# The Inhibition of Institutional Investor Clique on the Tunneling Behavior

Authors: Qi Luo; Fang Fang; Yanfei Zhang
Journal: Mobile Information Systems
 (2023)

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## Abstract

The development of communication technology has accumulated a large amount of data in the field of finance, and analyzing this data can better portray the behavior of financial entities, which is crucial to the progress of corporate finance. Based on the theory of social network and the classic “prisoner’s dilemma” model, this article finds that institutional investors will cooperate to participate in the governance of the listed companies. Then, by using the Louvain algorithm, institutional investor cliques have been derived from institutional investor networks based on nonfinancial listed companies in China between 2007 and 2020. The study uncovers the inhibition effect of the institutional investor clique on the tunneling behavior of the listed companies, and the higher the shareholding ratio and centrality of the institutional investor clique, the stronger its inhibitory strength. This paper extends the concepts and methods from the field of information communication to the analysis of financial institutional investors, offering a theoretical and empirical foundation for the interdisciplinary research of network algorithms and finance.


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## Body

## 1. Introduction

Since an institutional investor manages a large amount of capital and has a professional investment team, an increase in the ratio of institutional investors’ shareholding is believed to help improve the governance of the listed companies, such as promoting rationalization of management remuneration, alleviating the insufficient participation of minority shareholders in corporate governance, reducing information asymmetry between market investors [1, 2]. Previous studies have mostly believed that institutional investors can maintain their independence in the governance of the listed companies. But in practice, through the sharing of information and the coholding of shares in a company, a single institutional investor often has various relationships with other institutional investors and formed a certain investor network [3]. In the network, there are special subnetworks that are closely interconnected, namely, globally coupled networks, often referred to as institutional investor cliques, representing the smoothest internal connection groups between institutional investors [4].Some studies have found that the institutional investor network improves corporate governance while improving the welfare of institutional investors [5, 6]. Some studies suggest that the institutional investor network is detrimental to corporate governance and can even increase the risk of stock market crashes [7, 8]. However, scholars have mostly empirically studied the governance capability of institutional investors without deep analyzing why institutional investors in a specific network cooperate. Also, there are also few studies on the governance effect of institutional investor cliques.At the end of 2020, the number of institutional investors on the Shanghai and Shenzhen stock exchanges in China was approximately 417,200, and institutional investors held 39 trillion yuan circulating shares of the A-share market (the main market of Chinese stock, whose participating investors are only Chinese mainland institutions or individuals), accounting for 68.53% of the total value of the A-share market. An institutional investor has appeared in 4,171 listed companies and has gradually replaced retail investors as the main body of the Chinese capital market. As institutional investor has flourished, it has not only influenced stock pricing but also corporate governance. Institutional investors, who are more knowledgeable and consistent in their actions about financial investments, often influenced governance through cooperation. Accordingly, it is necessary to know how institutional investors establish a social network and its effect on corporate governance.This paper takes as a sample the nonfinancial listed companies of China’s capital market from 2007 to 2020 and establishes a network based on the connection criteria that the total combined shareholding of institutional investors in a given listed company is not less than 5%. Then, by using the Louvain algorithm to extract institutional investor cliques from the abovementioned networks, and with the shareholding ratio and centrality of institutional investor cliques as explanatory variables, the tunneling behavior of the controlling shareholder as interpreted variables, this article employs a fixed effect model to examine the impact of the institutional investor clique on the tunneling behavior of the controlling shareholder.The results show that (1) in the repeated game of the securities market, institutional investors in a specific network will jointly act to participate in the governance of the listed companies because the total benefits of cooperation are greater than the total benefits of noncooperation; (2) information sharing within the institutional investor clique inhibits the tunneling behavior of the controlling shareholder, and the higher the shareholding ratio and centrality of the institutional investor clique, the stronger its inhibitory effect on the tunneling behavior.Compared with previous studies, the innovations in this paper are as follows:(1)
Innovation in Theory. Previously, scholars often analyzed the impact of institutional investor cliques on the governance of the listed companies directly from the empirical level, rarely explaining why institutional investors in specific networks acted jointly. Drawing on the classic “prisoner’s dilemma” model, this article finds that in the repeated market games, for institutional investors, the total benefits of cooperation are greater than noncooperation, which explains why institutional investors choose to cooperate in the governance of the listed companies at the theoretical level.(2)
Innovation in Interdisciplinary Research. This paper applies the concepts (such as networks, nodes, centrality, and modularity) and methods in the field of information communication to the analysis of financial institutional investors, which is pioneering research on the integration of network algorithm and finance. The network algorithm in this paper captures the interactive relationship between institutional investors and finds that the institutional investor clique has weakened the tunneling behavior of controlling shareholders, which enriches the boundary of the institutional investor study and deepens the understanding of institutional investor behavior.In addition to the introduction, the rest of this paper is organized as follows: in Section2, the related research is discussed. In Section 3, the trend of cooperative governance of institutional investors in China has been described. In Section 4, theoretical analysis is addressed. In Section 5, the empirical test of whether institutional investor clique has inhabited the tunneling behavior of controlling shareholders is carried out. Section 6 summarizes the whole article.


## 2. Related Research

In the actual world, through diversification of investments and information communication, a single institutional investor has a variety of relationships with other institutional investors [9]. When there are intricate interactions between individuals in the game, individuals are more inclined to take joint action [10–12]. Therefore, through private contact, the joint shareholding of institutional investors of a listed company is complete, and a certain investor network forms [13]. Previous work focused mainly on the impact of the institutional investors’ network on corporate governance.Some studies have found that the institutional investors’ network improves corporate governance while enhancing the welfare of institutional investors. An institutional investor is more likely than retail investors to access information and share resources from the network, and can act jointly in enterprises, increasing the voice of institutional investors in corporate governance [14]. The huddle behavior of the institutional investor makes the dissemination of information more wider and can further alleviate information asymmetry between market participants [15], reduces agency costs [16], reduces operational and default risks [17, 18], and improves purchasing performance [19]. The authors of reference [20] also argue information sharing between institutional investors reduces the possibility of a stock price crash and improves the pricing efficiency of the market. The authors of reference [21] find that directors can obtain more information with the help of network resources, and effectively play a supervisory role in corporate mergers and acquisitions. In reference [22], the authors also point out that chief executive of the network can more effectively gather and control private information, enabling better merger and acquisition decisions. Furthermore, studies have shown that investor organizations, such as the Institutional Shareholder Service Incorporation and the American Shareholders Association, can alleviate the hitchhiking problem through the joint action of the institutional investors, which facilitates the participation of the institutional investors in the governance of the listed companies [23, 24].Some studies doubt the value of the institutional investor network. In reference [25], the authors believe the governance effect of other shareholders will only be stronger if the controlling shareholder is more likely to encroach on the interests of the company. Meanwhile, in references [3, 4], the authors argue that cooperation has also made many institutional investors intertwined, which will reduce the credibility of the “exit threat” of a single institution and be detrimental to the supervision of the listed companies. Improvement in stock liquidity also increases the probability that major institutional shareholders vote with their feet, without relying on the institutional investor network [26–28].Some studies suggest that the institutional investor network not only undermines corporate governance but also increases the risk of a stock market crash. Institutional investors may also use the power of the network to lead the establishment of “collusion alliances,” hide real accounting information, and deepen the information asymmetry [29, 30]. At the same time, the author of reference [7] argue that institutional investors under the “herd effect” not only do not make the stock price reflect the real information of the company but will also use their advantage to further increase the opacity of the stock price. In reference [31], the authors prove that institutional cooperation in information sharing will increase the probability of “black swans” in stocks from the perspective of serious homogenization of investment and lack of market liquidity. In reference [32], the authors also argue that the institutional investor network increases the financialization of firms and reduces their value.In studying the characteristics of the institutional investor network, some scholars have found that institutional investors in different positions on the network will also have varying effects on corporate governance. The author of reference [33] was the first to systematically classify the relevant concepts and measurement indicators of the centrality of social networks. The author of reference [34] find that the closer an investor is to the center of the network, the faster it can receive information. In reference [35], the author establishes an insider trading network and finds that the more central an insider trader is, the more investment profits and returns he can get. In reference [36], the authors find venture capital institutions can obtain a higher investment performance based on their position in the network and therefore are more likely to successfully exit. In addition, the authors of reference [37] believe that the higher the network density, the smaller the average path length of the network and it is easier for the members to cooperate. The authors of reference [34] also find that networks with medium levels of connectivity are more likely to cause abnormal changes in stock prices, while large or small information networks do not. Moreover, in addition to joint holding that can form connections, other social relationships can also serve as the basis for connections. The scholars have structured different social networks on venture capital, lead underwriters [38], chief executive officers [22], distributors [39], and independent directors.Scholars have focused on institutional investor networks and their external governance capabilities, but most of them are empirical studies, without an in-depth analysis of the motivational mechanism of network cooperation, and there is an insufficient theoretical explanation for why institutional investors in specific networks cooperate. For this reason, it is crucial to further investigate the impact of the investor network from the perspective of interdisciplinary study of network algorithms and financial research.


## 3. The Trend of Cooperative Governance of Institutional Investors in China

Figure1 shows that between 2007 and 2020, institutional investors owned shares in more than 98% of Chinese listed companies. Furthermore, the proportion of the value of the institutional investors’ stock market to the value of the circulating market has also been long over 50%.Figure 1
Institutional investors’ holding share of the listed companies, estimated from Wind Database Institutional Research Subdatabase.As shown in Figure2, nearly 80% of the listed companies in 2020 were jointly held by more than 2 institutional investors, and more than 10% of the listed companies had more than 50 institutional shareholders. By cross-shareholding in the same company, a connection between institutional investors has been established and the efficiency of information exchange between the investors has improved. The shareholding of the institutional investors presents a huddle phenomenon.Figure 2
Number of institutional investors jointly holding share of the listed companies in 2020, estimated from the Wind Database Institutional Research Subdatabase.Multiple institutional investors often exert influence over the company through joint actions because each investor has limited sway due to their small shareholding. By collaborating through the network, institutional investors have gained greater power to form equity checks and supervision over the listed companies.


## 4. Theoretical Analysis

### 4.1. The Condition for Cooperative Governance of Institutional Investors: Get Out of the “Prisoner’s Dilemma”

The prisoner’s dilemma in game theory is a classic nonzero-sum game, which expresses the conflict between individual rationality and collective rationality, showing that if everyone with individual rationality acts egoistically and it often leads to losses for everyone in the collective. To analyze the condition of cooperative governance, the game model between institutional investors will be established based on the analytical framework of the prisoner’s dilemma, and the following assumptions will be made: (1) two institutional investors have the same level of scale; (2) two institutional investors jointly hold the same company in the same share number of S; (3) the original share price isPb if institutional investor does not take an active governance action; if the institutional investor takes active governance actions, business conditions will improve and the share price will rise to Pa; (4) The cost of a single institutional investor participating in the governance of the listed company is C and the cost of joint governance is Tc; (5) If the institutional investor does not cooperate, the cost of separate governance is often high, so assume (Pa−Pb) S–C<0. The cost of each institutional investor can be reduced in cooperative governance, and it is assumed Tc<2C; and (6) Institutional investors make decisions at the same time and have complete information about each other’s profits.


#### 4.1.1. Complete Information Static Game

Two institutional investors choose their respective strategies at the same time, and the game occurs only once, which is a static game. Solving the game model shows that when institutional investor 1 chooses cooperation and the income of institutional investor 2’s noncooperationPa−Pb S is greater than the income of cooperation Pa−Pb S−Tc/2. So, the dominant strategy of institutional investor 2 is noncooperation. When institutional investor 1 selects noncooperation, the benefit of institutional investor 2’s noncooperation is 0, greater than the benefit of cooperation Pa−Pb S–C. Therefore, the dominant strategy of the institutional investor 2 is still noncooperation. So, the only Nash equilibrium of the game is (noncooperation).


