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Article

Underwriter Discourse, IPO Profit Distribution, and Audit Quality: An Entropy Study from the Perspective of an Underwriter–Auditor Network

1
School of Economics and Management, Bei**g University of Technology, Bei**g 100124, China
2
School of Public Policy and Management, Tsinghua University, Bei**g 100084, China
*
Authors to whom correspondence should be addressed.
Entropy 2024, 26(5), 393; https://doi.org/10.3390/e26050393
Submission received: 17 March 2024 / Revised: 25 April 2024 / Accepted: 29 April 2024 / Published: 30 April 2024
(This article belongs to the Special Issue Complexity in Financial Networks)

Abstract

:
Underwriters play a pivotal role in the IPO process. Information entropy, a tool for measuring the uncertainty and complexity of information, has been widely applied to various issues in complex networks. Information entropy can quantify the uncertainty and complexity of nodes in the network, providing a unique analytical perspective and methodological support for this study. This paper employs a bipartite network analysis method to construct the relationship network between underwriters and accounting firms, using the centrality of underwriters in the network as a measure of their influence to explore the impact of underwriters’ influence on the distribution of interests and audit outcomes. The findings indicate that a more pronounced influence of underwriters significantly increases the ratio of underwriting fees to audit fees. Higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals that companies underwritten by more influential underwriters experience a decline in audit quality. Finally, the study reveals that a well-structured audit committee governance and the rationalization of market sentiments can mitigate the negative impacts of underwriters’ influence. The innovation of this paper is that it enriches the content related to underwriters by constructing the relationship network between underwriters and accounting firms for the first time using a bipartite network through the lens of information entropy. This conclusion provides new directions for thinking about the motives and possibilities behind financial institutions’ cooperation, offering insights for market regulation and policy formulation.

1. Introduction

Networks enhance organizational performance through knowledge transfer and information sharing (Zhao et al., 2023; Chahine et al., 2019) [1,2]. The role of underwriter networks in the IPO (Initial Public Offering) process has increasingly attracted scholarly and industry-wide attention (Rumokoy et al., 2019; Bajo et al., 2016; Chuluun, 2015) [3,4,5]. The network of underwriters connected by the lead underwriter (through participation in various IPO syndicates) plays a critical role in information extraction and dissemination during the IPO underwriting process (Corwin and Schultz, 2005) [6]. The central position of underwriters within their peer networks affects multiple IPO characteristics of the listed companies, including the likelihood and magnitude of IPO offer revisions, as well as short-term and long-term returns (Vithanage et al., 2016) [7]. Moreover, as underwriters often collaborate in syndicates during the IPO process, they naturally leverage their peer networks to enhance underwriting performance. Although underwriters can significantly impact various aspects of the IPO through access to additional information and channels via their relationship networks, research on underwriter relationship networks remains insufficiently explored, especially regarding their connections with other financial institutions. This paper aims to better examine the role of underwriter relationship networks.
In fact, beyond the underwriter-to-underwriter relationship networks, underwriters also establish close connections with accounting firms through repeated collaborations. These connections enable underwriters to acquire valuable information more accurately and comprehensively, reducing information asymmetry between underwriters, listed companies, and accounting firms. On the other hand, close relationships between underwriters and accounting firms could potentially affect the audit independence of the accounting firms (DeFond et al., 1999) [8]. Current research has not addressed the impact of the relationship networks between underwriters and auditors on IPOs. Our study focuses on how the central position of underwriters in their relationship networks with auditors impacts the distribution of interests between the two parties.
Claude Shannon, the father of information theory, drew from thermodynamics concepts to propose in 1948 that all information contains redundancy, and the average amount of information after excluding redundancy is termed “information entropy”. As a physical quantity measuring the disorder of a system, entropy is widely used in the social sciences to analyze complex networks and uncertainty issues (** to mitigate problems of information asymmetry and uncertainty. Information can be categorized into private and public. On one hand, private information flows within relationships, reducing information asymmetry among related parties. On the other hand, institutions with strong relationships often leverage these networks to seek economic benefits. Notably, the business of IPO underwriting is relationship-intensive, making it theoretically and practically significant to study how underwriters leverage relational networks to gain economic benefits in the specific context of China.
Third, there are challenges to the full independence of auditors. According to the “Chinese Certified Public Accountants Professional Ethics Code”, accounting firms should not adopt charging arrangements that result in severe adverse effects on their own interests due to direct or indirect forms of compensation, as no safeguards could reduce this to an acceptable level. However, data published on the China Securities Regulatory Commission’s official website indicate the existence of contingent fee clauses in IPO project business agreements with accounting firms, where some fees are collected after the fundraising is completed or upon registration and review completion, making some fees dependent on the final outcome of the IPO project. This suggests that the independence of accounting firms in China’s IPO market faces challenges. Indeed, research indicates that in China, the choice of auditors is more likely based on mutual practical needs rather than auditors’ capabilities (** the distribution of interests through acquiring and exchanging information, resources, and other social capital. Given the issuance fee set by the company, underwriters might choose specific accounting firms, thus turning the right of selection to their own benefit, thereby increasing the proportion of underwriting fees to audit fees. Therefore, we propose our first hypothesis:
H1. 
Underwriters with greater influence will significantly increase the proportion of underwriting and auditing fees.
The influence wielded by underwriters in the network of relationships with accounting firms extends beyond just audit quality. While it is true that the level of their influence can impact audit quality through factors like auditor independence, auditor professionalism, and audit work, the primary focus of Hypothesis H1 is the significant increase in the proportion of underwriting and auditing fees associated with more influential underwriters.
In the realm of auditor independence, it is worth noting that the existence of a relationship network between underwriters and accounting firms can indeed reduce the independence of the latter. Repeated collaborations between underwriters and auditors often signify a relationship that transcends mere professionalism. Scholars have observed (**e and Yan, 2013) [46] that signing auditors, in practice, may not exhibit substantial independence. Prolonged auditor–client relationships have the potential to undermine audit quality (Tepalagul and Lin, 2015) [47]. A lack of auditor independence might lead to an overreliance on client management, possible underestimation of risks, and consequently, a more lenient audit approach with inadequate or inappropriate procedures (Chi et al., 2009) [48].
Concerning auditor professionalism, greater influence from underwriters may prompt accounting firms to compromise on their professional standards for audits. Since underwriters occupy a prominent position in the IPO process, they might prefer accounting firms that are more aligned with their goals and responsive to their needs, as opposed to those renowned for their audit quality and professionalism.
When it comes to audit work, a stronger influence from underwriters can reinforce their interests, often leading to a reduction in audit fees. Lower audit fees might prompt accounting firms to adopt cost-cutting strategies, such as reducing auditor numbers or the depth of audit procedures. This can undermine the rigor and comprehensiveness of audits, making it challenging to identify potential financial irregularities. As a result, auditors may be more likely to conduct non-in-depth audits, ultimately compromising audit quality (Dye, 1993) [49].
H2. 
Higher underwriter influence leads to a decline in audit quality.
The H1 addresses the economic implications in terms of fee structures, while the H2 explores broader audit quality impacts. While the hypotheses are related, they each contribute to an understanding of a different aspect of the IPO process: the economic impact and the audit quality impact.

