographic distance between bank hierarchies results in higher losses and lower utilization rates of soft information. This reduces the incentive for operational departments to collect soft information, negatively impacting bank efficiency. The viewpoint was further confirmed by Presbitero et al. (2014) through a survey of the Italian banking industry, which revealed that bank headquarters tend to restrict the business activities of branch departments in remote areas. Under similar financial health conditions, the farther the geographical distance between a bank’s operating department and its headquarters in a particular region, the more restrictive clauses are included in loan contracts signed between the bank and enterprises in that region. Xu and Zou (2010) discovered in their research on China’s large- and medium-sized commercial banks serving small- and medium-sized enterprise financing that excessive use of credit approval authority, driven by the fact that branch offices possess more soft information about enterprises compared to headquarters, is detrimental not only to small- and medium-sized enterprise financing but also to bank profitability and local economic development. Agarwal and Hauswald (2010) proposed that to address the challenge of soft information transmission between bank hierarchies, commercial bank headquarters should delegate more decision-making power to bank branches located farther away from them. Based on a comprehensive literature review, it has been determined that geographical factors play a significant role in influencing the effectiveness of bank information collection and processing, in both the interactions between banks and enterprises and within banks. However, the existing studies primarily focus on examining the impact of geographical factors on corporate credit availability and local economic development, while providing limited insights into the influence of bank organizational structure spatial layout on bank credit risk from the banks’ perspective. This knowledge gap serves as the theoretical foundation for this study. The objective of this research is to develop a theoretical model centered on information asymmetry to analyze the relationship between the spatial layout of banking organizations and the credit risk, specifically within the framework of adverse selection between banks and enterprises. The main objective of the study is to examine the relationship between the spatial organizational structure of Chinese commercial banks and credit risk, considering the influence of geographical factors and information asymmetry.

3 Theoretical Analysis

In contemporary financial intermediary theory, the production of information serves as a crucial function of banks. Extant theoretical and empirical literature highlights the significance of acquiring accurate information pertaining to borrowers and their financing projects as a key determinant of bank loan decisions (Bhattacharya & Chiesa, 1995). The process of granting bank credit entails the exchange of both hard and soft information between potential borrowers and various departments within the banking institution, including the business departments and decision-making departments. Based on the available information, the decision-making department of the bank ultimately determines whether to approve the loan project, while the execution of these decisions falls under the purview of the banking department, which also oversees the borrower’s adherence to the contractual terms. Geographical factors can influence the exchange of information between banks and enterprises, subsequently impacting the transaction costs associated with credit activities. The transaction costs arising from information exchange between banks and enterprises reflect the challenges encountered in bank information production, thereby influencing the manner in which banks generate information and engage in credit-related behaviors. Simultaneously, transaction costs exert an influence on credit risk. Consequently, within the modern financial intermediary theory, the production of information remains a vital function of banks. The study is based on an adverse selection theoretical framework to analyze the associations between spatial arrangements, soft information, and credit risk. It aims to empirically test the proposition that geographical factors impact the credit risk by influencing the soft information production.

Assuming that the bank’s decision-making department is located in location C and the bank’s operations department is located in location P. The bank is in a perfect competition environment, and the deposit interest rate is r. In an uncertain economic environment, assume that the net return rate of the target enterprise is ω(ω ≥ 0), the probability distribution function of net return is F ( ω ) . The probability density function is f ( ω ) . The contract theory suggests that due to information asymmetry, verification of any output state requires payment of corresponding fees, and the optimal contract between borrowers and lenders should aim to minimize supervision costs and incentivize borrowers to disclose their true information (Bolton & Dewatripont, 2005). In this environment, Williamson (1986) demonstrated that the optimal form of contract between the borrower and the lender is as follows: When the actual amount that the borrower can repay is equal to or exceeds the agreed repayment target amount, the borrower only needs to repay the agreed amount. When the borrower’s actual repayment ability is less than the agreed repayment amount, the borrower needs to repay all of its repayable amounts to the lender. This study suggests that the optimal contract between a company and a bank is when the company’s net return rate ω ≥ R , the bank charges a loan interest rate of R. When the company’s net profit margin ω < R , the loan interest rate charged by the bank is ω . According to the basic formula of mathematical expectation, the income expectation of a bank is the weighted sum of the bank’s income under different repayment capacity states of the enterprise, and the weight is the probability of various states occurring. Therefore, under the aforementioned assumptions, the functional expression for the expected income of bank unit loans is given as follows :

In the above equation, E ( . ) is the expected income of the bank under different conditions of corporate returns and P ( . ) is the corresponding probability. It can be inferred from the assumption that the probability distribution function of a company’s net return rate is F ( ω ) . The probability density function is f ( ω ) . When the company’s net profit margin ω ≥ R , the loan interest rate charged by the bank is R , with a probability of 1 − F ( R ) . When ω < R , the interest rate charged by the bank is ω , The supervision cost paid is β p . The probability density function is f ( ω ) . Therefore, formula (1) can be rewritten as follows:

The expenditure of unit loans includes three parts. Part of it is the interest r paid by absorbing unit deposits. The other two parts are the cost of bank to enterprise information collection caused by information asymmetry between banks and enterprises β p . The operational costs arise from the transmission of information between different levels within the bank β c . Due to information asymmetry between banks and enterprises, when the net return rate of enterprises ω < R , if the bank branches of banks want to observe the true profits of the enterprise, each unit of loan needs to pay the cost of information collection β p . After collecting relevant information about loan application enterprises, the bank operations department needs to report the relevant information to the decision-making department. The decision-making department shall decide whether to approve the loan application of the enterprise and supervise the operation department to implement the relevant decisions. The principal agent problem caused by hierarchical information asymmetry during this process requires banks to pay operating costs per unit of loan β c .

Therefore, the expected cost function V of unit loans is given as follows:

In the aforemetioned equation, F ( R ) is the probability of bank supervision costs occurring ( ω < R ) . According to formula (3), the unit loan cost V of a bank is a monotonically increasing function of the information collection cost β p of the bank towards the enterprise. Therefore, keeping other conditions unchanged, there is a unique value range in this study β p * , making the bank’s unit loan income equal to the unit loan cost:

Therefore, the balance of payments equation for bank unit loans is calculated as follows:

Through simplification, it can be concluded that

The information exchange in credit activities exists not only between banks and enterprises but also between different levels within banks (operating departments and decision-making departments). They are all influenced by geographical factors. Therefore, this article draws on the existing literature (Alessandrini, 2009; Papi et al., 2017) and characterizes the geographical factors in credit activities into two parts: “operational distance” (i.e., the geographical distance between the bank’s operating department and the borrower) and “functional distance” (i.e., the geographical distance between the bank’s internal operating department and decision-making department). This study discusses their impact on credit risk separately.

Several studies have examined key aspects related to bank risk-taking, local government debt replacement, and the changing geography of banking and finance. Jiménez et al. (2013) found that increased competition within the banking sector leads to higher levels of risk-taking by banks, reinforcing the importance of understanding the relationship between competition and risk for effective management and regulation. Liang & Hao (2019) explored the effects of replacing local government debt on macroeconomic stability, revealing that debt replacement measures can mitigate macroeconomic risks associated with local government debt and contribute to overall economic stability. Alessandrini et al. (2009) discussed the evolving landscape of banking and finance, emphasizing the need to comprehend the main issues surrounding the geographic distribution of banking and financial activities to effectively address challenges and capitalize on opportunities in the industry. Liberti and Petersen (2019) underscored the significance of information, both hard and soft, in corporate finance decision-making, elucidating how different types of information can impact corporate strategies and outcomes. Agarwal and Hauswald (2010) investigated the impact of geographical distance on private information in lending transactions, revealing that distance can create informational barriers that influence lending decisions and outcomes. Collectively, these studies provide valuable insights into factors influencing decision-making processes, risk management strategies, and the overall stability of financial systems.

The operational distance of a bank measures the geopolitical intimacy between the bank’s operating department and the lending enterprise (Papi et al., 2017; Petersen & Rajan, 2002). Although the advancement of information technology has expanded the scope of hard information usage, to prevent credit risks, banks cannot simply be satisfied with collecting hard information such as financial reports from credit recipients. Commercial banks also need to collect and process soft information such as corporate reputation, business leaders’ operational capabilities, and risk preferences. Commercial banks use this information to make comprehensive and objective judgments about the financing projects of enterprises. Due to the strong regional nature of soft information, there is no unified quantitative method or evaluation standard. Its collection and translation rely on the local social and cultural environment (Liberti & Petersen, 2019). Therefore, the geographical intimacy between the operational departments of commercial banks and local enterprises is particularly important for banks to collect and process soft information. Banks with geographical proximity advantages can better understand the local social and cultural environment and establish long-term and stable social connections with enterprises. This behavior is beneficial for the bank operation department to collect and interpret information on corporate financing projects and also for supervising the execution of corporate credit contracts. It reduces the cost of information collection by banks for enterprises. Based on this, this study draws on the setting of bank supervision costs by Hongfei et al. (2020) and Porteous (1997), and sets the expression of the cost β p of bank information collection for loan enterprises as follows:

In the aforementioned equation, β p f ( β p f > 0 ) is an indicator of the transparency of the enterprise’s own information. Ope represents the operating distance of the bank. The meaning of formula (7) is that the opacity of enterprise information is the basis for the cost of bank information collection in the credit process (Gou & Huang, 2014; Zhao et al., 2010). The geographical distance between banks and enterprises will exacerbate the difficulty of banks in collecting enterprise information. The larger the operating distance Ope , the lower the degree of geographic intimacy between the bank’s operating department and enterprises and therefore, the higher the cost for banks to collect information from enterprises.