#### 4.1.2. Complete Information Dynamic Game

Institutional investors have a hard time cooperating, as shown by an analysis of the complete information static game. But the game between institutional investors will not only occur once but will also repeat. In repeated games, a certain strategy choice of the institutional investor will impact the game later, and the individual reputation comes from the historical choice of the game. Betrayal will damage its reputation in the market, so it will lose the trust of other institutional investors, which is not conducive to future cooperation. The institutional investor can adopt a brutal strategy in repetitive games to achieve cooperative equilibrium, that is, the institutional investor firmly chooses cooperation in the initial game stage and not to cooperate in the later stages of the game if the other institutional investor chooses not to cooperate.The sum of the earnings of the institutional investor at each stage is the total return of repeated games. If the sum of the cooperative present value obtained by the institutional investor in the repeated games is greater than the sum of the present value of noncooperation, cooperative governance is selected. Now, suppose that institutional investor 1 chooses cooperation in the first stage, consider the choice of institutional investor 2 in the first stage of the game.If institutional investor 2 also chooses to cooperate, then institutional investor 1 will choose cooperation in subsequent stages. The expected return stream for each period of institutional investor 2 is as follows:(1)Ui=Pa−PbS−Tc2,i=1,2,3,….If the discount rate is expressed inδ (0 < δ < 1), the present value of the total revenue of institutional investor 2 is as follows:(2)Et=∑i=1∞δi−1Ui=Pa−PbS−Tc211−δ.If institutional investor 2 chooses not to cooperate, then institutional investor 1 will always choose not to cooperate. The expected return stream for each period of institutional investor 2 is as follows:(3)U1=Pa−PbS,Ui=0,i=2,3,….If the discount rate is expressed inδ (0 < δ < 1), the present value of the total revenue of institutional investor 2 is as follows:(4)Ef=Pa−PbS.As long as ΔE = Et-Ef=Pa−PbS1/1−δ−1−Tc/21−δ>0, that is, in the long run, the total benefits of cooperation are greater than the total benefits of betrayal, institutional investor will choose to cooperate in corporate governance. ΔE mainly on the governance effect Pa−Pb, number of institutional investor shares S, the discount coefficient δ, and the cost of supervision Tc. Then, the main determinants of institutional investor cooperative governance are the cost of cooperative governance Tc and the number of institutional investor shares S.


### 4.2. The Reduction of Cooperation Governance

From the abovementioned analysis, we can see that the constraint of institutional investor cooperative governance is mainly decided by cooperative governance costTc and shareholding (S). As institutional investor continues to expand nowadays, the number of its shareholding (S) has also increased. Let us analyze how cooperation can reduce governance costs. The “learning curve effect” caused by the increase in institutional shareholding varieties and the “scale effect” brought about by the increase in institutional shareholding proportion are conducive to reducing the cost of cooperative governance.


#### 4.2.1. Learning Curve Effect

The following formula illustrates the impact of the number of companies on the returns of their governance actions.(5)profit=∑Pai×Si−∑Pbi×Si−Tc.Among them,Pai indicates the share price of institutional investor after the governance of the company, and if the institutional investor does not take action, the stock price is Pbi. Si Signifies the number of institutional investor shares in the i-company, Tc represents institutional investor’s total cost of the institutional investor to multiple corporate governance. If Ci indicates the cost of institutional investor governance in each listed company, due to the knowledge of corporate governance is shareable, so that the number of companies held by institutional investor exceeds 1, Tc will be less than ∑Ci. Morever, as the number of firms increases, Tc will be smaller than ∑Ci to a greater extent. This effect is known as the learning curve effect. The larger the number of companies in the institutional investor network, the easier it will be for institutional investors to facilitate information sharing and learning with each other. The cooperation of institutional investors reduces the cost of governance, so that the profit is greater, and the institutional investor is more motivated to participate in corporate governance.


#### 4.2.2. Scale Effect

Due to its increasing proportion of shares, the market has shown a trend of institutionalization of shares. The following formula clarifies the effect of an increase in institutional investor’s shareholding on the expected returns of their participation in corporate governance.(6)profit=Pa−Pb+C∑Si,there into, ∂C/∂∑Si<0.Pa is the stock price after the listed company is governed, and Pb is the original stock price; if multiple institutional investors act jointly, the total cost of governance is C; the i-th institutional investor in the institutional investor clique is recorded as Si. The specific economic implications expressed by the model are: if Pa>Pb+C/∑Si, multiple institutional investors will take joint actions to participate in the governance of the listed companies; if Pa<Pb+C/∑Si, these institutional investors will not act together. ∑Si reflects the total number of institutional investor holdings and the more institutional investors participating in joint operations, the higher the total shareholding, and the lower the cost C of joint governance actions, which is also a reflection of economies of scale. Reflected in the formula, i.e., ∂C/∂∑Si<0, governance costs have been reduced, which means a greater net benefit of the institution from corporate governance, thereby driving the institutional investor to adopt positive governance behaviors.


### 4.3. Network Effects of Institutional Investors’ Cooperative Governance

#### 4.3.1. Institutional Investor Clique and Corporate Governance

Generally, there are various forms of connectivity in the network, and the joint shareholding of institutional investors can also be used as a connection to build an institutional investor network centered on the shareholding of the same listed company. Information flows through the network, and members of institutions in the network can also share network resources. Moreover, there are special subnetworks in institutional investor networks that are closely interconnected, namely, the global coupled network, often referred to as the institutional investor clique. In the following Figure3, in the institutional investor clique, the direct connection between members allows information to flow quickly between any two in Diagram (a), and information transmission is more efficient, without information leakage and delay. However, in Diagram (b), information cannot move easily from all nodes to all other nodes in the normal network. For example, if A wants the information of E, the message must move through D, C, and B, or move through F, G, and H. Coordination is more difficult by the lack of direct connection between any two institutional investors in the network.Figure 3
Diagram of the dynamical interactions between institutional investors. (a) Clique. (b) Not a clique.
(a)(b)According to the theory of social capital, the network can quickly aggregate the scarce resources of network members and pass these resources between members in the connection, to achieve the effective utilization of resources. Institutional investors have extensive funding and governance experience. If operated jointly, they can not only exchange information to improve external governance knowledge but also enhance the voice of the institutional investor side with an increased proportion of overall shareholding, which can generate greater negotiation pressure on the listed companies and strengthen external supervision of corporate governance. Therefore, we can lead to the following proposition:Proposition 1.
Institutional investor clique improves the effectiveness of corporate governance.


#### 4.3.2. The Governance Power of the Institutional Investor Clique with Different Centralities

The location of the network reflects an individual’s ability to acquire and control network resources, and individuals in central positions on the network can serve as a bridge to maintain cooperative relations, thus promoting the generation and continuation of cooperation. Furthermore, centrality is often used as a measure to represent the status and power of the institutional investor’s network. This paper draws on the author of reference [33] centrality theory and adopts the indicators of degree centrality, betweenness centrality, and closeness centrality to measure the cyber power of institutional investors.(1) Degree Centrality. The degree centrality measures the number of points that are directly connected to the node. The greater the degree of centrality, the wider the network of relationships associated with that point. In the institutional investor network, degree centrality refers to the number of other institutional investors who have a common shareholding relationship with the key institutional investor, reflecting the degree of activity of the key institutional investor in the network.(2) Betweenness Centrality. Betweenness Centrality measures the number of nodes that are not directly related to each other but are connected by the key node, the greater the centrality of the Betweenness, the stronger the node’s ability to control communication between other nodes. Betweenness centrality can describe the extent to which the key institutional investor affects the communication between other members of the network.(3) Closeness Centrality. Close centrality measures the reciprocal of the average shortest distance between a node and each node that can be connected to it. The greater the close centrality, the shorter the average connection path between this institutional investor and other institutional investors and the faster the information is transmitted. Close centrality can paint a picture of whether institutional investor market connections are more direct and effective, as well as the speed of information transfer.According to the theory of social networks, the more central an institutional investor’s position in the network, the more social capital he can obtain, therefore, the better it can facilitate corporative governance. On the one hand, the central institutional investor which has richer and more effective information resources is more likely to be trusted and followed by network members and leads other institutional investors to form a synergy in corporate governance; on the other hand, the central institutional investor tends to hold more shares in the listed companies and has more knowledge and experience in corporate governance, and its ability and effect for external governance are stronger.Meanwhile, the centrality of the institutional investor clique is the weighted average of the centrality of each institutional investor. The degree centrality of an institutional investor clique represents the number of other institutional investors who have a common shareholding relationship with each institutional investor, and the greater the number, the closer the relationship within the institutional investor clique; the betweenness centrality of the institutional investor clique indicates the influence of the institutional investors on the communication between other network members, and the higher the betweenness centrality, the higher the mutual influence between institutional investors; closeness centrality means the average connection path of each institutional investor to other institutional investors, and the higher the closeness centrality, the shorter the connection path between institutional investors, the faster the information is transmitted. In general, the centrality of the institutional investor clique represents the close connection and information exchange between institutional investors within the clique.Therefore, we can lead to the proposition:Proposition 2.
Institutional investor clique with higher centrality has stronger governance effectiveness.


## 4.1. The Condition for Cooperative Governance of Institutional Investors: Get Out of the “Prisoner’s Dilemma”

The prisoner’s dilemma in game theory is a classic nonzero-sum game, which expresses the conflict between individual rationality and collective rationality, showing that if everyone with individual rationality acts egoistically and it often leads to losses for everyone in the collective. To analyze the condition of cooperative governance, the game model between institutional investors will be established based on the analytical framework of the prisoner’s dilemma, and the following assumptions will be made: (1) two institutional investors have the same level of scale; (2) two institutional investors jointly hold the same company in the same share number of S; (3) the original share price isPb if institutional investor does not take an active governance action; if the institutional investor takes active governance actions, business conditions will improve and the share price will rise to Pa; (4) The cost of a single institutional investor participating in the governance of the listed company is C and the cost of joint governance is Tc; (5) If the institutional investor does not cooperate, the cost of separate governance is often high, so assume (Pa−Pb) S–C<0. The cost of each institutional investor can be reduced in cooperative governance, and it is assumed Tc<2C; and (6) Institutional investors make decisions at the same time and have complete information about each other’s profits.


### 4.1.1. Complete Information Static Game

Two institutional investors choose their respective strategies at the same time, and the game occurs only once, which is a static game. Solving the game model shows that when institutional investor 1 chooses cooperation and the income of institutional investor 2’s noncooperationPa−Pb S is greater than the income of cooperation Pa−Pb S−Tc/2. So, the dominant strategy of institutional investor 2 is noncooperation. When institutional investor 1 selects noncooperation, the benefit of institutional investor 2’s noncooperation is 0, greater than the benefit of cooperation Pa−Pb S–C. Therefore, the dominant strategy of the institutional investor 2 is still noncooperation. So, the only Nash equilibrium of the game is (noncooperation).


### 4.1.2. Complete Information Dynamic Game

Institutional investors have a hard time cooperating, as shown by an analysis of the complete information static game. But the game between institutional investors will not only occur once but will also repeat. In repeated games, a certain strategy choice of the institutional investor will impact the game later, and the individual reputation comes from the historical choice of the game. Betrayal will damage its reputation in the market, so it will lose the trust of other institutional investors, which is not conducive to future cooperation. The institutional investor can adopt a brutal strategy in repetitive games to achieve cooperative equilibrium, that is, the institutional investor firmly chooses cooperation in the initial game stage and not to cooperate in the later stages of the game if the other institutional investor chooses not to cooperate.The sum of the earnings of the institutional investor at each stage is the total return of repeated games. If the sum of the cooperative present value obtained by the institutional investor in the repeated games is greater than the sum of the present value of noncooperation, cooperative governance is selected. Now, suppose that institutional investor 1 chooses cooperation in the first stage, consider the choice of institutional investor 2 in the first stage of the game.If institutional investor 2 also chooses to cooperate, then institutional investor 1 will choose cooperation in subsequent stages. The expected return stream for each period of institutional investor 2 is as follows:(1)Ui=Pa−PbS−Tc2,i=1,2,3,….If the discount rate is expressed inδ (0 < δ < 1), the present value of the total revenue of institutional investor 2 is as follows:(2)Et=∑i=1∞δi−1Ui=Pa−PbS−Tc211−δ.If institutional investor 2 chooses not to cooperate, then institutional investor 1 will always choose not to cooperate. The expected return stream for each period of institutional investor 2 is as follows:(3)U1=Pa−PbS,Ui=0,i=2,3,….If the discount rate is expressed inδ (0 < δ < 1), the present value of the total revenue of institutional investor 2 is as follows:(4)Ef=Pa−PbS.As long as ΔE = Et-Ef=Pa−PbS1/1−δ−1−Tc/21−δ>0, that is, in the long run, the total benefits of cooperation are greater than the total benefits of betrayal, institutional investor will choose to cooperate in corporate governance. ΔE mainly on the governance effect Pa−Pb, number of institutional investor shares S, the discount coefficient δ, and the cost of supervision Tc. Then, the main determinants of institutional investor cooperative governance are the cost of cooperative governance Tc and the number of institutional investor shares S.