5. Data and Methods

5.1. Data and Sample Selection

First, we filter out all Chinese A-share companies listed on the Shanghai and Shenzhen Stock Exchanges from 2014 to 2022 whose data are available in the China Stock Market and Accounting Research (CSMAR) database. The construction of the underwriter–accounting firm bipartite network and company-specific financial data are derived from the CSMAR database. Our initial sample selection is as follows: (1) Due to the unique nature of enterprises in the financial sector, we exclude them from our research sample; (2) To avoid the influence of abnormal company data on our research results, we eliminate companies whose stock codes begin with “ST”; (3) We exclude observations missing data. Ultimately, we obtained 1468 company-year observations. To mitigate the impact of outliers, all continuous variables were winsorized at the 1% upper and lower levels.

5.2. Methods

Information entropy, a concept originally introduced by Claude Shannon, provides a mathematical framework to measure the uncertainty or randomness in a given system. In the context of underwriter relationship networks, this metric can be adapted to quantify the centrality of individual underwriters.
To calculate the centrality of underwriters using information entropy, we first need to construct a network model where nodes represent underwriters and accounting firms, and edges represent their relationships or collaborations. The strength of these relationships can be weighted based on factors such as the frequency or value of their collaborations.
Once the network is established, we can compute the centrality of each underwriter by considering their connectivity within the network. A highly central underwriter will have a large number of strong connections, indicating their importance in the network.
Information entropy comes into play when we consider the distribution of these connections. If an underwriter has a highly uneven distribution of connections (i.e., they are strongly connected to only a few other underwriters), their centrality will be reflected in a lower entropy value. Conversely, if their connections are more evenly distributed, the entropy value will be higher.
In summary, the use of information entropy to quantify the centrality of underwriters in the network provides a valuable tool for understanding their influence and role in the IPO process. This metric not only helps to identify key players but also sheds light on how their position affects the distribution of benefits and audit outcomes.

6. Measures of Underwriter Influence and Distribution of Interests

6.1. Characteristics Representing Underwriter Influence

We hypothesize that the extent of collaboration between underwriters and accounting firms in their network during an IPO influences the pattern of interest distribution in the IPO. If an underwriter and an accounting firm have previously participated in the same IPO, we consider them to be connected. We describe the position of underwriters within the bipartite network of connections with accounting firms using various SNA measures, which we refer to as centrality measures.
To calculate these centrality measures, we need to construct an adjacency matrix X, which is an N × M matrix (where N is the number of underwriters in the network, and M is the number of accounting firms). If underwriter i and accounting firm j have jointly participated in k IPOs, then xij = k; if underwriter i and accounting firm j have not jointly participated in any IPOs, then xij = 0.
Given the dynamic nature of the network of relationships between underwriters and accounting firms, we construct the underwriter centrality network on a rolling basis using data from the three years preceding the IPO. Specifically, the network of relationships for underwriters in 2021 is constructed based on every collaboration between underwriters and accounting firms from 2018 to 2020. A visualization analysis is presented in Figure 1:
In the constructed bipartite network of underwriters and accounting firms, network centrality is applied to measure the industry standing of underwriters. Given the more complex structure of bipartite networks compared to unipartite networks, this study uses three centrality measures for assessment in the bipartite network: Degree Centrality, Closeness Centrality, and Betweenness Centrality. The specific introductions to these measures are as follows:
Degree Centrality refers to the number of connections or degree of a node, which is the count of direct connections that the node has with other nodes. In the constructed bipartite network of underwriters and accounting firms, a higher degree centrality of an underwriter indicates a greater number of connected accounting firms, meaning the underwriter plays a more significant role in the entire network. The Formula (1) for calculating this measure is as follows:
D e g r e e i = x i j n 1
where xij Equation (1) represents that there is a cooperative relationship between underwriter i and j, and n equals the number of underwriters in the bipartite network of underwriters and accounting firms.
It measures how close a node is to all other nodes in the network. In the bipartite network of underwriters and accounting firms, closeness centrality can describe the role of a certain underwriter in transmitting information and resources among other accounting firms.
Specifically, in a bipartite network, underwriters and accounting firms represent two important types of nodes. If an underwriter has many connections with an accounting firm, then this underwriter has a high closeness centrality. This means they can more easily connect with other accounting firms and transmit information and resources to them; dij is the shortest path length between underwriter i and accounting firm j. The Formula (2) for calculating this measure is as follows:
C l o s e n e s s i = j = 1 n d i j n 1
In the bipartite network of underwriters and accounting firms, a higher betweenness centrality for an underwriter indicates that the underwriter is closer to other accounting firms, facilitating easier exchange of information and sharing of resources with other accounting firms, as well as enabling more efficient dissemination of information within the network; bjk is the number of shortest paths between accounting firm j and accounting firm k, while bjk(i) is the number of shortest paths between accounting firm j and accounting firm k that pass through underwriter i. The Formula (3) for calculating this measure is as follows:
B e t w e e n n e s s i = 2 j n k n b j k ( i ) n 2 3 n + 2
Formula (4) for calculating the weighted average of degree centrality, closeness centrality, and betweenness centrality for each underwriter in the bipartite network of underwriters and accounting firms as the network centrality of the underwriter (LIU et al., 2021) [50] is as follows:
C e n t r a l i t y = D e g r e e + C l o s e n e s s + B e t w e e n n e s s 3