Compared to the measurement of geographic intimacy between banks and enterprises based on operational distance, functional distance reflects the impact of geographic factors on information exchange between internal levels of banks (Alessandrini, 2009). Due to the obvious regional nature of soft information, the greater the spatial distance between bank operational departments and decision-making departments, the lower the degree of geographic intimacy. The difficulty of transmitting and processing soft information within banks also increases. The problem of information asymmetry between bank hierarchy is becoming more severe. Therefore, the geographical distance between bank hierarchy not only incurs information processing costs within the bank but also leads to conflicts of interest goals between decision-making and operational departments due to information asymmetry between hierarchical department (Agarwal & Hauswald, 2010). They will undoubtedly reduce the efficiency of bank credit decision-making and increase the operating costs of banks in credit activities. Based on this, referring to the existing literature on the relationship between bank functional distance and hierarchical information friction (Stein, 2002; Zhao et al., 2010), this article sets the expression for the internal information processing cost β c of the bank as follows:

In the aforementioned equation, β c f ( β c f > 0 ) represents the reciprocal of the bank’s internal control level. Fun represents the bank’s distance. The meaning of formula (8) is that the level of internal control in a bank determines the degree of information asymmetry between bank hierarchy’s (Wang & Zhang, 2019). The functional distance of banks will exacerbate the impact of internal control levels on the degree of information asymmetry between banks. The larger the functional distance Fun, the higher the internal information processing cost of commercial banks.

Combining formula (4), when the bank’s credit balance is β p = β p * , we obtain

For a specific bank, when the spatial distribution of its operating departments remains unchanged (i.e., Ope is a fixed value), if the enterprise information transparency indicator β p f > β p f * is used, the bank will be unable to maintain a balance of income and expenditure. Therefore, commercial banks are unable to issue loans to the enterprise. So β p f * is the minimum requirement for enterprise information transparency in bank credit decisions.

This study substituted formulas (8) and (9) into formula (6) to obtain:

Because of E ( β p f * ) > 0 , R − ∫ 0 R F ( ω ) d ω − ( r + Fun × E ( β c f ) ) > 0 , therefore,

According to formulas (12) and (13), it can be seen that the critical value β p f * of the transparency of enterprise information that can obtain loans is negatively correlated with the operational distance Ope and functional distance Fun of the bank. Due to the smaller β p f * , transparency of enterprise information is higher. The negative correlation between β p f * and Ope and Fun indicates that the greater the operational and functional distance of banks, the higher the requirement for information transparency of loan application enterprises. Due to the fact that information transparency is a reflection of the quality of hard information (Gou & Huang, 2014; Zhong & Chuanwei, 2010), banks have higher requirements for enterprise information transparency, which means that they are increasingly relying on the use of hard information in credit activities. The production of soft information by banks is becoming increasingly scarce. This is because as the operational and functional distance of banks expands, bank branches may find it difficult to collect soft information from enterprises or be unable to effectively transmit it to decision-making departments. Therefore, whether from the perspective of soft information collection volume or the efficiency of soft information processing, the expansion of bank operation distance and functional distance will result in a decrease in bank soft information production. Therefore, the process of expanding the operational and functional distance of bank branches is also a continuous suppression of soft information by hard information. The interpretation of hard information’s practical significance relies on the incorporation of soft information. As the functional and operational distance between bank branches and enterprises expands, the ability to effectively gather and analyze soft information becomes crucial in detecting shifts in the relationship between enterprise hard information and credit risk. Consequently, if banks are unable to adequately collect and process soft information, it becomes challenging to ascertain the reliability of hard information provided by loan applicants. This, in turn, hampers banks’ ability to differentiate pricing between enterprises that possess similar hard information attributes but exhibit varying levels of risk. Under such circumstances, commercial banks can only establish loan interest rates based on anticipated returns.

In the formula, R b and R g are the highest interest rates that can be accepted for loans to high-risk and low-risk enterprises, respectively. At this point, only high-risk enterprises will accept loan contracts, while low-risk enterprises will turn to other banks. This leads to a serious problem of adverse selection. It can lead to high-risk characteristics in bank loan projects.