## 4.1.1. Complete Information Static Game

Two institutional investors choose their respective strategies at the same time, and the game occurs only once, which is a static game. Solving the game model shows that when institutional investor 1 chooses cooperation and the income of institutional investor 2’s noncooperationPa−Pb S is greater than the income of cooperation Pa−Pb S−Tc/2. So, the dominant strategy of institutional investor 2 is noncooperation. When institutional investor 1 selects noncooperation, the benefit of institutional investor 2’s noncooperation is 0, greater than the benefit of cooperation Pa−Pb S–C. Therefore, the dominant strategy of the institutional investor 2 is still noncooperation. So, the only Nash equilibrium of the game is (noncooperation).


## 4.1.2. Complete Information Dynamic Game

Institutional investors have a hard time cooperating, as shown by an analysis of the complete information static game. But the game between institutional investors will not only occur once but will also repeat. In repeated games, a certain strategy choice of the institutional investor will impact the game later, and the individual reputation comes from the historical choice of the game. Betrayal will damage its reputation in the market, so it will lose the trust of other institutional investors, which is not conducive to future cooperation. The institutional investor can adopt a brutal strategy in repetitive games to achieve cooperative equilibrium, that is, the institutional investor firmly chooses cooperation in the initial game stage and not to cooperate in the later stages of the game if the other institutional investor chooses not to cooperate.The sum of the earnings of the institutional investor at each stage is the total return of repeated games. If the sum of the cooperative present value obtained by the institutional investor in the repeated games is greater than the sum of the present value of noncooperation, cooperative governance is selected. Now, suppose that institutional investor 1 chooses cooperation in the first stage, consider the choice of institutional investor 2 in the first stage of the game.If institutional investor 2 also chooses to cooperate, then institutional investor 1 will choose cooperation in subsequent stages. The expected return stream for each period of institutional investor 2 is as follows:(1)Ui=Pa−PbS−Tc2,i=1,2,3,….If the discount rate is expressed inδ (0 < δ < 1), the present value of the total revenue of institutional investor 2 is as follows:(2)Et=∑i=1∞δi−1Ui=Pa−PbS−Tc211−δ.If institutional investor 2 chooses not to cooperate, then institutional investor 1 will always choose not to cooperate. The expected return stream for each period of institutional investor 2 is as follows:(3)U1=Pa−PbS,Ui=0,i=2,3,….If the discount rate is expressed inδ (0 < δ < 1), the present value of the total revenue of institutional investor 2 is as follows:(4)Ef=Pa−PbS.As long as ΔE = Et-Ef=Pa−PbS1/1−δ−1−Tc/21−δ>0, that is, in the long run, the total benefits of cooperation are greater than the total benefits of betrayal, institutional investor will choose to cooperate in corporate governance. ΔE mainly on the governance effect Pa−Pb, number of institutional investor shares S, the discount coefficient δ, and the cost of supervision Tc. Then, the main determinants of institutional investor cooperative governance are the cost of cooperative governance Tc and the number of institutional investor shares S.


## 4.2. The Reduction of Cooperation Governance

From the abovementioned analysis, we can see that the constraint of institutional investor cooperative governance is mainly decided by cooperative governance costTc and shareholding (S). As institutional investor continues to expand nowadays, the number of its shareholding (S) has also increased. Let us analyze how cooperation can reduce governance costs. The “learning curve effect” caused by the increase in institutional shareholding varieties and the “scale effect” brought about by the increase in institutional shareholding proportion are conducive to reducing the cost of cooperative governance.


### 4.2.1. Learning Curve Effect

The following formula illustrates the impact of the number of companies on the returns of their governance actions.(5)profit=∑Pai×Si−∑Pbi×Si−Tc.Among them,Pai indicates the share price of institutional investor after the governance of the company, and if the institutional investor does not take action, the stock price is Pbi. Si Signifies the number of institutional investor shares in the i-company, Tc represents institutional investor’s total cost of the institutional investor to multiple corporate governance. If Ci indicates the cost of institutional investor governance in each listed company, due to the knowledge of corporate governance is shareable, so that the number of companies held by institutional investor exceeds 1, Tc will be less than ∑Ci. Morever, as the number of firms increases, Tc will be smaller than ∑Ci to a greater extent. This effect is known as the learning curve effect. The larger the number of companies in the institutional investor network, the easier it will be for institutional investors to facilitate information sharing and learning with each other. The cooperation of institutional investors reduces the cost of governance, so that the profit is greater, and the institutional investor is more motivated to participate in corporate governance.


### 4.2.2. Scale Effect

Due to its increasing proportion of shares, the market has shown a trend of institutionalization of shares. The following formula clarifies the effect of an increase in institutional investor’s shareholding on the expected returns of their participation in corporate governance.(6)profit=Pa−Pb+C∑Si,there into, ∂C/∂∑Si<0.Pa is the stock price after the listed company is governed, and Pb is the original stock price; if multiple institutional investors act jointly, the total cost of governance is C; the i-th institutional investor in the institutional investor clique is recorded as Si. The specific economic implications expressed by the model are: if Pa>Pb+C/∑Si, multiple institutional investors will take joint actions to participate in the governance of the listed companies; if Pa<Pb+C/∑Si, these institutional investors will not act together. ∑Si reflects the total number of institutional investor holdings and the more institutional investors participating in joint operations, the higher the total shareholding, and the lower the cost C of joint governance actions, which is also a reflection of economies of scale. Reflected in the formula, i.e., ∂C/∂∑Si<0, governance costs have been reduced, which means a greater net benefit of the institution from corporate governance, thereby driving the institutional investor to adopt positive governance behaviors.


## 4.2.1. Learning Curve Effect

The following formula illustrates the impact of the number of companies on the returns of their governance actions.(5)profit=∑Pai×Si−∑Pbi×Si−Tc.Among them,Pai indicates the share price of institutional investor after the governance of the company, and if the institutional investor does not take action, the stock price is Pbi. Si Signifies the number of institutional investor shares in the i-company, Tc represents institutional investor’s total cost of the institutional investor to multiple corporate governance. If Ci indicates the cost of institutional investor governance in each listed company, due to the knowledge of corporate governance is shareable, so that the number of companies held by institutional investor exceeds 1, Tc will be less than ∑Ci. Morever, as the number of firms increases, Tc will be smaller than ∑Ci to a greater extent. This effect is known as the learning curve effect. The larger the number of companies in the institutional investor network, the easier it will be for institutional investors to facilitate information sharing and learning with each other. The cooperation of institutional investors reduces the cost of governance, so that the profit is greater, and the institutional investor is more motivated to participate in corporate governance.


## 4.2.2. Scale Effect

Due to its increasing proportion of shares, the market has shown a trend of institutionalization of shares. The following formula clarifies the effect of an increase in institutional investor’s shareholding on the expected returns of their participation in corporate governance.(6)profit=Pa−Pb+C∑Si,there into, ∂C/∂∑Si<0.Pa is the stock price after the listed company is governed, and Pb is the original stock price; if multiple institutional investors act jointly, the total cost of governance is C; the i-th institutional investor in the institutional investor clique is recorded as Si. The specific economic implications expressed by the model are: if Pa>Pb+C/∑Si, multiple institutional investors will take joint actions to participate in the governance of the listed companies; if Pa<Pb+C/∑Si, these institutional investors will not act together. ∑Si reflects the total number of institutional investor holdings and the more institutional investors participating in joint operations, the higher the total shareholding, and the lower the cost C of joint governance actions, which is also a reflection of economies of scale. Reflected in the formula, i.e., ∂C/∂∑Si<0, governance costs have been reduced, which means a greater net benefit of the institution from corporate governance, thereby driving the institutional investor to adopt positive governance behaviors.


## 4.3. Network Effects of Institutional Investors’ Cooperative Governance

### 4.3.1. Institutional Investor Clique and Corporate Governance

Generally, there are various forms of connectivity in the network, and the joint shareholding of institutional investors can also be used as a connection to build an institutional investor network centered on the shareholding of the same listed company. Information flows through the network, and members of institutions in the network can also share network resources. Moreover, there are special subnetworks in institutional investor networks that are closely interconnected, namely, the global coupled network, often referred to as the institutional investor clique. In the following Figure3, in the institutional investor clique, the direct connection between members allows information to flow quickly between any two in Diagram (a), and information transmission is more efficient, without information leakage and delay. However, in Diagram (b), information cannot move easily from all nodes to all other nodes in the normal network. For example, if A wants the information of E, the message must move through D, C, and B, or move through F, G, and H. Coordination is more difficult by the lack of direct connection between any two institutional investors in the network.Figure 3
Diagram of the dynamical interactions between institutional investors. (a) Clique. (b) Not a clique.
(a)(b)According to the theory of social capital, the network can quickly aggregate the scarce resources of network members and pass these resources between members in the connection, to achieve the effective utilization of resources. Institutional investors have extensive funding and governance experience. If operated jointly, they can not only exchange information to improve external governance knowledge but also enhance the voice of the institutional investor side with an increased proportion of overall shareholding, which can generate greater negotiation pressure on the listed companies and strengthen external supervision of corporate governance. Therefore, we can lead to the following proposition:Proposition 1.
Institutional investor clique improves the effectiveness of corporate governance.


### 4.3.2. The Governance Power of the Institutional Investor Clique with Different Centralities

The location of the network reflects an individual’s ability to acquire and control network resources, and individuals in central positions on the network can serve as a bridge to maintain cooperative relations, thus promoting the generation and continuation of cooperation. Furthermore, centrality is often used as a measure to represent the status and power of the institutional investor’s network. This paper draws on the author of reference [33] centrality theory and adopts the indicators of degree centrality, betweenness centrality, and closeness centrality to measure the cyber power of institutional investors.(1) Degree Centrality. The degree centrality measures the number of points that are directly connected to the node. The greater the degree of centrality, the wider the network of relationships associated with that point. In the institutional investor network, degree centrality refers to the number of other institutional investors who have a common shareholding relationship with the key institutional investor, reflecting the degree of activity of the key institutional investor in the network.(2) Betweenness Centrality. Betweenness Centrality measures the number of nodes that are not directly related to each other but are connected by the key node, the greater the centrality of the Betweenness, the stronger the node’s ability to control communication between other nodes. Betweenness centrality can describe the extent to which the key institutional investor affects the communication between other members of the network.(3) Closeness Centrality. Close centrality measures the reciprocal of the average shortest distance between a node and each node that can be connected to it. The greater the close centrality, the shorter the average connection path between this institutional investor and other institutional investors and the faster the information is transmitted. Close centrality can paint a picture of whether institutional investor market connections are more direct and effective, as well as the speed of information transfer.According to the theory of social networks, the more central an institutional investor’s position in the network, the more social capital he can obtain, therefore, the better it can facilitate corporative governance. On the one hand, the central institutional investor which has richer and more effective information resources is more likely to be trusted and followed by network members and leads other institutional investors to form a synergy in corporate governance; on the other hand, the central institutional investor tends to hold more shares in the listed companies and has more knowledge and experience in corporate governance, and its ability and effect for external governance are stronger.Meanwhile, the centrality of the institutional investor clique is the weighted average of the centrality of each institutional investor. The degree centrality of an institutional investor clique represents the number of other institutional investors who have a common shareholding relationship with each institutional investor, and the greater the number, the closer the relationship within the institutional investor clique; the betweenness centrality of the institutional investor clique indicates the influence of the institutional investors on the communication between other network members, and the higher the betweenness centrality, the higher the mutual influence between institutional investors; closeness centrality means the average connection path of each institutional investor to other institutional investors, and the higher the closeness centrality, the shorter the connection path between institutional investors, the faster the information is transmitted. In general, the centrality of the institutional investor clique represents the close connection and information exchange between institutional investors within the clique.Therefore, we can lead to the proposition:Proposition 2.
Institutional investor clique with higher centrality has stronger governance effectiveness.


## 4.3.1. Institutional Investor Clique and Corporate Governance

Generally, there are various forms of connectivity in the network, and the joint shareholding of institutional investors can also be used as a connection to build an institutional investor network centered on the shareholding of the same listed company. Information flows through the network, and members of institutions in the network can also share network resources. Moreover, there are special subnetworks in institutional investor networks that are closely interconnected, namely, the global coupled network, often referred to as the institutional investor clique. In the following Figure3, in the institutional investor clique, the direct connection between members allows information to flow quickly between any two in Diagram (a), and information transmission is more efficient, without information leakage and delay. However, in Diagram (b), information cannot move easily from all nodes to all other nodes in the normal network. For example, if A wants the information of E, the message must move through D, C, and B, or move through F, G, and H. Coordination is more difficult by the lack of direct connection between any two institutional investors in the network.Figure 3
Diagram of the dynamical interactions between institutional investors. (a) Clique. (b) Not a clique.
(a)(b)According to the theory of social capital, the network can quickly aggregate the scarce resources of network members and pass these resources between members in the connection, to achieve the effective utilization of resources. Institutional investors have extensive funding and governance experience. If operated jointly, they can not only exchange information to improve external governance knowledge but also enhance the voice of the institutional investor side with an increased proportion of overall shareholding, which can generate greater negotiation pressure on the listed companies and strengthen external supervision of corporate governance. Therefore, we can lead to the following proposition:Proposition 1.
Institutional investor clique improves the effectiveness of corporate governance.