6.2. Characteristics Representing Underwriter Interest Distribution

This paper adopts the interest distribution measure using the ratio of underwriting fees to auditing fees (SharingRatio) to represent the situation of underwriter interest distribution. Following the practices of existing literature, the model includes the following control variables: Big4 is a dummy variable, assigned a value of 1 if the company is audited by one of the Big Four accounting firms (PricewaterhouseCoopers (London, UK), Deloitte (London, UK), KPMG (Seoul, Republic of Korea), Ernst & Young (London, UK)), and 0 otherwise. Size is the natural logarithm of the company’s total annual assets, and age measures the company’s years since listing. REC is receivables, calculated as the latest annual receivables before listing divided by total assets, and INV is inventory, calculated as the latest annual inventory before listing divided by total assets. REC and INV reflect the complexity of the enterprise. Studies on the British audit market have found that the size and complexity of listed companies explain 79% of audit fees (Pronobis and Schaeuble, 2022) [51]. Lev is the leverage ratio, calculated as total liabilities at year-end divided by total assets at year-end. Roa is the return on assets, calculated by dividing net profit by the average balance of total assets. These two indicators comprehensively reflect the company’s performance and risk. Soe is a dummy variable, assigned a value of 1 for state-owned enterprises and 0 otherwise. Board reflects the number of members on the company’s board of directors. To test Hypotheses 1 and 2, this paper employs the following regression models:
SharingRatio = α 0 + α 1 c e n t r a l i t y + α j c o n t r o l i + ε
r e s t a t e = α 0 + α 1 c e n t r a l i t y + α j c o n t r o l i + ε
c s c o r e = α 0 + α 1 c e n t r a l i t y + α j c o n t r o l i + ε
Each variable is defined as shown in Table 1:

7. Empirical Testing

Table 2 presents the descriptive statistics of the sample. The column N represents the number of samples, the column mean represents the mean of the sample, sd represents the standard deviation, min represents the minimum, max represents the maximum, and p50 represents the median. The average value of the SharingRatio is 8.1231, with a minimum value of 1.6308 and a maximum value of 46.5338, indicating that the ratio of underwriting fees to auditing fees for listed companies varies from 1.6308 to 46.5338. This suggests significant variation in this ratio among different companies, which could be influenced by various factors such as company size, business complexity, market environment, or pricing strategies between underwriters and auditing institutions. The average value of centrality is 0.3218, indicating that the centrality of nodes in the network is generally at a medium level. However, the large gap between its minimum value of 0 and maximum value of 0.4783 reveals clear centrality differences within the network. This means that the cooperative relationships between underwriters and accounting firms are not balanced, with some underwriters occupying more central positions in the network and having access to more resources.
Table 3 and Table 4 report the frequency of collaboration between lead underwriters and accounting firms and the statistics on the number of IPOs undertaken by lead underwriters, respectively. The results show that the average number of collaborations between lead underwriters and accounting firms is 8.57, indicating that lead underwriters and accounting firms have established relatively stable cooperative relationships in the IPO process. The maximum number of collaborations is 23, further highlighting the high degree of dependence between certain lead underwriters and specific accounting firms. A significant number of underwriters collaborate with accounting firms from between 2 to 10 times. The average number of IPOs undertaken by lead underwriters is 22.58 times, with a maximum of 123 times, demonstrating significant differences in the resources controlled by different underwriters in the IPO process. These differences are influenced by the underwriter’s market position, professional capability, capital strength, and the closeness of relationships with issuers, regulatory bodies, and other parties.
Table 5 reports the regression results on the impact of underwriter influence within the bipartite network of underwriters and accounting firms on the distribution of IPO interests. The regression controls for year and industry fixed effects, and the empirical results show a significant positive correlation between the centrality of underwriters in the bipartite network and the proportion of underwriting and auditing fees, significant at the 1% level. In other words, the higher the network centrality of the underwriter, indicating greater influence, the higher the proportion of underwriting and auditing fees. These regression results validate Hypothesis H1. In the competitive IPO market, higher network centrality of underwriters, indicating stronger influence, consolidates their interests, thereby leading to a decrease in the proportion of audit fees.
Table 6 reports the regression analysis on the distribution of IPO interests within the bipartite network of underwriters and accounting firms, employing the degree centrality, closeness centrality, and betweenness centrality of underwriters as new explanatory variables to measure the level of underwriter influence. The regression controls for year and industry fixed effects and the results show that degree centrality, closeness centrality, and betweenness centrality have a significant positive correlation with the proportion of underwriting and auditing fees, reaching a significant level of 1%, thus validating the previous hypothesis.
Specifically, we find that in the bipartite network of underwriters and accounting firms, network centrality has an important impact on the distribution of IPO interests. The degree centrality of an underwriter reflects their level of connection with other accounting firms within the network, closeness centrality indicates the distance between the underwriter and other accounting firms, and betweenness centrality measures the importance of the underwriter as a mediator of information within the bipartite network. These centrality indicators, substituting for the core explanatory variable of underwriter influence–network centrality, allow for a more comprehensive consideration of the level of underwriter influence within the bipartite network.
In the main regression tests, we employ data from the three years prior to the IPO to construct the underwriters’ network centrality on a rolling basis. Since the network of relationships between underwriters and accounting firms is dynamically changing, here we construct the underwriters’ centrality network on a rolling basis using data from the five years preceding the IPO. Specifically, the network of relationships for underwriters in 2021 is based on every collaboration between underwriters and accounting firms from 2016 to 2020. Table 7 reports that in the five-year rolling bipartite network of underwriters and accounting firms, there is a significant positive correlation between underwriters’ network centrality and the proportion of underwriting and auditing fees, significant at the 1% level. This means that the higher the network centrality of the underwriter, indicating greater influence, the higher the proportion of underwriting and auditing fees, suggesting that the results are robust.
Table 8 reports the regression analysis conducted using different estimation methods. Column 1 controls for fixed effects of the year, industry, and region; Column 2 controls for individual and regional fixed effects; Column 3 controls for industry and regional fixed effects; Column 4 controls for the interaction of year and regional fixed effects; Column 5 controls for the interaction of year and industry as well as the interaction of year and regional fixed effects. The results still indicate that within the bipartite network of underwriters and accounting firms, there is a significant positive correlation between the centrality of underwriters in the network and the proportion of underwriting and auditing fees, significant at the 1% level.
To more comprehensively depict and understand the IPO market, we include market influence factors as control variables. We use the cumulative market return 120 trading days before the IPO, the standard deviation of the cumulative return, and the natural logarithm of the number of companies listed 120 trading days before the IPO plus one as standards for measuring market sentiment. The regression results in Table 9 show that after including the three control variables, there is a significant positive correlation between the centrality of underwriters in the bipartite network of underwriters and accounting firms and the proportion of underwriting and auditing fees, significant at the 1% level. The results remain robust.
In the bipartite network of underwriters and accounting firms, due to potential endogeneity between underwriters’ network centrality and other factors, this suggests that the centrality of underwriters in the network could be influenced by the underwriters’ reputation and the number of IPOs they handle. To mitigate the issue of endogeneity and accurately identify the independent impact of underwriters’ influence on the distribution of IPO interests, this paper selects the underwriters’ market share in IPOs as a proxy for the underwriters’ reputation and the number of IPOs handled by the underwriters as instrumental variables. An underwriter’s market share can indirectly reflect its reputation. In general, underwriters with larger market shares tend to have higher reputations because they are able to attract more IPO business. Therefore, it is reasonable to use market share as a proxy variable for reputation. The number of IPOs handled by the underwriters is a variable that is correlated with the centrality of the underwriter network, but not directly with the distribution of IPO benefits. It can be used as a valid instrumental variable to help determine the independent effect of underwriter influence on the distribution of IPO benefits. By using this instrumental variable, we can control for the number of IPOs handled by underwriters and thus more accurately estimate the impact of underwriter network centrality on other variables. The study employs a two-stage least squares (TSLS) regression analysis. The regression results show that Kleibergen–Paap rk LM statistic is significant at the 1% level, rejecting the hypothesis of insufficient identification of instrumental variables; the Cragg–Donald Wald F statistic is larger than the critical value at the 10% significance level of the Stock–Yogo weak instrumental variable identification F test which rejects the original hypothesis of weak instrumental variables; in conclusion, the instrumental variables selected in this paper are reasonable and reliable. The regression results in Table 10 show that the coefficients for the underwriters’ IPO market share, a measure of underwriters’ reputation, and the number of IPOs handled by underwriters are statistically significant and positive at the 1% level. This further validates the reliability of the conclusions, meaning that the underwriters’ IPO market share and the number of IPOs independently influence the distribution of IPO interests. The research findings address the endogeneity issue between underwriters’ network centrality and other factors and draw reliable conclusions about the impact of underwriters’ influence on the distribution of IPO interests.
Table 11 reports a regression analysis on abnormal underwriting fees within the bipartite network of underwriters and accounting firms. The regression results indicate a significant positive correlation between the centrality of underwriters and abnormal underwriting fees, reaching a significant level of 1%.
Specifically, there is a positive correlation between the influence of underwriters and the underwriting fees they receive. Underwriters with higher influence are often able to raise funds more effectively for issuing companies, reduce issuance risks, and provide more value-added services. Consequently, issuing companies are more willing to pay higher fees for these services. Additionally, highly influential underwriters may also leverage their market influence to increase underwriting fees, thereby earning higher profits. This situation could lead to an abnormal increase in underwriting fees. For issuing companies and investors, understanding and reasonably evaluating this relationship is crucial for ensuring the efficient operation of the capital market and resource allocation.
Table 12 reports a regression analysis on the audit quality of listed companies underwritten within the bipartite network of underwriters and accounting firms. The audit quality of the companies is measured by the likelihood of financial statement restatements and the robustness of accounting practices using the Cscore model for the fiscal year of the company’s listing. The regression results show a decrease in audit quality for listed companies underwritten by underwriters with higher influence, specifically indicated by an increased probability of financial statement restatements during the year of listing and a reduction in financial robustness.
Specifically, audit quality is an important indicator of the accuracy and reliability of audit work. A decline in audit quality means there is an increased risk of significant errors or misleading information in the financial statements. This may compromise the independence and objectivity of the audit.
Further, this decline in audit quality is specifically reflected in an increased likelihood of financial statement restatements in the year of listing. Financial statement restatement refers to the process of identifying and correcting errors or misleading information in financial statements of previous years. If underwriters interfere with the preparation of financial statements during the listing process, these errors or misleading pieces of information are likely to be discovered and required to be restated in subsequent financial statements.
Lastly, such intervention and manipulation could also lead to weakened financial robustness of the company. Financial robustness refers to the ability of a company to maintain financial stability and continuous operation in the face of uncertainty and risk. When underwriters intervene in financial statements for their own benefit, they may conceal the true financial condition and risks of the company, thereby weakening its financial robustness.
Therefore, in the capital market, there should be strengthened regulation and constraint of underwriters to ensure the fairness and legality of their actions, protect the interests of investors, and promote the healthy development of the capital market.
Table 13 reports that in the heterogeneity test, a well-structured audit committee governance and the rationalization of market sentiment can mitigate the negative impact of underwriters’ influence to a certain extent. The regression results show a significant positive correlation between underwriters with higher influence and higher audit quality.
Specifically, as a crucial component of the corporate governance structure, the audit committee significantly influences the quality of financial reporting and information disclosure. The independence and expertise of the audit committee can enhance its supervisory capacity and governance effectiveness, improving the accuracy and reliability of financial reporting, thereby reducing the impact of underwriters’ influence on investors’ decisions.
The rationalization of market sentiment can also weaken the negative impact of underwriters’ influence. Underwriters often exploit market sentiment for their benefit, and the rationalization of market sentiment can reduce the occurrence of such manipulative behaviors, enabling investors to make more rational decisions, thus diminishing the negative impact of underwriters’ influence on the market.
In summary, a well-structured audit committee governance and the rationalization of market sentiment can mitigate the negative impact of underwriters’ influence to some extent, enhancing market stability and the quality of investors’ decisions.