Based on the aforementioned analysis, this study proposes the following propositions:

4 Research Design

5 Empirical Analysis

This study applies a mediating effect model to empirically analyze the theoretical proposition proposed in the third section. Recognizing the potential presence of path dependence in the bank’s credit risk indicator (Ris) and soft information indicator (lnSof), the study incorporates the lagged value of the dependent variable in the explanatory variable to control for the influence of historical factors on the current period’s dependent variable. However, to address endogeneity issues associated with including the lagged term of the dependent variable in the independent variable, the study employs the generalized method of moments (GMM) estimation for regression analysis of the mediating effect econometric equation, aiming to obtain more accurate and unbiased results. The GMM estimation method includes two forms: differential generalized method of moments (Diff-GMMs) and system generalized method of moments (Sys-GMM). Compared to differential GMM, system GMM can solve the problem of weak instrumental variables and improve estimation efficiency. Therefore, this article chooses the system GMM estimation method. The use of the GMM method requires the assumption that the instrumental variables are set reasonably. The model disturbance terms do not have autocorrelation. These two tests can be achieved through Hansen and AR (2) statistics, respectively. The original assumptions are that all instrumental variables are valid, and there is no second-order autocorrelation in the model residual term. To control for the impact of heteroscedasticity on regression results, this article used robust standard error in regression.

The study employs GMM to address endogeneity. System GMM is chosen over differential GMM to effectively handle weak instruments and improve efficiency, ensuring appropriate technique selection. In our study, we employ the GMM to mitigate endogeneity concerns arising from the inclusion of lagged dependent variables as explanatory variables. By utilizing instrumental variables, the GMM method facilitates consistent and efficient estimation, thereby enhancing the validity of our findings. We specifically choose the system GMM approach over differential GMM due to its capacity to effectively handle weak instrumental variables and improve estimation efficiency. This deliberate selection ensures that the adoption of the GMM method is grounded in methodological considerations rather than arbitrary choice. Regarding the selection between fixed effects (FE) and random effects (RE), we justify our preference for FE estimation. We underscore that FE estimation allows us to account for unobservable time-invariant heterogeneity across banks, a crucial aspect in our study. By incorporating FE, we effectively address potential omitted variable bias originating from unobserved factors that may impact both the explanatory variables and the dependent variables.

The use of the GMM method for regression requires setting the predetermined and endogenous variables in the model. In terms of the relationship between the dependent variable bank risk Ris, the intermediary variable soft information lnSof, and the core explanatory variables bank operational distance lnOpe and functional distance lnFun, according to the theoretical analysis in this article, operational distance and functional distance can affect credit risk by influencing soft information. However, the spatial layout of banking organizations may also be affected by credit risks and soft information collection. Commercial banks will fully consider their own risk control and information collection capabilities in the region when selecting branch locations. To avoid the impact of endogeneity caused by bidirectional causality on the regression results of this article, the instrumental variable method is adopted in the following regression. Referring to the approach in the literature, this article selects the average values of operating distance lnOpe and functional distance lnFun of the same type of bank in the same year, mean_lnOpe and mean_lnFun as instrumental variables for both. For the purpose of the robustness test, this article also gives the regression results of fixed effect instrumental variable regression (FE_IV) and Diff-GMM. If the regression results of the three methods are relatively consistent, it indicates that the regression results in this article are robust.

The existing literature in the field of banking and finance has explored several important aspects related to bank stability, risk governance, and the impact of financial technology (FinTech) on financial stability. This literature review will discuss three relevant studies that contribute to our understanding of these topics. Nguyen (2022a) investigates the relationship between audit committee structure, institutional quality, and bank stability in ASEAN countries. The study finds that a strong audit committee and higher institutional quality are associated with enhanced bank stability. The findings highlight the importance of effective governance mechanisms in mitigating risks and promoting financial stability in the banking sector. In another study by Nguyen (2022b), the determinants of bank risk governance structure are examined through a cross-country analysis. The research identifies various factors that influence the choice of risk governance structures in different countries. The study emphasizes the significance of regulatory frameworks, legal systems, and market characteristics in shaping risk governance practices in banks.

The impact of FinTech development on financial stability in emerging markets is explored by Nguyen (2022c). The study investigates the role of market discipline in moderating the relationship between FinTech development and financial stability. The findings suggest that a well-functioning market discipline mechanism can mitigate the potential risks associated with the rapid growth of FinTech and contribute to overall financial stability in emerging markets.

From the regression results in Tables 4–6, it can be seen that P-values of Hansen and Ar (2) tests are both greater than 0.1. It indicates that the instrumental variable setting is effective, and there is no sequence autocorrelation in the second-order difference of the perturbation term. Therefore, the regression results of Sys GMM in this article are effective. The regression results of the Sys-GMM are consistent with the coefficient sign and significance of the FE_IV method and Diff-GMM regression results. It indicates that the regression results in this article are robust. Therefore, this article will mainly conduct empirical analysis based on the regression results of the system GMM model.

6 Conclusion and Suggestion