## 4.3.2. The Governance Power of the Institutional Investor Clique with Different Centralities

The location of the network reflects an individual’s ability to acquire and control network resources, and individuals in central positions on the network can serve as a bridge to maintain cooperative relations, thus promoting the generation and continuation of cooperation. Furthermore, centrality is often used as a measure to represent the status and power of the institutional investor’s network. This paper draws on the author of reference [33] centrality theory and adopts the indicators of degree centrality, betweenness centrality, and closeness centrality to measure the cyber power of institutional investors.(1) Degree Centrality. The degree centrality measures the number of points that are directly connected to the node. The greater the degree of centrality, the wider the network of relationships associated with that point. In the institutional investor network, degree centrality refers to the number of other institutional investors who have a common shareholding relationship with the key institutional investor, reflecting the degree of activity of the key institutional investor in the network.(2) Betweenness Centrality. Betweenness Centrality measures the number of nodes that are not directly related to each other but are connected by the key node, the greater the centrality of the Betweenness, the stronger the node’s ability to control communication between other nodes. Betweenness centrality can describe the extent to which the key institutional investor affects the communication between other members of the network.(3) Closeness Centrality. Close centrality measures the reciprocal of the average shortest distance between a node and each node that can be connected to it. The greater the close centrality, the shorter the average connection path between this institutional investor and other institutional investors and the faster the information is transmitted. Close centrality can paint a picture of whether institutional investor market connections are more direct and effective, as well as the speed of information transfer.According to the theory of social networks, the more central an institutional investor’s position in the network, the more social capital he can obtain, therefore, the better it can facilitate corporative governance. On the one hand, the central institutional investor which has richer and more effective information resources is more likely to be trusted and followed by network members and leads other institutional investors to form a synergy in corporate governance; on the other hand, the central institutional investor tends to hold more shares in the listed companies and has more knowledge and experience in corporate governance, and its ability and effect for external governance are stronger.Meanwhile, the centrality of the institutional investor clique is the weighted average of the centrality of each institutional investor. The degree centrality of an institutional investor clique represents the number of other institutional investors who have a common shareholding relationship with each institutional investor, and the greater the number, the closer the relationship within the institutional investor clique; the betweenness centrality of the institutional investor clique indicates the influence of the institutional investors on the communication between other network members, and the higher the betweenness centrality, the higher the mutual influence between institutional investors; closeness centrality means the average connection path of each institutional investor to other institutional investors, and the higher the closeness centrality, the shorter the connection path between institutional investors, the faster the information is transmitted. In general, the centrality of the institutional investor clique represents the close connection and information exchange between institutional investors within the clique.Therefore, we can lead to the proposition:Proposition 2.
Institutional investor clique with higher centrality has stronger governance effectiveness.


## 5. Empirical Results

### 5.1. Research Design

#### 5.1.1. Data Source

After 2007, China’s listed companies began making financial disclosures under the new accounting standard, so this article limits the sample to Shanghai and Shenzhen A-share listed companies from 2007 to 2020. The financial data of the listed companies comes from the China Stock Market & Accounting Research Database Company Research Subdatabase, and the institutional investor shareholding data comes from the WIND Database Institutional Research Subdatabase. The data are processed as follows: (1) deleting companies with ST and∗ST which mean risks of delisting, and listed companies in the financial industry; (2) referring to reference [40], to delete companies that do not have controlling shareholders; and (3) all continuous variables in the text were Winsorized by 1%.


#### 5.1.2. Variable definitions

(1) Explanatory Variables. This paper draws on the methods of reference [4] to identify institutional investors’ network cliques. Drawing on the research of references [22, 38], the network centrality index is measured.(1)
Institutional investor clique’s share ratioMany studies have mentioned that large shareholders with more than 5% shareholding have strong governance effectiveness [41, 42]. At the same time, the 5% shareholding ratio is a warning line for major equity changes in the China’s securities market, which can affect the daily operation and governance of the listed companies. Therefore, the institutional investor network in this paper is constructed by the connection standard that the sum of the joint shareholding of institutional investors of not less than 5% of the same listed company. Second, using on the processing method of reference [4], the Louvain algorithm is used to continuously optimize the modularity for the identification of network cliques. Finally, the following formula is used to calculate the shareholding ratio of the institutional investor clique.(7)Workneti=∑j=1NInvestijTradesharei.Among them, theWorkneti represents the shareholding ratio of the institutional investor clique, N represents the total number of institutional investor cliques owned by the identified i-listed company; Investij indicates the number of shares held by the J clique in the i-listed company; Tradesharei indicates the number of circulating shares at the end of the period of the i-listed company.(2)
Degree centralityThe degree centrality measures the proportion of connection betweeni nodes and other nodes DiJ to the total number of nodes N in the network. The greater the degree of centrality, the wider the network of relationships associated with the point, reflecting the active level of the institutional investors in the network. The closer the degree centrality to 1, the more fully the information exchange between the institutional investors in the network. The specific calculation formula is as follows:(8)Degree=DiJn−1,(3)
Betweenness centralityBetweenness centrality measures how many points are connected byi nodes that are not originally related directly. The greater the betweenness centrality of the i node, the stronger the control ability of the node over other nodes and the transmission of network information. Pikj is the number of nodes in the shortest distance between the nodes k and j, while P (kj) is the shortest distance between k nodes and j nodes. (n-2) (n-1)/2 in the denominator represents the sum of the shortest paths that exist between all nodes in the network, calculated as follows:(9)Between=∑k≠j,i∉k,jPikj\\/Pkjn−2n−1/2,(4)
Closeness centralityCloseness centrality measures the sum of the number of all nodes that have a direct and indirect relationship to the i-node divided by the shortest distance the i-node has reached the other nodes and normalized with the number of all nodes (N−1)., the greater the closeness centrality, the shorter the average connection path between the node and other nodes. The more direct and effective the connection between the key institutional investor and other institutional investors is, the faster the speed of information transmission. The specific calculation formula is as follows:(10)Close=N−1∑j=1Ndi,j.(2) Explanatory Variables. Corporate governance mainly involves two types of agency issues for the listed companies. One is the conflict of interest between management and shareholders, and the other is the conflict of interest between controlling shareholders and other shareholders. As an emerging capital market, the equity of the listed companies in China is still relatively concentrated, which alleviates the first type of conflict to some certain extent. However, the controlling shareholder may use a variety of unfair means to tunnel the listed company, that is, to extract profits from the listed company and convey it, infringing the interests of other shareholders, which will not only harm the equity of institutional investor but will also jeopardize the value of the company stock. So, an institutional investor has the incentive to govern it. To measure the governance effectiveness of the institutional investors, this article focuses on the inhibitory effect of institutional investors on controlling tunneling behavior of shareholders, specifically using two proxy variables: (1)
Appropriation of funds by controlling shareholders.The controlling shareholder of a listed company can directly occupy the funds of the listed company, which is reflected mainly in other receivables, prepaid accounts, and investment funds in the statement, especially the black box of “other receivables,” which can accommodate a variety of interest transmission transactions of the controlling shareholder. In addition, other receivables are long-lived and difficult to collect, which has become the main channel for controlling shareholders to occupy funds. Therefore, the controlling shareholder’s appropriation of funds is measured by dividing the year-end balance of other receivables by the year-end balance of total assets, which is recorded as appropriation of funds.(2)
Occupation of related party transactions.Related party transactions refer to transactions between the listed companies and related parties. Affiliates may use the right of enterprise control to harm the company’s interest. According to the classification standards of the China Stock Market & Accounting Research Database, related party transactions include 17 categories of matters: commodity transactions, asset transactions, and capital transactions, since it is difficult for cooperation projects, licensing agreements, and the remuneration of key management personnel. To be related to the private interests of controlling shareholders, drawing on the research of reference [43], these categories in related party transactions are excluded, and then, other related party transactions are added and divided by total assets to measure the occupation of related party transactions, which are recorded as related party transactions.(3) Control Variables. This paper mainly studies the governance effect of institutional investor cliques and measures the level of corporate governance by the tunneling behavior of the controlling shareholder. Except for the influence of the institutional investor, factors such as corporate fundamentals and national policies will also affect the level of corporate governance. To make the empirical results more accurate, drawing on existing research [44], this paper makes the company’s operation and management the control variable of the research. In addition, this article controls for industries and years. In summary, Table 1 shows the details of all the variables selected in this article.Table 1
Definition of main variable in this study.
The variable typesVariable meaningMeasurement methodsInterpreted variablesAppropriation of fundsOther receivables/period-end total assetsRelated party transactionsThe ratio of the sum of related party transactions after removing “noise” to total assets at the end of the yearExplanatory variablesInstitutional investor clique’s share ratioIdentify the institutional investor clique by louvain algorithm and add the share ratios of cliques owned by the same companyDegree centralityCalculate annually the degree centrality of each institution in the institutional investor clique, and then, the degree centrality of the clique is weighted by the ratio of each institution’s shareholdingBetweenness centralityCalculate annually the betweenness centrality of each institution in the institutional investor clique, and then, the betweenness centrality of the clique is weighted by the ratio of each institution’s shareholdingCloseness centralityCalculate annually the closeness centrality of each institution in the institutional investor clique, and then, the closeness centrality of the clique is weighted by the ratio of each institution’s shareholdingControl variablesCompany sizeThe natural logarithm of the total assets at the end of the periodMarket valueAnnual average market capitalizationCompany ageThe natural logarithm of the company’s years of existenceShareholding by controlling shareholdersThe share proportion of the listed company held by controlling shareholdersManagement shareholdingThe share proportion of the listed company held by the managementBoard sizeThe natural logarithm of numbers of board directorsSeparation of two rightsThe difference between control and ownershipNumber of general meetingsThe number of annual general meetings of shareholdersNature of the audit firmWhen the company’s audit firm belongs to the “top ten,” the value is 1, and the value is 0 for other firmsAnnualAnnual dummy variableIndustryIndustry dummy variablesEquity checks and balancesRatio: the sum of the shareholding ratios of the second to ten largest shareholders to the shareholding ratio of the controlling shareholdersAppropriation of funds, appropriation of funds by controlling shareholders; related party transactions, occupation of related party transactions.


### 5.2. Regression Models

In order to examine the impact of the institutional investor clique on the tunneling behavior of controlling shareholders of the listed companies, this paper uses the following fixed effect panel model:(11)Tunneli,t=α0+α1workneti,t+α2∑Controli,t+Year+industry+εi,t.Tunneli,t is the proxy variable for the tunneling behavior of the majority shareholder, represented by the appropriation of funds and related party transactions, respectively; workneti,t is the institutional investor clique’s share ratio; Controli,t describes the control variables in this article. Furthermore, the model controls for the fixed effects of year and industry, and εi,t are residual terms.In order to investigate the influence of institutional investor clique centrality on the tunneling behavior of controlling shareholders of the listed companies, the following three models are designed and fixed effect tests are carried out:(12)Tunneli,t=α0+α1Centralityi,t+α2∑Controli,t+Year+industry+εi,t.Among them,Tunneli,t is the proxy variables for the tunneling behavior of the majority shareholder, represented by appropriation of funds and related party transaction, respectively; Centrality is the proxy variable for the centrality of the institutional investor clique, including degree centrality, betweenness centrality, and closeness centrality; Controli,t represents the control variables for this article. Furthermore, the model controls for the fixed effects of year and industry, and εi,t are residual terms.