8. Research Conclusions and Policy Recommendations

This paper introduces the concept of information entropy and selects 1468 IPOs of companies listed on the Shanghai and Shenzhen A-share markets from 2014 to 2022 as samples. Using the Ucinet (6.186) software, it constructs a bipartite network of underwriters and accounting firms during the IPO process and calculates the network centrality indicators within the bipartite network to measure the influence of underwriters. It empirically tests the significant role and mechanisms of underwriters’ influence on the distribution of IPO interests. Information entropy, as a tool to measure information uncertainty and complexity, provides a unique analytical perspective and methodological support for this study.
The main conclusions include the following points: when underwriters possess more significant influence, the ratio of underwriting fees to auditing fees significantly increases. Furthermore, more evidence suggests that higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals a decline in audit quality for companies underwritten by underwriters with higher influence, specifically indicated by an increased likelihood of financial statement restatements in the year of listing and weakened financial robustness. Lastly, the study reveals that a well-structured audit committee governance and rationalization of market sentiment can mitigate the negative impact of underwriters’ influence to some extent. Information entropy, a measure of the uncertainty or randomness of information, plays a crucial role in this context.
In financial markets, the cooperative relationship between underwriters and accounting firms may lead to moral hazards and conflicts of interest in some cases. Underwriters’ influence might also compromise auditors’ independence. There exists a close interest relationship between underwriters and clients, where underwriters can influence auditors’ interpretation of clients’ economic conditions and financial reports, potentially negatively impacting audit quality and investors’ interests.
The research in this paper has the following limitations: Firstly, the scope of the study is relatively narrow, as this study mainly focuses on the underwriters’ influence in the IPO process and its impact on the distribution of benefits, without delving into the network of relationships among other financial institutions and how these networks jointly affect the entire process and outcome of IPOs. Future research could further expand the scope of the study to explore a wider range of relationship networks and mechanisms. Secondly, while the findings of this study provide empirical evidence of the important role and mechanisms of underwriters in the distribution of IPO benefits, more theoretical and empirical support is needed to further validate and refine these findings. Future research could explore underwriters’ influence and its long-term impact on the IPO market in depth from more perspectives and levels. Finally, we will not only focus on quantitative analysis in our follow-up study but will also include characteristics of underwriters and accounting firms for better qualitative analysis.
Based on our findings, we make a number of policy recommendations. Firstly, regulatory authorities must establish stricter rules and monitoring systems to oversee the relationship between underwriters and accounting firms, ensuring transparency and preventing conflicts of interest, while conducting regular audits to address any potential moral hazards. Secondly, to improve audit quality, accounting firms should be encouraged to maintain their independence from underwriters, with measures put in place to prohibit underwriters from influencing audit results. Thirdly, to enhance market competitiveness and transparency, regulators should consider policies that encourage diversity among underwriters and accounting firms, such as rotating underwriters and auditors, ultimately protecting investor interests and maintaining high-quality audits and underwriting services.

Author Contributions

Conceptualization, S.Y.; methodology, Q.Z.; software, Y.C. (Yu Cao).; validation, Y.T.; formal analysis, Y.C. (Yunzhu Chen).; investigation, S.Y.; resources, Y.T.; data curation, Q.Z.; writing—original draft preparation, Q.Z.; writing—review and editing, Y.T.; visualization, Y.C. (Yunzhu Chen).; supervision, Y.T.; project administration, Y.C. (Yu Cao). All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the National Social Science Foundation of China, grant number 21ASH003; National Social Science Fund youth project of China, grant number 2023-SKJJ-C-080.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

All data used are available in published sources.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Table A1. Summary of issuance expenses for newly listed companies from 2011 to 2022.
Table A1. Summary of issuance expenses for newly listed companies from 2011 to 2022.
Summary of Issuance Expenses for Newly Listed Companies from 2011 to 2022
MetricTotal Fundraising Amount (Billion)Issuance Expenses (Million)Underwriting Fees (Million)Audit Fees (Million)Legal Fees (Million)Disclosure Fees (Million)Other Fees (Million)Issuance Expenses as % of Total FundraisingAudit Fees as % of Total FundraisingRatio of Issuance Fees to Underwriting Fees
Average10.166719.565138.48643.47372.56371.21252.7410.39%1.14%1.37
Median5.565502.533950552.85300424.53809.77%0.88%1.34
Maximum532.3062,432.6960,173.267016.463750845.488421.3834.88%6.92%2.39
Minimum0.38898.82400355.328.32.670.13%0.12%1.03
Standard Deviation24.614565.444139.06501.57286.18173.64465.630.04550.01020.1865