### 5.3. Descriptive Statistics of Variables

Table2 presents descriptive statistics for each variable in the study. As can be seen in Table 2, the average shareholding ratio of the institutional investor clique is 6.48%, and the highest can reach 31.75%, which has a certain say in the governance of the listed companies; there are large differences in the three indicators of network centrality, indicating that there is an obvious different ability in the information exchange of the institutional investors at the clique level.Table 2
Descriptive statistics of the main variables, estimated from the Wind Database Institutional Research Subdatabase and the CSMAR database.
Variable namesNumber of samplesMeanStandard deviationMinimumMaximumInstitutional investor clique’s share ratio202416.487.0490.004531.75Degree centrality202410.3570.2260.00031.874Betweenness centrality202410.02950.007400.0419Closeness centrality202410.00550.005700.128Appropriation of funds202410.05330.086700.734Related party transactions202410.320.4190.00012.726Company size2024122.261.29519.2926.05Market value2024122.791.13820.4526.12Company age2024136.4315.050.2376.07The shareholding ratio of the controlling shareholder2024112.4919.13070.7Management shareholding202415.047.595028.15Board size202418.6681.727318Separation of two rights2024137.375.559.0980Number of general meetings202413.4051.89133Nature of the audit firm202410.5460.49801Equity checks and balances202410.930.8050.017.046


### 5.4. Empirical Test and Result Analysis

In columns (1) and (2) of Table3, the regression results based on equation (12) show that the regression coefficients of the institutional investor clique’s share ratio for capital occupation and related party transactions are significantly negative, and the regression coefficients are −0.0010 and −0.0015, respectively, the significance level are 1% and 10%, respectively, which means that the institutional investor clique has a significant negative correlation with the tunneling behavior of the controlling shareholder, and the higher the clique shareholding ratio, the more it can weaken the tunneling behavior of the controlling shareholder. It can be said that the institutional investor clique has enhanced its overall governance capabilities, and Proposition 1 has been verified.Table 3
The impact of institutional investor clique on tunneling behavior.
Variable names(1)(2)(3)(4)Fixed effectHysteresis effectAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsInstitutional investor clique’s share ratio−0.0010∗∗∗−0.0015∗(−7.0863)(−1.9533)The institutional investor clique that is lagging for one period−0.0008∗∗∗−0.001∗(−5.6417)(−1.9709)Company size−0.0327∗∗∗−0.0297∗∗−0.0258∗∗∗−0.0163(−6.9354)(−2.0493)(−5.9841)(−1.0560)Market value0.0325∗∗∗0.0220.0254∗∗∗0.0014−6.9931−1.4447−5.9053−0.0857The shareholding ratio of the controlling shareholder−0.0008∗∗∗−0.0005−0.0007∗∗∗−0.0004(−9.5862)(−1.2148)(−8.6907)(−0.8240)Management shareholding−0.0003∗∗∗−0.0022∗∗∗−0.0002∗∗∗−0.0021∗∗∗(−4.7924)(−7.4665)(−3.1775)(−6.5030)Separation of two rights−0.0003∗∗0.0009−0.0003∗∗0.001(−2.4973)−1.1914(−2.1232)−1.2349Company age0.0007∗∗∗0.0043∗∗∗0.0005∗∗0.0036∗∗∗−3.081−3.7444−2.0656−2.9654Board size−0.0006−0.000400.0007(−0.7728)(−0.1104)(−0.0183)−0.161Number of general meetings0.0034∗∗∗0.0405∗∗∗0.0033∗∗∗0.0419∗∗∗−7.1606−14.2918−6.5102−13.4608Nature of the firm−0.0031∗−0.0029−0.00150.0017(−1.7258)(−0.3230)(−0.8104)−0.1681Equity checks and balances−0.0065∗∗∗−0.0343∗∗∗−0.0071∗∗∗−0.0362∗∗∗(−5.2499)(−5.4514)(−5.3599)(−5.1188)Constant terms0.0671∗∗0.3524∗∗0.0689∗∗0.5105∗∗∗−2.5648−2.4859−2.44−3.2573N21,24021,24017,49617,496Robust standard errors in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.In addition, considering that the corporate governance effect of institutional investor cliques may lag behind, in order to control the endogeneity caused by two-way causality, calculating the lag period of institutional investor clique shareholding ratio, making it an explanatory variable and regressed again, the test results are shown in column (3) and (4) in Table3. The regression coefficients of the institutional investor clique for capital occupation and related party transactions were still significantly negative, with regression coefficients of −0.0008 and −0.0013, respectively, and the significance level was 1% and 10%, which also supports Proposition 1.The institutional investor clique enhances overall governance. The higher the shareholding ratio of the institutional investor clique, the stronger its inhibitory effect on the tunneling behavior of the listed companies, and after considering the lag effect, the institutional investor clique can still significantly inhibit the tunneling behavior. This is because the joint action of institutional shareholders has more voting rights and corresponding shareholder rights and can exert more pressure in consultation with the company’s management, thus improving the governance effectiveness of the listed companies.Table4 shows the regression results based on formula (12), and the regression coefficients of the three centrality indicators of the institutional investor clique are significantly negative for capital occupation and related party transactions, among which the regression coefficients for degree centrality were −0.0121 and −0.0271, the regression coefficients for betweenness centrality were −0.0045 and −0.0054, and the regression coefficients for closeness centrality were −2.9710 and −7.8864. This means that the communication and interaction of information in the institutional investor clique inhibit the tunneling behavior of the controlling shareholder, and the greater the centrality of the clique, the stronger the ability to control the information and the inhibition of the tunneling behavior of the controlling shareholders.Table 4
The impact of institutional investor clique centrality on tunneling behavior.
Variable namesDegree centralityBetweenness centralityCloseness to centralityAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsCentrality indicator−0.0121∗∗∗−0.0271∗∗∗−0.0045∗∗∗−0.0054∗−2.9710∗∗∗−7.8864∗∗∗(−7.6365)(−5.0972)(−4.0558)(−1.7703)(−7.2601)(−5.7685)Company size−0.0283∗∗∗−0.0223−0.0281∗∗∗−0.0212−0.0298∗∗∗−0.0258∗(−6.4263)(−1.5859)(−6.3404)(−1.4907)(−6.6238)(−1.8315)Market value0.0295∗∗∗0.02030.0251∗∗∗0.010.0325∗∗∗0.0294∗−6.6037−1.3756−5.9585−0.6806−7.0093−1.9461The shareholding ratio of the controlling shareholder−0.0007∗∗∗−0.0005−0.0007∗∗∗−0.0005−0.0008∗∗∗−0.0006(−9.1812)(−1.0706)(−9.3346)(−1.0620)(−9.6658)(−1.3564)Management shareholding−0.0002∗∗∗−0.0021∗∗∗−0.0003∗∗∗−0.0022∗∗∗−0.0001∗∗−0.0018∗∗∗(−4.2513)(−7.1826)(−4.9375)(−7.5166)(−2.1317)(−5.8747)Separation of two rights−0.0004∗∗∗0.0008−0.0004∗∗∗0.0009−0.0004∗∗∗0.0009(−2.8419)−1.1015(−2.9110)−1.1329(−2.7166)−1.1678Company age0.0006∗∗∗0.0042∗∗∗0.0007∗∗∗0.0043∗∗∗0.0006∗∗∗0.0041∗∗∗−2.9867−3.6974−3.1618−3.7527−2.8199−3.6115Board size−0.00030−0.0003−0.0003−0.00030(−0.4354)(−0.0084)(−0.4612)(−0.0678)(−0.4228)−0.0048Number of general meetings0.0030∗∗∗0.0397∗∗∗0.0031∗∗∗0.0400∗∗∗0.0031∗∗∗0.0398∗∗∗−6.2882−14.068−6.5908−14.1199−6.4702−14.1043Nature of the firm−0.0023−0.0015−0.0027−0.0018−0.0025−0.0019(−1.2895)(−0.1682)(−1.4841)(−0.1949)(−1.4022)(−0.2063)Equity checks and balances−0.0085∗∗∗−0.0378∗∗∗−0.0082∗∗∗−0.0362∗∗∗−0.0072∗∗∗−0.0346∗∗∗(−6.6499)(−6.0355)(−6.4837)(−5.7878)(−5.6799)(−5.5537)Constant terms0.01390.18260.0995∗∗∗0.3945∗∗∗0.0834∗∗∗0.3211∗∗−0.5219−1.2536−3.8963−2.8253−3.3113−2.2869N21,24021,24021,20321,20321,24021,240Robust standard errors in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.Further regression analysis is carried out with the network centrality of the institutional investor clique with a lag period as the explanatory variable, and the results are shown in Table5, and the regression coefficients of the three centrality indicators are still significantly negative for capital occupation and related party transactions, again proving that the stronger the clique centrality, the greater the inhibition on tunneling behavior.Table 5
Hysteresis effect of institutional investor clique centrality on tunneling behavior.
Variable namesDegree centralityBetweenness centralityCloseness centralityAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsA central indicator of a lagging period−0.0050∗∗∗−0.0241∗∗∗−0.0018∗∗∗−0.0033∗−1.9525∗∗∗−8.1285∗∗∗(−3.0089)(−3.9302)(−4.2875)(−1.7574)(−4.0951)(−4.9103)Company size−0.0227∗∗∗−0.0084−0.0229∗∗∗−0.0119−0.0232∗∗∗−0.0112(−5.5924)(−0.5484)(−5.6450)(−0.7759)(−5.6260)(−0.7382)Market value0.0213∗∗∗−0.00230.0200∗∗∗−0.00570.0237∗∗∗0.0073−5.2436(−0.1446)−5.1445(−0.3569)−5.5785−0.4629The shareholding ratio of the controlling shareholder−0.0007∗∗∗−0.0004−0.0007∗∗∗−0.0004−0.0007∗∗∗−0.0005(−8.2618)(−0.7597)(−8.2687)(−0.7767)(−8.5724)(−1.0856)Management shareholding−0.0002∗∗∗−0.0021∗∗∗−0.0002∗∗∗−0.0021∗∗∗−0.0001∗∗−0.0018∗∗∗(−3.3147)(−6.4718)(−3.4384)(−6.4932)(−1.9880)(−5.3340)Separation of two rights−0.0003∗∗0.001−0.0003∗∗0.001−0.0003∗∗0.001(−2.3639)−1.1639(−2.3711)−1.1901(−2.2854)−1.2352Company age0.0005∗∗0.0036∗∗∗0.0005∗∗0.0036∗∗∗0.0004∗0.0034∗∗∗−2.0563−2.9334−2.0938−2.9397−1.9323−2.857Board size0.00010.00090.00010.00090.00010.0009−0.1773−0.2057−0.1429−0.2134−0.1711−0.2002Number of general meetings0.0030∗∗∗0.0412∗∗∗0.0031∗∗∗0.0417∗∗∗0.0030∗∗∗0.0411∗∗∗−6.0048−13.2377−6.183−13.3967−5.9716−13.246Nature of the firm−0.00110.0025−0.00110.0028−0.00120.002(−0.5617)−0.2502(−0.5760)−0.2789(−0.6207)−0.2009Equity checks and balances−0.0078∗∗∗−0.0386∗∗∗−0.0076∗∗∗−0.0378∗∗∗−0.0073∗∗∗−0.0364∗∗∗(−5.7461)(−5.4474)(−5.6908)(−5.3463)(−5.4913)(−5.1529)Constant terms0.0771∗∗∗0.3805∗∗0.1098∗∗∗0.5480∗∗∗0.0984∗∗∗0.4951∗∗∗−2.7333−2.4593−4.0025−3.6079−3.6607−3.2664N17,49617,49617,47517,47517,49617,496Robust standard errors in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.As can be seen, the greater the degree of centrality, the greater the number of investors working within the institutional investor clique and the broader the network relationship; the greater the betweenness centrality, the more the institutional investors can influence the communication between each other and drive other institutional investors to share information; the greater the closeness centrality, the shorter the average connection path between institutional investors and the faster the information transfer. In a word, with a higher centrality, an institutional investor clique has a stronger inhibitory effect on the tunneling behavior of controlling shareholders.


### 5.5. Robust Inspection

Due to the dramatic changes in the China stock market in 2008, 2009, and 2015, the huddling behavior of institutional investors will also be affected by the economic environment. Moreover, to reduce market risks, nonclique members will also choose the same decision as the institutional investor clique, and the illusion of cooperation appears. Therefore, this paper deletes these three years to regress. As shown in Tables6 and 7, tunneling behavior is still significantly negatively correlated with institutional investor clique shareholding, and the clique centricity indicator is also significantly negatively correlated, once again verifying the positive role of the institutional investor clique on the tunneling behavior of the listed company.Table 6
Institutional investor clique’s robustness test on tunneling behavior.
Variable names(1)(2)Appropriation of fundsRelated party transactionsInstitutional investor clique’s share ratio−0.0010∗∗∗−0.0024∗∗∗(−6.4471)(−3.1366)Company size−0.0306∗∗∗−0.0219(−6.4000)(−1.4755)Market value0.0310∗∗∗0.0183−6.5149−1.1645The shareholding ratio of the controlling shareholder−0.0008∗∗∗−0.0008∗(−9.7744)(−1.8813)Management shareholding−0.0003∗∗∗−0.0020∗∗∗(−4.5749)(−6.7457)Separation of two rights−0.0003∗∗0.0007(−2.4420)−0.992Company age0.0006∗∗∗0.0038∗∗∗−2.6132−3.3661Board size−0.0006−0.0003(−0.7692)(−0.0833)Number of general meetings0.0034∗∗∗0.0402∗∗∗−6.8655−13.9292Nature of the firm−0.0025−0.0019(−1.3744)(−0.2060)Equity checks and balances−0.0066∗∗∗−0.0344∗∗∗(−5.2242)(−5.3760)Constant terms0.0624∗∗0.2658∗−2.3389−1.8574N18,03918,039Robust standard error in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.Table 7
Robustness test of institutional investor clique centrality on tunneling behavior.
Variable namesDegree centralityBetweenness centralityCloseness centralityAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsDegree centrality−0.0115∗∗∗−0.0222∗∗∗(−7.1409)(−4.0432)Mediation centrality−0.0041∗∗∗0.0001∗(−3.2857)(−1.7454)Close to centrality−2.7716∗∗∗−7.7477∗∗∗(−6.6617)(−5.5834)Company size−0.0264∗∗∗−0.0126−0.0264∗∗∗−0.0125−0.0276∗∗∗−0.015(−5.9180)(−0.8794)(−5.9143)(−0.8670)(−6.1095)(−1.0513)Market value0.0279∗∗∗0.00990.0239∗∗∗0.00280.0307∗∗∗0.0202−6.168−0.6619−5.6175−0.1858−6.5068−1.3152Shareholding by controlling shareholders−0.0008∗∗∗−0.0007∗−0.0008∗∗∗−0.0007−0.0008∗∗∗−0.0008∗(−9.4367)(−1.7029)(−9.5154)(−1.6224)(−9.8153)(−1.9568)Management shareholding−0.0002∗∗∗−0.0019∗∗∗−0.0003∗∗∗−0.0020∗∗∗−0.0001∗∗−0.0016∗∗∗(−4.1621)(−6.6195)(−4.7676)(−6.8999)(−2.0594)(−5.2019)Separation of two rights−0.0004∗∗∗0.0006−0.0004∗∗∗0.0007−0.0004∗∗∗0.0007(−2.8323)−0.832(−2.8358)−0.9111(−2.7052)−0.8939Company age0.0006∗∗∗0.0038∗∗∗0.0006∗∗∗0.0038∗∗∗0.0005∗∗0.0037∗∗∗−2.5957−3.376−2.7353−3.4017−2.4345−3.2787Board size−0.00040.0001−0.0004−0.0001−0.00040.0002(−0.5089)−0.0282(−0.5309)(−0.0148)(−0.4817)−0.0496Number of general meetings0.0030∗∗∗0.0393∗∗∗0.0031∗∗∗0.0396∗∗∗0.0030∗∗∗0.0393∗∗∗−6.1435−13.6592−6.4307−13.726−6.2415−13.661Nature of the firm−0.0017−0.0002−0.0021−0.0003−0.0019−0.0003(−0.9340)(−0.0175)(−1.1602)(−0.0316)(−1.0281)(−0.0271)Equity checks and balances−0.0086∗∗∗−0.0386∗∗∗−0.0082∗∗∗−0.0363∗∗∗−0.0073∗∗∗−0.0358∗∗∗(−6.5881)(−6.0496)(−6.3448)(−5.7003)(−5.6804)(−5.6507)Constant terms0.01890.20580.0991∗∗∗0.3902∗∗∗0.0791∗∗∗0.2872∗∗−0.6969−1.4041−3.8276−2.7989−3.0952−2.0461N180391803918008180081803918039Robust standard error in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.


## 5.1. Research Design

### 5.1.1. Data Source

After 2007, China’s listed companies began making financial disclosures under the new accounting standard, so this article limits the sample to Shanghai and Shenzhen A-share listed companies from 2007 to 2020. The financial data of the listed companies comes from the China Stock Market & Accounting Research Database Company Research Subdatabase, and the institutional investor shareholding data comes from the WIND Database Institutional Research Subdatabase. The data are processed as follows: (1) deleting companies with ST and∗ST which mean risks of delisting, and listed companies in the financial industry; (2) referring to reference [40], to delete companies that do not have controlling shareholders; and (3) all continuous variables in the text were Winsorized by 1%.


### 5.1.2. Variable definitions

(1) Explanatory Variables. This paper draws on the methods of reference [4] to identify institutional investors’ network cliques. Drawing on the research of references [22, 38], the network centrality index is measured.(1)
Institutional investor clique’s share ratioMany studies have mentioned that large shareholders with more than 5% shareholding have strong governance effectiveness [41, 42]. At the same time, the 5% shareholding ratio is a warning line for major equity changes in the China’s securities market, which can affect the daily operation and governance of the listed companies. Therefore, the institutional investor network in this paper is constructed by the connection standard that the sum of the joint shareholding of institutional investors of not less than 5% of the same listed company. Second, using on the processing method of reference [4], the Louvain algorithm is used to continuously optimize the modularity for the identification of network cliques. Finally, the following formula is used to calculate the shareholding ratio of the institutional investor clique.(7)Workneti=∑j=1NInvestijTradesharei.Among them, theWorkneti represents the shareholding ratio of the institutional investor clique, N represents the total number of institutional investor cliques owned by the identified i-listed company; Investij indicates the number of shares held by the J clique in the i-listed company; Tradesharei indicates the number of circulating shares at the end of the period of the i-listed company.(2)
Degree centralityThe degree centrality measures the proportion of connection betweeni nodes and other nodes DiJ to the total number of nodes N in the network. The greater the degree of centrality, the wider the network of relationships associated with the point, reflecting the active level of the institutional investors in the network. The closer the degree centrality to 1, the more fully the information exchange between the institutional investors in the network. The specific calculation formula is as follows:(8)Degree=DiJn−1,(3)
Betweenness centralityBetweenness centrality measures how many points are connected byi nodes that are not originally related directly. The greater the betweenness centrality of the i node, the stronger the control ability of the node over other nodes and the transmission of network information. Pikj is the number of nodes in the shortest distance between the nodes k and j, while P (kj) is the shortest distance between k nodes and j nodes. (n-2) (n-1)/2 in the denominator represents the sum of the shortest paths that exist between all nodes in the network, calculated as follows:(9)Between=∑k≠j,i∉k,jPikj\\/Pkjn−2n−1/2,(4)
Closeness centralityCloseness centrality measures the sum of the number of all nodes that have a direct and indirect relationship to the i-node divided by the shortest distance the i-node has reached the other nodes and normalized with the number of all nodes (N−1)., the greater the closeness centrality, the shorter the average connection path between the node and other nodes. The more direct and effective the connection between the key institutional investor and other institutional investors is, the faster the speed of information transmission. The specific calculation formula is as follows:(10)Close=N−1∑j=1Ndi,j.(2) Explanatory Variables. Corporate governance mainly involves two types of agency issues for the listed companies. One is the conflict of interest between management and shareholders, and the other is the conflict of interest between controlling shareholders and other shareholders. As an emerging capital market, the equity of the listed companies in China is still relatively concentrated, which alleviates the first type of conflict to some certain extent. However, the controlling shareholder may use a variety of unfair means to tunnel the listed company, that is, to extract profits from the listed company and convey it, infringing the interests of other shareholders, which will not only harm the equity of institutional investor but will also jeopardize the value of the company stock. So, an institutional investor has the incentive to govern it. To measure the governance effectiveness of the institutional investors, this article focuses on the inhibitory effect of institutional investors on controlling tunneling behavior of shareholders, specifically using two proxy variables: (1)
Appropriation of funds by controlling shareholders.The controlling shareholder of a listed company can directly occupy the funds of the listed company, which is reflected mainly in other receivables, prepaid accounts, and investment funds in the statement, especially the black box of “other receivables,” which can accommodate a variety of interest transmission transactions of the controlling shareholder. In addition, other receivables are long-lived and difficult to collect, which has become the main channel for controlling shareholders to occupy funds. Therefore, the controlling shareholder’s appropriation of funds is measured by dividing the year-end balance of other receivables by the year-end balance of total assets, which is recorded as appropriation of funds.(2)
Occupation of related party transactions.Related party transactions refer to transactions between the listed companies and related parties. Affiliates may use the right of enterprise control to harm the company’s interest. According to the classification standards of the China Stock Market & Accounting Research Database, related party transactions include 17 categories of matters: commodity transactions, asset transactions, and capital transactions, since it is difficult for cooperation projects, licensing agreements, and the remuneration of key management personnel. To be related to the private interests of controlling shareholders, drawing on the research of reference [43], these categories in related party transactions are excluded, and then, other related party transactions are added and divided by total assets to measure the occupation of related party transactions, which are recorded as related party transactions.(3) Control Variables. This paper mainly studies the governance effect of institutional investor cliques and measures the level of corporate governance by the tunneling behavior of the controlling shareholder. Except for the influence of the institutional investor, factors such as corporate fundamentals and national policies will also affect the level of corporate governance. To make the empirical results more accurate, drawing on existing research [44], this paper makes the company’s operation and management the control variable of the research. In addition, this article controls for industries and years. In summary, Table 1 shows the details of all the variables selected in this article.Table 1
Definition of main variable in this study.
The variable typesVariable meaningMeasurement methodsInterpreted variablesAppropriation of fundsOther receivables/period-end total assetsRelated party transactionsThe ratio of the sum of related party transactions after removing “noise” to total assets at the end of the yearExplanatory variablesInstitutional investor clique’s share ratioIdentify the institutional investor clique by louvain algorithm and add the share ratios of cliques owned by the same companyDegree centralityCalculate annually the degree centrality of each institution in the institutional investor clique, and then, the degree centrality of the clique is weighted by the ratio of each institution’s shareholdingBetweenness centralityCalculate annually the betweenness centrality of each institution in the institutional investor clique, and then, the betweenness centrality of the clique is weighted by the ratio of each institution’s shareholdingCloseness centralityCalculate annually the closeness centrality of each institution in the institutional investor clique, and then, the closeness centrality of the clique is weighted by the ratio of each institution’s shareholdingControl variablesCompany sizeThe natural logarithm of the total assets at the end of the periodMarket valueAnnual average market capitalizationCompany ageThe natural logarithm of the company’s years of existenceShareholding by controlling shareholdersThe share proportion of the listed company held by controlling shareholdersManagement shareholdingThe share proportion of the listed company held by the managementBoard sizeThe natural logarithm of numbers of board directorsSeparation of two rightsThe difference between control and ownershipNumber of general meetingsThe number of annual general meetings of shareholdersNature of the audit firmWhen the company’s audit firm belongs to the “top ten,” the value is 1, and the value is 0 for other firmsAnnualAnnual dummy variableIndustryIndustry dummy variablesEquity checks and balancesRatio: the sum of the shareholding ratios of the second to ten largest shareholders to the shareholding ratio of the controlling shareholdersAppropriation of funds, appropriation of funds by controlling shareholders; related party transactions, occupation of related party transactions.


## 5.1.1. Data Source

After 2007, China’s listed companies began making financial disclosures under the new accounting standard, so this article limits the sample to Shanghai and Shenzhen A-share listed companies from 2007 to 2020. The financial data of the listed companies comes from the China Stock Market & Accounting Research Database Company Research Subdatabase, and the institutional investor shareholding data comes from the WIND Database Institutional Research Subdatabase. The data are processed as follows: (1) deleting companies with ST and∗ST which mean risks of delisting, and listed companies in the financial industry; (2) referring to reference [40], to delete companies that do not have controlling shareholders; and (3) all continuous variables in the text were Winsorized by 1%.