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Figure 1. Underwriter–accounting firm network visualization.
Figure 1. Underwriter–accounting firm network visualization.
Entropy 26 00393 g001
Table 1. Definition of variables.
Table 1. Definition of variables.
StatsDefinition
SharingRatioThe ratio of underwriting fees to auditing fees for listed companies
centralityThe average of degree centrality, closeness centrality, and betweenness centrality
restateRestatement of financial statements in the year of a company’s listing
cscoreCscore model
degreeDegree centrality: the number of accounting firms with which the underwriter collaborates
closenessCloseness centrality: the underwriter’s ability to transmit information and resources
betweennessBetweenness centrality: the underwriter’s capacity to act as a mediator
big4A company audited by one of the Big Four (PricewaterhouseCoopers, Deloitte, KPMG, Ernst & Young) is marked as 1, otherwise 0
sizeThe natural logarithm of annual total assets
levTotal liabilities at year-end divided by total assets at year-end
roaNet profit divided by the average balance of total assets
soeState-owned enterprises are marked as 1, others as 0
recThe ratio of net receivables to total assets
invThe ratio of net inventory to total assets
ageln (year of listing—year of establishment +1)
boardThe natural logarithm of the number of board members
marketCumulative market return 120 trading days before the IPO
market.stdStandard deviation of daily market returns 120 trading days before the IPO
hotHot market, the number of companies listed 120 trading days before the IPO plus one, taken as the natural logarithm
underwriterUnderwriter market share
abnormalAbnormal underwriting fees
Table 2. Descriptive statistics.
Table 2. Descriptive statistics.
StatsNMeansdMinMaxp50
SharingRatio14688.12316.71651.630846.53386.1038
centrality14680.32180.09840.00000.47830.3397
degree14680.26740.14050.00000.55900.2780
closeness14680.66670.15360.00000.80800.7080
betweenness14680.03130.02600.00000.11900.0270
big414680.05930.23620.00001.00000.0000
size146820.85360.920319.316024.181720.6962
lev14680.35160.16410.06530.75760.3361
roa14680.07570.03660.01130.21650.0715
soe14680.08990.28620.00001.00000.0000
rec14680.14030.10260.00070.45370.1214
inv14680.11300.08430.00040.43010.0961
age14682.74940.34361.94593.52642.7726
board14682.08520.17711.60942.48492.1972
market14680.21890.3143−0.21651.61350.1626
Market.std14681.39830.44150.85733.37981.2764
hot14685.02250.62783.04455.72685.2883
Table 3. Frequency of collaboration between lead underwriters and accounting firms.
Table 3. Frequency of collaboration between lead underwriters and accounting firms.
Panel A
Collaboration FrequencyNumber of UnderwritersMeanStandard DeviationMinimumMaximumMedian
1710111
2–5203.551.01254
6–10177.41.466107
11–15912.41.13111412
16–20818.80.5172018
21–25422.50.58222322.5
Panel B
Total658.576.571236
Table 4. Number of IPOs undertaken by lead underwriters.
Table 4. Number of IPOs undertaken by lead underwriters.
Panel C
Number of IPOs UndertakenNumber of UnderwritersMeanStandard DeviationMinimumMaximumMedian
1–5232.831.56152
6–10138.151.406108
11–20615.163.43112015
21–401127.725.12213628
41–60354.338.14456058
61–80570.46.54648068
80 or more496.518.868312390
Panel D
Total6522.5828.0611239
Table 5. Underwriter influence and interest distribution.
Table 5. Underwriter influence and interest distribution.
(1)(2)(3)(4)(5)
VariablesSharingratioSharingratioSharingratioSharingratioSharingratio
centrality7.6713 ***5.7153 ***5.5301 ***5.1673 ***5.0994 ***
(4.77)(3.63)(3.48)(3.25)(3.16)
big4 1.74431.78531.51221.4991
(1.60)(1.64)(1.39)(1.40)
size 1.6540 ***1.4426 ***1.4147 ***1.3740 ***
(5.47)(4.55)(4.47)(4.43)
lev −9.2104 ***−8.8441 ***−6.9868 ***−7.0763 ***
(−6.56)(−6.34)(−4.90)(−4.99)
roa 5.73546.40354.61175.8556
(1.10)(1.22)(0.88)(1.11)
soe 2.1577 **2.0407 **1.9817 **
(2.46)(2.30)(2.19)
rec −4.8528 ***−4.4990 ***
(−2.96)(−2.78)
inv −6.7535 ***−6.7457 ***
(−3.12)(−3.11)
age −0.9517 *
(−1.84)
board 1.5659
(1.54)
Constant6.7763 ***−24.4491 ***−20.1696 ***−19.0026 ***−19.1863 ***
(3.96)(−3.99)(−3.13)(−2.97)(−2.72)
Observations14681468146814681468
Adjusted R-squared0.0330.0930.1000.1080.110
Note: the value in brackets is t; *, ** and ***, respectively, indicate that the index is significant at the significance level of 10%, 5% and 1%.
Table 6. Substituting core explanatory variables.
Table 6. Substituting core explanatory variables.
(1)(2)(3)(4)(5)(6)
VariablesSharingratioSharingratioSharingratioSharingratioSharingratioSharingratio
degree6.1703 *** 4.3819 ***
(5.00) (3.59)
closeness 3.6677 *** 2.1966 **
(3.99) (2.33)
betweenness 25.5740 *** 17.1131 ***
(3.86) (2.63)
big4 1.45621.54261.5233
(1.37)(1.44)(1.42)
size 1.3565 ***1.4049 ***1.3790 ***
(4.37)(4.52)(4.42)
lev −7.0323 ***−7.1228 ***−7.0436 ***
(−4.96)(−5.02)(−4.95)
roa 5.85815.88216.0653
(1.12)(1.12)(1.15)
soe 2.0097 **1.9825 **2.0283 **
(2.23)(2.19)(2.24)
rec −4.4658 ***−4.5880 ***−4.5539 ***
(−2.76)(−2.83)(−2.81)
inv −6.7373 ***−6.8183 ***−6.7155 ***
(−3.12)(−3.14)(−3.12)
age −0.9206 *−0.9910 *−0.9486 *
(−1.78)(−1.91)(−1.83)
board 1.58751.52101.5955
(1.56)(1.50)(1.57)
Constant7.7261 ***6.7094 ***8.3198 ***−18.3942 ***−19.4972 ***−18.3757 ***