## 5.1.2. Variable definitions

(1) Explanatory Variables. This paper draws on the methods of reference [4] to identify institutional investors’ network cliques. Drawing on the research of references [22, 38], the network centrality index is measured.(1)
Institutional investor clique’s share ratioMany studies have mentioned that large shareholders with more than 5% shareholding have strong governance effectiveness [41, 42]. At the same time, the 5% shareholding ratio is a warning line for major equity changes in the China’s securities market, which can affect the daily operation and governance of the listed companies. Therefore, the institutional investor network in this paper is constructed by the connection standard that the sum of the joint shareholding of institutional investors of not less than 5% of the same listed company. Second, using on the processing method of reference [4], the Louvain algorithm is used to continuously optimize the modularity for the identification of network cliques. Finally, the following formula is used to calculate the shareholding ratio of the institutional investor clique.(7)Workneti=∑j=1NInvestijTradesharei.Among them, theWorkneti represents the shareholding ratio of the institutional investor clique, N represents the total number of institutional investor cliques owned by the identified i-listed company; Investij indicates the number of shares held by the J clique in the i-listed company; Tradesharei indicates the number of circulating shares at the end of the period of the i-listed company.(2)
Degree centralityThe degree centrality measures the proportion of connection betweeni nodes and other nodes DiJ to the total number of nodes N in the network. The greater the degree of centrality, the wider the network of relationships associated with the point, reflecting the active level of the institutional investors in the network. The closer the degree centrality to 1, the more fully the information exchange between the institutional investors in the network. The specific calculation formula is as follows:(8)Degree=DiJn−1,(3)
Betweenness centralityBetweenness centrality measures how many points are connected byi nodes that are not originally related directly. The greater the betweenness centrality of the i node, the stronger the control ability of the node over other nodes and the transmission of network information. Pikj is the number of nodes in the shortest distance between the nodes k and j, while P (kj) is the shortest distance between k nodes and j nodes. (n-2) (n-1)/2 in the denominator represents the sum of the shortest paths that exist between all nodes in the network, calculated as follows:(9)Between=∑k≠j,i∉k,jPikj\\/Pkjn−2n−1/2,(4)
Closeness centralityCloseness centrality measures the sum of the number of all nodes that have a direct and indirect relationship to the i-node divided by the shortest distance the i-node has reached the other nodes and normalized with the number of all nodes (N−1)., the greater the closeness centrality, the shorter the average connection path between the node and other nodes. The more direct and effective the connection between the key institutional investor and other institutional investors is, the faster the speed of information transmission. The specific calculation formula is as follows:(10)Close=N−1∑j=1Ndi,j.(2) Explanatory Variables. Corporate governance mainly involves two types of agency issues for the listed companies. One is the conflict of interest between management and shareholders, and the other is the conflict of interest between controlling shareholders and other shareholders. As an emerging capital market, the equity of the listed companies in China is still relatively concentrated, which alleviates the first type of conflict to some certain extent. However, the controlling shareholder may use a variety of unfair means to tunnel the listed company, that is, to extract profits from the listed company and convey it, infringing the interests of other shareholders, which will not only harm the equity of institutional investor but will also jeopardize the value of the company stock. So, an institutional investor has the incentive to govern it. To measure the governance effectiveness of the institutional investors, this article focuses on the inhibitory effect of institutional investors on controlling tunneling behavior of shareholders, specifically using two proxy variables: (1)
Appropriation of funds by controlling shareholders.The controlling shareholder of a listed company can directly occupy the funds of the listed company, which is reflected mainly in other receivables, prepaid accounts, and investment funds in the statement, especially the black box of “other receivables,” which can accommodate a variety of interest transmission transactions of the controlling shareholder. In addition, other receivables are long-lived and difficult to collect, which has become the main channel for controlling shareholders to occupy funds. Therefore, the controlling shareholder’s appropriation of funds is measured by dividing the year-end balance of other receivables by the year-end balance of total assets, which is recorded as appropriation of funds.(2)
Occupation of related party transactions.Related party transactions refer to transactions between the listed companies and related parties. Affiliates may use the right of enterprise control to harm the company’s interest. According to the classification standards of the China Stock Market & Accounting Research Database, related party transactions include 17 categories of matters: commodity transactions, asset transactions, and capital transactions, since it is difficult for cooperation projects, licensing agreements, and the remuneration of key management personnel. To be related to the private interests of controlling shareholders, drawing on the research of reference [43], these categories in related party transactions are excluded, and then, other related party transactions are added and divided by total assets to measure the occupation of related party transactions, which are recorded as related party transactions.(3) Control Variables. This paper mainly studies the governance effect of institutional investor cliques and measures the level of corporate governance by the tunneling behavior of the controlling shareholder. Except for the influence of the institutional investor, factors such as corporate fundamentals and national policies will also affect the level of corporate governance. To make the empirical results more accurate, drawing on existing research [44], this paper makes the company’s operation and management the control variable of the research. In addition, this article controls for industries and years. In summary, Table 1 shows the details of all the variables selected in this article.Table 1
Definition of main variable in this study.
The variable typesVariable meaningMeasurement methodsInterpreted variablesAppropriation of fundsOther receivables/period-end total assetsRelated party transactionsThe ratio of the sum of related party transactions after removing “noise” to total assets at the end of the yearExplanatory variablesInstitutional investor clique’s share ratioIdentify the institutional investor clique by louvain algorithm and add the share ratios of cliques owned by the same companyDegree centralityCalculate annually the degree centrality of each institution in the institutional investor clique, and then, the degree centrality of the clique is weighted by the ratio of each institution’s shareholdingBetweenness centralityCalculate annually the betweenness centrality of each institution in the institutional investor clique, and then, the betweenness centrality of the clique is weighted by the ratio of each institution’s shareholdingCloseness centralityCalculate annually the closeness centrality of each institution in the institutional investor clique, and then, the closeness centrality of the clique is weighted by the ratio of each institution’s shareholdingControl variablesCompany sizeThe natural logarithm of the total assets at the end of the periodMarket valueAnnual average market capitalizationCompany ageThe natural logarithm of the company’s years of existenceShareholding by controlling shareholdersThe share proportion of the listed company held by controlling shareholdersManagement shareholdingThe share proportion of the listed company held by the managementBoard sizeThe natural logarithm of numbers of board directorsSeparation of two rightsThe difference between control and ownershipNumber of general meetingsThe number of annual general meetings of shareholdersNature of the audit firmWhen the company’s audit firm belongs to the “top ten,” the value is 1, and the value is 0 for other firmsAnnualAnnual dummy variableIndustryIndustry dummy variablesEquity checks and balancesRatio: the sum of the shareholding ratios of the second to ten largest shareholders to the shareholding ratio of the controlling shareholdersAppropriation of funds, appropriation of funds by controlling shareholders; related party transactions, occupation of related party transactions.


## 5.2. Regression Models

In order to examine the impact of the institutional investor clique on the tunneling behavior of controlling shareholders of the listed companies, this paper uses the following fixed effect panel model:(11)Tunneli,t=α0+α1workneti,t+α2∑Controli,t+Year+industry+εi,t.Tunneli,t is the proxy variable for the tunneling behavior of the majority shareholder, represented by the appropriation of funds and related party transactions, respectively; workneti,t is the institutional investor clique’s share ratio; Controli,t describes the control variables in this article. Furthermore, the model controls for the fixed effects of year and industry, and εi,t are residual terms.In order to investigate the influence of institutional investor clique centrality on the tunneling behavior of controlling shareholders of the listed companies, the following three models are designed and fixed effect tests are carried out:(12)Tunneli,t=α0+α1Centralityi,t+α2∑Controli,t+Year+industry+εi,t.Among them,Tunneli,t is the proxy variables for the tunneling behavior of the majority shareholder, represented by appropriation of funds and related party transaction, respectively; Centrality is the proxy variable for the centrality of the institutional investor clique, including degree centrality, betweenness centrality, and closeness centrality; Controli,t represents the control variables for this article. Furthermore, the model controls for the fixed effects of year and industry, and εi,t are residual terms.


## 5.3. Descriptive Statistics of Variables

Table2 presents descriptive statistics for each variable in the study. As can be seen in Table 2, the average shareholding ratio of the institutional investor clique is 6.48%, and the highest can reach 31.75%, which has a certain say in the governance of the listed companies; there are large differences in the three indicators of network centrality, indicating that there is an obvious different ability in the information exchange of the institutional investors at the clique level.Table 2
Descriptive statistics of the main variables, estimated from the Wind Database Institutional Research Subdatabase and the CSMAR database.
Variable namesNumber of samplesMeanStandard deviationMinimumMaximumInstitutional investor clique’s share ratio202416.487.0490.004531.75Degree centrality202410.3570.2260.00031.874Betweenness centrality202410.02950.007400.0419Closeness centrality202410.00550.005700.128Appropriation of funds202410.05330.086700.734Related party transactions202410.320.4190.00012.726Company size2024122.261.29519.2926.05Market value2024122.791.13820.4526.12Company age2024136.4315.050.2376.07The shareholding ratio of the controlling shareholder2024112.4919.13070.7Management shareholding202415.047.595028.15Board size202418.6681.727318Separation of two rights2024137.375.559.0980Number of general meetings202413.4051.89133Nature of the audit firm202410.5460.49801Equity checks and balances202410.930.8050.017.046