(4.62)(3.92)(5.14)(−2.61)(−2.75)(−2.61)
Observations146814681468146814681468
Adjusted R-squared0.0370.0280.0310.1130.1080.109
Note: the value in brackets is t; *, ** and ***, respectively, indicate that the index is significant at the significance level of 10%, 5% and 1%.
Table 7. Using five-year rolling indicators.
Table 7. Using five-year rolling indicators.
(1)(2)(3)(4)
VariablesSharingratioSharingratioSharingratioSharingratio
centrality_55.0505 ***
(2.83)
degree_5 3.7661 ***
(3.27)
closeness_5 2.3072 *
(1.96)
betweenne_5 15.8649 **
(2.08)
big41.54121.50641.57211.5611
(1.44)(1.41)(1.47)(1.45)
size1.3797 ***1.3664 ***1.4085 ***1.4027 ***
(4.44)(4.39)(4.54)(4.50)
lev−7.0678 ***−7.0161 ***−7.1249 ***−7.0789 ***
(−4.99)(−4.95)(−5.02)(−4.98)
roa5.96915.98155.97056.0351
(1.13)(1.14)(1.13)(1.14)
soe2.0158 **2.0377 **2.0050 **2.0706 **
(2.23)(2.26)(2.22)(2.29)
rec−4.4901 ***−4.5501 ***−4.5183 ***−4.6975 ***
(−2.77)(−2.81)(−2.79)(−2.90)
inv−6.8887 ***−6.8398 ***−6.9433 ***−6.8425 ***
(−3.17)(−3.16)(−3.19)(−3.16)
age−0.9476 *−0.9265 *−0.9844 *−0.9764 *
(−1.83)(−1.79)(−1.90)(−1.88)
board1.62561.64601.55551.6225
(1.59)(1.62)(1.52)(1.60)
Constant−19.4019 ***−18.5470 ***−19.6860 ***−18.9792 ***
(−2.74)(−2.63)(−2.77)(−2.69)
Observations1468146814681468
Adjusted R-squared0.1100.1110.1070.108
Note: the value in brackets is t; *, ** and ***, respectively, indicate that the index is significant at the significance level of 10%, 5% and 1%.
Table 8. Robustness test: changing estimation methods.
Table 8. Robustness test: changing estimation methods.
(1)(2)(3)(4)(5)
VariablesSharingratio3Sharingratio3Sharingratio3Sharingratio3Sharingratio3
centrality5.4184 ***5.4522 ***5.4184 ***5.4513 ***4.5809 ***
(3.39)(3.09)(3.04)(3.60)(3.08)
big41.51061.6012 **1.5106 **1.61551.4383
(1.41)(2.17)(2.01)(1.49)(1.30)
size81.3769 ***1.3692 ***1.3769 ***1.3914 ***1.4952 ***
(4.42)(5.92)(5.79)(4.54)(4.67)
lev−6.9291 ***−7.1888 ***−6.9291 ***−7.2057 ***−6.8066 ***
(−4.87)(−5.29)(−4.95)(−5.05)(−4.44)
roa16.42356.35976.42356.23175.6953
(1.22)(1.27)(1.28)(1.14)(1.03)
soe1.8594 **1.9135 ***1.8594 ***1.8518 **2.1743 **
(2.07)(3.07)(2.84)(2.25)(2.44)
rec−4.4445 ***−4.5200 **−4.4445 **−4.7893 ***−4.6626 ***
(−2.74)(−2.57)(−2.44)(−3.08)(−2.71)
inv−6.5207 ***−5.2109 **−6.5207 ***−5.3808 ***−7.8839 ***
(−2.98)(−2.54)(−2.88)(−2.70)(−3.25)
firmage−0.8686 *−0.9435 *−0.8686 *−0.9404 *−1.0192 **
(−1.66)(−1.91)(−1.73)(−1.87)(−1.97)
board1.30951.24451.30951.20771.5186
(1.27)(1.27)(1.33)(1.18)(1.44)
Constant−18.8054 ***−18.4730 ***−19.7054 ***−18.1075 ***−17.6367 **
(−2.65)(−3.72)(−3.59)(−2.62)(−2.43)
Observations14681468146814681468
AdjustedR-squared0.1120.0960.0930.1170.155
Note: the value in brackets is t; *, ** and ***, respectively, indicate that the index is significant at the significance level of 10%, 5% and 1%.
Table 9. Adding control variables, including market influence factors.
Table 9. Adding control variables, including market influence factors.
(1)(2)(3)(4)
VariablesSharingratioSharingratioSharingratioSharingratio
centrality4.7814 ***4.9022 ***4.8827 ***4.8829 ***
(2.99)(3.06)(3.05)(3.05)
big41.28511.33911.34791.3477
(1.21)(1.27)(1.28)(1.28)
size1.6304 ***1.6176 ***1.6167 ***1.6166 ***
(4.89)(4.88)(4.88)(4.87)
lev−7.0661 ***−7.1597 ***−7.1644 ***−7.1647 ***
(−4.99)(−5.07)(−5.07)(−5.06)
roa6.80906.91116.85666.8549
(1.30)(1.33)(1.32)(1.32)
soe1.8997 **1.8780 **1.8844 **1.8842 **
(2.10)(2.07)(2.08)(2.09)
rec−5.0026 ***−4.8909 ***−4.8962 ***−4.8969 ***
(−3.07)(−3.01)(−3.01)(−3.03)
inv−6.7191 ***−6.6149 ***−6.5964 ***−6.5959 ***
(−3.10)(−3.07)(−3.06)(−3.07)
age−0.7889−0.8206−0.8250−0.8250
(−1.52)(−1.58)(−1.59)(−1.59)
board1.28751.23271.22731.2273
(1.26)(1.21)(1.20)(1.20)
market 1.9534 ***1.8994 ***1.9029 **
(2.93)(2.82)(2.25)
Market.std −0.2065−0.2089
(−0.35)(−0.32)
hot −0.0057
(−0.01)
Constant−24.6458 ***−24.6324 ***−24.2855 ***−24.2615 ***
(−3.27)(−3.28)(−3.25)(−2.95)
Observations1468146814681468
Adjusted R-squared0.1190.1220.1210.121
Note: the value in brackets is t; ** and ***, respectively, indicate that the index is significant at the significance level of 5% and 1%.
Table 10. Endogeneity test.
Table 10. Endogeneity test.
(1)(2)(3)(4)
VariablesCentralitySharingratioCentralitySharingratio
marketshares1.7229 ***
(23.27)
underwriter 0.0815 ***
(36.99)
centrality 7.8174 ** 6.7170 ***
(2.46) (2.73)
big4−0.00991.4594−0.00611.4754
(−1.12)(1.38)(−0.94)(1.40)
size0.00031.3380 ***0.00101.3526 ***
(0.09)(4.35)(0.49)(4.43)
lev0.0067−7.0437 ***0.0008−7.0569 ***
(0.41)(−5.01)(0.06)(−5.03)
roa−0.00965.76970.00555.8045
(−0.16)(1.11)(0.13)(1.12)
soe0.00291.9490 **0.0096 *1.9623 **
(0.46)(2.18)(1.81)(2.19)
rec−0.0254−4.3729 ***−0.0282−4.4240 ***
(−1.12)(−2.71)(−1.52)(−2.77)
inv−0.0260−6.6448 ***−0.0160−6.6856 ***
(−0.87)(−3.10)(−0.70)(−3.14)
age0.0016−0.9154 *0.0031−0.9301 *
(0.29)(−1.78)(0.69)(−1.82)
board−0.01841.6139−0.00651.5945
(−1.46)(1.59)(−0.64)(1.58)
Constant0.2968 ***−19.4853 ***−0.0466−19.3642 ***
(4.67)(−2.78)(−0.92)(−2.76)
Observations1468146814681468
Adjusted R-squared0.3600.1090.5910.110
Kleibergen–Paap rk LM statistic 420.963 344.661
Cragg–Donald Wald F statistic 608.368 1760.601
[16.38] [16.38]
Note: ***, **, and * indicate significance levels at 1%, 5%, and 10%, respectively; within [ ] are the critical values at the 10% level for the Stock–Yogo weak identification test. Same as below. Columns (2) and (4) report the regression results of the second stage of the instrumental variable method.
Table 11. Underwriter influence and abnormal underwriting fees.
Table 11. Underwriter influence and abnormal underwriting fees.
(1)(2)(3)(4)
VariablesAbnormalAbnormalAbnormalAbnormal
centrality0.0213 ***
(3.08)
degree 0.0099 **
(1.96)
closeness 0.0175 ***
(4.13)
betweenness 0.0210
(0.79)
big40.00130.00130.00130.0015
(0.45)(0.47)(0.48)(0.54)
size−0.0068 ***−0.0067 ***−0.0068 ***−0.0066 ***
(−7.63)(−7.51)(−7.67)(−7.40)
lev0.00250.00250.00240.0024
(0.44)(0.43)(0.41)(0.41)
roa−0.0094−0.0090−0.0098−0.0086
(−0.50)(−0.48)(−0.52)(−0.46)
soe0.0069 **0.0070 **0.0066 **0.0071 **
(2.48)(2.55)(2.40)(2.57)
rec0.0360 ***0.0356 ***0.0362 ***0.0353 ***
(4.84)(4.78)(4.88)(4.71)
inv0.01100.01060.01110.0105
(1.17)(1.13)(1.19)(1.10)
age0.00020.00010.0001−0.0000
(0.10)(0.07)(0.07)(−0.00)
board0.0121 ***0.0119 ***0.0120 ***0.0118 ***
(3.01)(2.97)(3.02)(2.93)
Constant0.1139 ***0.1167 ***0.1093 ***0.1165 ***
(5.17)(5.31)(4.95)(5.31)
Observations1468146814681468
Adjusted R-squared0.0700.0670.0740.065
Note: the value in brackets is t; ** and ***, respectively, indicate that the index is significant at the significance level of 5% and 1%.
Table 12. Underwriter influence and audit quality.
Table 12. Underwriter influence and audit quality.
(1)(2)(3)(4)(5)(6)(7)(8)
VariablesRestateRestateRestateRestateCscoreCscoreCscoreCscore
centrality0.1704 ** −0.7114 **
(2.34) (−2.17)
degree 0.1013 * −0.4119 **
(1.81) (−1.97)
closeness 0.1108 *** −0.4834 **
(2.85) (−1.96)
betweenne 0.5235 −1.8197 *
(1.50) (−1.92)
big40.02060.02040.02150.02150.14240.14300.13880.1373
(0.62)(0.61)(0.65)(0.65)(0.78)(0.79)(0.76)(0.75)
size−0.0030−0.0027−0.0026−0.00270.1022 **0.1007 **0.1008 **0.0994 **
(−0.25)(−0.22)(−0.21)(−0.22)(2.29)(2.27)(2.26)(2.22)
lev0.05330.05370.05200.0541−0.1366−0.1380−0.1313−0.1381
(0.75)(0.75)(0.73)(0.76)(−0.67)(−0.67)(−0.64)(−0.67)
roa−0.0438−0.0421−0.0452−0.03690.44100.43340.44820.4134
(−0.22)(−0.21)(−0.22)(−0.18)(0.48)(0.47)(0.48)(0.44)
soe0.00800.00920.00700.0096−0.2942 **−0.2996 **−0.2894 **−0.3011 **
(0.29)(0.34)(0.26)(0.35)(−2.01)(−2.05)(−1.97)(−2.06)
rec0.2034 **0.2017 **0.2029 **0.2010 **0.18180.18940.18230.1954
(2.20)(2.18)(2.19)(2.17)(0.76)(0.79)(0.75)(0.81)
inv−0.1580−0.1597−0.1584−0.15760.38670.39460.38750.3898
(−1.52)(−1.54)(−1.53)(−1.51)(1.29)(1.31)(1.29)(1.30)
age−0.0100−0.0100−0.0108−0.01010.06770.06790.07080.0696
(−0.44)(−0.43)(−0.47)(−0.44)(0.92)(0.93)(0.95)(0.95)
board−0.0529−0.0533−0.0536−0.0523−0.0402−0.0381−0.0376−0.0404
(−1.16)(−1.17)(−1.18)(−1.15)(−0.26)(−0.25)(−0.24)(−0.26)
Constant0.4605 *0.4846 *0.43530.4869 *−3.2240 ***−3.3240 ***−3.1104 ***−3.3288 ***
(1.68)(1.76)(1.58)(1.77)(−2.91)(−2.99)(−2.80)(−2.99)
Observations14681468146814681468146814681468
Adjusted R-squared0.1060.1050.1060.1050.1240.1230.1250.123
Note: the value in brackets is t; *, ** and ***, respectively, indicate that the index is significant at the significance level of 10%, 5% and 1%.
Table 13. Corporate governance, auditor governance, and market sentiment heterogeneity test.
Table 13. Corporate governance, auditor governance, and market sentiment heterogeneity test.
(1)(2)(3)(4)
VariablesSharingratioSharingratioSharingratioSharingratio
Low Governance High Sentiment
centrality6.2903 ***2.97711.97979.0129 ***
(2.76)(1.34)(0.98)(3.35)
big42.06100.83643.0200 **0.0207
(1.25)(0.54)(2.05)(0.01)
size1.3649 ***1.4405 ***1.0075 **1.8214 ***
(3.16)(3.19)(2.24)(4.49)
lev−7.8217 ***−6.3330 ***−6.0594 ***−7.8383 ***
(−3.83)(−3.09)(−3.25)(−3.51)
roa0.583013.117212.5584 *1.2893
(0.09)(1.51)(1.71)(0.17)
soe2.2721 *2.2491 *2.7342 **1.1336
(1.72)(1.92)(2.06)(0.98)
rec−4.2518 **−4.1362 *−2.6905−6.7537 ***
(−1.99)(−1.71)(−1.15)(−2.91)
inv−5.7637 *−7.7964 ***−1.2259−11.8110 ***
(−1.82)(−2.65)(−0.43)(−3.44)
age−0.9434−1.1424−1.2121 *−0.6761
(−1.43)(−1.48)(−1.68)(−0.90)
board0.96362.06141.61721.6582
(0.73)(1.34)(0.98)(1.31)
Constant−19.1325 *−18.2867 *−13.5615−25.8886 ***
(−1.87)(−1.86)(−1.29)(−2.99)
Observations734734734734
Adjusted R-squared0.1240.0870.0740.144
Note: the value in brackets is t; *, ** and ***, respectively, indicate that the index is significant at the significance level of 10%, 5% and 1%.
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Yang, S.; Tai, Y.; Cao, Y.; Chen, Y.; Zhang, Q. Underwriter Discourse, IPO Profit Distribution, and Audit Quality: An Entropy Study from the Perspective of an Underwriter–Auditor Network. Entropy 2024, 26, 393. https://doi.org/10.3390/e26050393

AMA Style

Yang S, Tai Y, Cao Y, Chen Y, Zhang Q. Underwriter Discourse, IPO Profit Distribution, and Audit Quality: An Entropy Study from the Perspective of an Underwriter–Auditor Network. Entropy. 2024; 26(5):393. https://doi.org/10.3390/e26050393

Chicago/Turabian Style

Yang, Songling, Yafei Tai, Yu Cao, Yunzhu Chen, and Qiuyue Zhang. 2024. "Underwriter Discourse, IPO Profit Distribution, and Audit Quality: An Entropy Study from the Perspective of an Underwriter–Auditor Network" Entropy 26, no. 5: 393. https://doi.org/10.3390/e26050393

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