## 5.4. Empirical Test and Result Analysis

In columns (1) and (2) of Table3, the regression results based on equation (12) show that the regression coefficients of the institutional investor clique’s share ratio for capital occupation and related party transactions are significantly negative, and the regression coefficients are −0.0010 and −0.0015, respectively, the significance level are 1% and 10%, respectively, which means that the institutional investor clique has a significant negative correlation with the tunneling behavior of the controlling shareholder, and the higher the clique shareholding ratio, the more it can weaken the tunneling behavior of the controlling shareholder. It can be said that the institutional investor clique has enhanced its overall governance capabilities, and Proposition 1 has been verified.Table 3
The impact of institutional investor clique on tunneling behavior.
Variable names(1)(2)(3)(4)Fixed effectHysteresis effectAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsInstitutional investor clique’s share ratio−0.0010∗∗∗−0.0015∗(−7.0863)(−1.9533)The institutional investor clique that is lagging for one period−0.0008∗∗∗−0.001∗(−5.6417)(−1.9709)Company size−0.0327∗∗∗−0.0297∗∗−0.0258∗∗∗−0.0163(−6.9354)(−2.0493)(−5.9841)(−1.0560)Market value0.0325∗∗∗0.0220.0254∗∗∗0.0014−6.9931−1.4447−5.9053−0.0857The shareholding ratio of the controlling shareholder−0.0008∗∗∗−0.0005−0.0007∗∗∗−0.0004(−9.5862)(−1.2148)(−8.6907)(−0.8240)Management shareholding−0.0003∗∗∗−0.0022∗∗∗−0.0002∗∗∗−0.0021∗∗∗(−4.7924)(−7.4665)(−3.1775)(−6.5030)Separation of two rights−0.0003∗∗0.0009−0.0003∗∗0.001(−2.4973)−1.1914(−2.1232)−1.2349Company age0.0007∗∗∗0.0043∗∗∗0.0005∗∗0.0036∗∗∗−3.081−3.7444−2.0656−2.9654Board size−0.0006−0.000400.0007(−0.7728)(−0.1104)(−0.0183)−0.161Number of general meetings0.0034∗∗∗0.0405∗∗∗0.0033∗∗∗0.0419∗∗∗−7.1606−14.2918−6.5102−13.4608Nature of the firm−0.0031∗−0.0029−0.00150.0017(−1.7258)(−0.3230)(−0.8104)−0.1681Equity checks and balances−0.0065∗∗∗−0.0343∗∗∗−0.0071∗∗∗−0.0362∗∗∗(−5.2499)(−5.4514)(−5.3599)(−5.1188)Constant terms0.0671∗∗0.3524∗∗0.0689∗∗0.5105∗∗∗−2.5648−2.4859−2.44−3.2573N21,24021,24017,49617,496Robust standard errors in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.In addition, considering that the corporate governance effect of institutional investor cliques may lag behind, in order to control the endogeneity caused by two-way causality, calculating the lag period of institutional investor clique shareholding ratio, making it an explanatory variable and regressed again, the test results are shown in column (3) and (4) in Table3. The regression coefficients of the institutional investor clique for capital occupation and related party transactions were still significantly negative, with regression coefficients of −0.0008 and −0.0013, respectively, and the significance level was 1% and 10%, which also supports Proposition 1.The institutional investor clique enhances overall governance. The higher the shareholding ratio of the institutional investor clique, the stronger its inhibitory effect on the tunneling behavior of the listed companies, and after considering the lag effect, the institutional investor clique can still significantly inhibit the tunneling behavior. This is because the joint action of institutional shareholders has more voting rights and corresponding shareholder rights and can exert more pressure in consultation with the company’s management, thus improving the governance effectiveness of the listed companies.Table4 shows the regression results based on formula (12), and the regression coefficients of the three centrality indicators of the institutional investor clique are significantly negative for capital occupation and related party transactions, among which the regression coefficients for degree centrality were −0.0121 and −0.0271, the regression coefficients for betweenness centrality were −0.0045 and −0.0054, and the regression coefficients for closeness centrality were −2.9710 and −7.8864. This means that the communication and interaction of information in the institutional investor clique inhibit the tunneling behavior of the controlling shareholder, and the greater the centrality of the clique, the stronger the ability to control the information and the inhibition of the tunneling behavior of the controlling shareholders.Table 4
The impact of institutional investor clique centrality on tunneling behavior.
Variable namesDegree centralityBetweenness centralityCloseness to centralityAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsCentrality indicator−0.0121∗∗∗−0.0271∗∗∗−0.0045∗∗∗−0.0054∗−2.9710∗∗∗−7.8864∗∗∗(−7.6365)(−5.0972)(−4.0558)(−1.7703)(−7.2601)(−5.7685)Company size−0.0283∗∗∗−0.0223−0.0281∗∗∗−0.0212−0.0298∗∗∗−0.0258∗(−6.4263)(−1.5859)(−6.3404)(−1.4907)(−6.6238)(−1.8315)Market value0.0295∗∗∗0.02030.0251∗∗∗0.010.0325∗∗∗0.0294∗−6.6037−1.3756−5.9585−0.6806−7.0093−1.9461The shareholding ratio of the controlling shareholder−0.0007∗∗∗−0.0005−0.0007∗∗∗−0.0005−0.0008∗∗∗−0.0006(−9.1812)(−1.0706)(−9.3346)(−1.0620)(−9.6658)(−1.3564)Management shareholding−0.0002∗∗∗−0.0021∗∗∗−0.0003∗∗∗−0.0022∗∗∗−0.0001∗∗−0.0018∗∗∗(−4.2513)(−7.1826)(−4.9375)(−7.5166)(−2.1317)(−5.8747)Separation of two rights−0.0004∗∗∗0.0008−0.0004∗∗∗0.0009−0.0004∗∗∗0.0009(−2.8419)−1.1015(−2.9110)−1.1329(−2.7166)−1.1678Company age0.0006∗∗∗0.0042∗∗∗0.0007∗∗∗0.0043∗∗∗0.0006∗∗∗0.0041∗∗∗−2.9867−3.6974−3.1618−3.7527−2.8199−3.6115Board size−0.00030−0.0003−0.0003−0.00030(−0.4354)(−0.0084)(−0.4612)(−0.0678)(−0.4228)−0.0048Number of general meetings0.0030∗∗∗0.0397∗∗∗0.0031∗∗∗0.0400∗∗∗0.0031∗∗∗0.0398∗∗∗−6.2882−14.068−6.5908−14.1199−6.4702−14.1043Nature of the firm−0.0023−0.0015−0.0027−0.0018−0.0025−0.0019(−1.2895)(−0.1682)(−1.4841)(−0.1949)(−1.4022)(−0.2063)Equity checks and balances−0.0085∗∗∗−0.0378∗∗∗−0.0082∗∗∗−0.0362∗∗∗−0.0072∗∗∗−0.0346∗∗∗(−6.6499)(−6.0355)(−6.4837)(−5.7878)(−5.6799)(−5.5537)Constant terms0.01390.18260.0995∗∗∗0.3945∗∗∗0.0834∗∗∗0.3211∗∗−0.5219−1.2536−3.8963−2.8253−3.3113−2.2869N21,24021,24021,20321,20321,24021,240Robust standard errors in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.Further regression analysis is carried out with the network centrality of the institutional investor clique with a lag period as the explanatory variable, and the results are shown in Table5, and the regression coefficients of the three centrality indicators are still significantly negative for capital occupation and related party transactions, again proving that the stronger the clique centrality, the greater the inhibition on tunneling behavior.Table 5
Hysteresis effect of institutional investor clique centrality on tunneling behavior.
Variable namesDegree centralityBetweenness centralityCloseness centralityAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsA central indicator of a lagging period−0.0050∗∗∗−0.0241∗∗∗−0.0018∗∗∗−0.0033∗−1.9525∗∗∗−8.1285∗∗∗(−3.0089)(−3.9302)(−4.2875)(−1.7574)(−4.0951)(−4.9103)Company size−0.0227∗∗∗−0.0084−0.0229∗∗∗−0.0119−0.0232∗∗∗−0.0112(−5.5924)(−0.5484)(−5.6450)(−0.7759)(−5.6260)(−0.7382)Market value0.0213∗∗∗−0.00230.0200∗∗∗−0.00570.0237∗∗∗0.0073−5.2436(−0.1446)−5.1445(−0.3569)−5.5785−0.4629The shareholding ratio of the controlling shareholder−0.0007∗∗∗−0.0004−0.0007∗∗∗−0.0004−0.0007∗∗∗−0.0005(−8.2618)(−0.7597)(−8.2687)(−0.7767)(−8.5724)(−1.0856)Management shareholding−0.0002∗∗∗−0.0021∗∗∗−0.0002∗∗∗−0.0021∗∗∗−0.0001∗∗−0.0018∗∗∗(−3.3147)(−6.4718)(−3.4384)(−6.4932)(−1.9880)(−5.3340)Separation of two rights−0.0003∗∗0.001−0.0003∗∗0.001−0.0003∗∗0.001(−2.3639)−1.1639(−2.3711)−1.1901(−2.2854)−1.2352Company age0.0005∗∗0.0036∗∗∗0.0005∗∗0.0036∗∗∗0.0004∗0.0034∗∗∗−2.0563−2.9334−2.0938−2.9397−1.9323−2.857Board size0.00010.00090.00010.00090.00010.0009−0.1773−0.2057−0.1429−0.2134−0.1711−0.2002Number of general meetings0.0030∗∗∗0.0412∗∗∗0.0031∗∗∗0.0417∗∗∗0.0030∗∗∗0.0411∗∗∗−6.0048−13.2377−6.183−13.3967−5.9716−13.246Nature of the firm−0.00110.0025−0.00110.0028−0.00120.002(−0.5617)−0.2502(−0.5760)−0.2789(−0.6207)−0.2009Equity checks and balances−0.0078∗∗∗−0.0386∗∗∗−0.0076∗∗∗−0.0378∗∗∗−0.0073∗∗∗−0.0364∗∗∗(−5.7461)(−5.4474)(−5.6908)(−5.3463)(−5.4913)(−5.1529)Constant terms0.0771∗∗∗0.3805∗∗0.1098∗∗∗0.5480∗∗∗0.0984∗∗∗0.4951∗∗∗−2.7333−2.4593−4.0025−3.6079−3.6607−3.2664N17,49617,49617,47517,47517,49617,496Robust standard errors in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.As can be seen, the greater the degree of centrality, the greater the number of investors working within the institutional investor clique and the broader the network relationship; the greater the betweenness centrality, the more the institutional investors can influence the communication between each other and drive other institutional investors to share information; the greater the closeness centrality, the shorter the average connection path between institutional investors and the faster the information transfer. In a word, with a higher centrality, an institutional investor clique has a stronger inhibitory effect on the tunneling behavior of controlling shareholders.


## 5.5. Robust Inspection

Due to the dramatic changes in the China stock market in 2008, 2009, and 2015, the huddling behavior of institutional investors will also be affected by the economic environment. Moreover, to reduce market risks, nonclique members will also choose the same decision as the institutional investor clique, and the illusion of cooperation appears. Therefore, this paper deletes these three years to regress. As shown in Tables6 and 7, tunneling behavior is still significantly negatively correlated with institutional investor clique shareholding, and the clique centricity indicator is also significantly negatively correlated, once again verifying the positive role of the institutional investor clique on the tunneling behavior of the listed company.Table 6
Institutional investor clique’s robustness test on tunneling behavior.
Variable names(1)(2)Appropriation of fundsRelated party transactionsInstitutional investor clique’s share ratio−0.0010∗∗∗−0.0024∗∗∗(−6.4471)(−3.1366)Company size−0.0306∗∗∗−0.0219(−6.4000)(−1.4755)Market value0.0310∗∗∗0.0183−6.5149−1.1645The shareholding ratio of the controlling shareholder−0.0008∗∗∗−0.0008∗(−9.7744)(−1.8813)Management shareholding−0.0003∗∗∗−0.0020∗∗∗(−4.5749)(−6.7457)Separation of two rights−0.0003∗∗0.0007(−2.4420)−0.992Company age0.0006∗∗∗0.0038∗∗∗−2.6132−3.3661Board size−0.0006−0.0003(−0.7692)(−0.0833)Number of general meetings0.0034∗∗∗0.0402∗∗∗−6.8655−13.9292Nature of the firm−0.0025−0.0019(−1.3744)(−0.2060)Equity checks and balances−0.0066∗∗∗−0.0344∗∗∗(−5.2242)(−5.3760)Constant terms0.0624∗∗0.2658∗−2.3389−1.8574N18,03918,039Robust standard error in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.Table 7
Robustness test of institutional investor clique centrality on tunneling behavior.
Variable namesDegree centralityBetweenness centralityCloseness centralityAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsAppropriation of fundsRelated party transactionsDegree centrality−0.0115∗∗∗−0.0222∗∗∗(−7.1409)(−4.0432)Mediation centrality−0.0041∗∗∗0.0001∗(−3.2857)(−1.7454)Close to centrality−2.7716∗∗∗−7.7477∗∗∗(−6.6617)(−5.5834)Company size−0.0264∗∗∗−0.0126−0.0264∗∗∗−0.0125−0.0276∗∗∗−0.015(−5.9180)(−0.8794)(−5.9143)(−0.8670)(−6.1095)(−1.0513)Market value0.0279∗∗∗0.00990.0239∗∗∗0.00280.0307∗∗∗0.0202−6.168−0.6619−5.6175−0.1858−6.5068−1.3152Shareholding by controlling shareholders−0.0008∗∗∗−0.0007∗−0.0008∗∗∗−0.0007−0.0008∗∗∗−0.0008∗(−9.4367)(−1.7029)(−9.5154)(−1.6224)(−9.8153)(−1.9568)Management shareholding−0.0002∗∗∗−0.0019∗∗∗−0.0003∗∗∗−0.0020∗∗∗−0.0001∗∗−0.0016∗∗∗(−4.1621)(−6.6195)(−4.7676)(−6.8999)(−2.0594)(−5.2019)Separation of two rights−0.0004∗∗∗0.0006−0.0004∗∗∗0.0007−0.0004∗∗∗0.0007(−2.8323)−0.832(−2.8358)−0.9111(−2.7052)−0.8939Company age0.0006∗∗∗0.0038∗∗∗0.0006∗∗∗0.0038∗∗∗0.0005∗∗0.0037∗∗∗−2.5957−3.376−2.7353−3.4017−2.4345−3.2787Board size−0.00040.0001−0.0004−0.0001−0.00040.0002(−0.5089)−0.0282(−0.5309)(−0.0148)(−0.4817)−0.0496Number of general meetings0.0030∗∗∗0.0393∗∗∗0.0031∗∗∗0.0396∗∗∗0.0030∗∗∗0.0393∗∗∗−6.1435−13.6592−6.4307−13.726−6.2415−13.661Nature of the firm−0.0017−0.0002−0.0021−0.0003−0.0019−0.0003(−0.9340)(−0.0175)(−1.1602)(−0.0316)(−1.0281)(−0.0271)Equity checks and balances−0.0086∗∗∗−0.0386∗∗∗−0.0082∗∗∗−0.0363∗∗∗−0.0073∗∗∗−0.0358∗∗∗(−6.5881)(−6.0496)(−6.3448)(−5.7003)(−5.6804)(−5.6507)Constant terms0.01890.20580.0991∗∗∗0.3902∗∗∗0.0791∗∗∗0.2872∗∗−0.6969−1.4041−3.8276−2.7989−3.0952−2.0461N180391803918008180081803918039Robust standard error in parentheses:∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.


## 6. Conclusions

Given the lack of in-depth analysis of the motivational mechanism of network cooperation and its corporate governance effects in previous studies, this article adopts the game theory method and the Louvain algorithm to examine the impact of institutional investor clique on the tunneling behavior of the controlling shareholder of the listed company and provides a certain theoretical and empirical basis for the interdisciplinary research of network algorithms and finance. It also highlights the possibility of utilizing machine learning algorithms in future financial research. The conclusions are as follows:(1) Institutional investors can cooperate to participate in the governance of the listed companies. When institutional investors adopt a brutal strategy in repetitive market games, the “learning curve effect” caused by an increasing shareholding variety and the “scale effect” caused by an increasing shareholding ratio under cooperation is conducive to lowering institutional investor’s respective costs of corporate governance, making the total benefits of cooperation greater than noncooperation and thus motivating institutional investors to act jointly in corporate governance. (2) The institutional investor clique has a significant negative correlation with the tunneling behavior of the controlling shareholders. The higher the shareholding ratio and centrality is, the more investors and active information sharing within the institutional investor clique, and thus, the stronger its inhibitory effect.In light of these findings, this article suggests the following policy implications: (1) Create a system to encourage institutional investors to participate in corporate governance. By improving the relevant laws and regulations governing institutional shareholder voting and cultivating some cooperative platforms and more institutional investors will jointly participate in corporate governance. (2) By well using the information transmission and sharing role of the investor network, the supervision cost of the listed companies will be reduced, and thereby a robust external governance mechanism will be established.



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