Fraud Transmission Mechanisms within Community: Peer Concealing and Hinting among Chinese Listed Corporations

Abstract

We explored the transmission mechanisms of corporate fraud and its punishments within social network communities. Using fraud triangle theory and trust triangle theory, we hypothesize four transmitting channels of how fraud commission and detection are affected by peers’ fraud and punishment. Based on Chinese listed corporations from 2008 to 2018, we first construct and detect interlocked social network communities with a community-detecting algorithm, and then examine hypotheses using a bivariate probit model with partial observability. Our findings indicate that peer-concealing and -hinting effects exist within social network communities. The peer-concealing effect decreases the likelihood of being detected when committing fraud, for those with more and closer fraudulent peers. The peer-hinting effect increases the likelihood of being detected when committing fraud, for those with more and closer punished peers. There is no evidence to support peer-contagion and vicarious-punishment effects. Thus, an improved understanding of the transmission mechanism of corporate fraud commission and detection within communities is provided to prevent and detect corporate fraud. In addition, stakeholders and regulators should be aware of the deviant subculture and social distancing in social network communities.

摘要

本文 探究了公司违法违规行为及其惩处在社会关系社群中的传播机制。基于舞弊三角理论和信任三角理论，本文假设了同伴的违法违规行为及其惩处如何影响目标公司违法违规行为的实施和检举。基于中国上市公司在 2008–2018 年的数据，本文利用社群发现算法在连锁董事网络中构造了上市公司社会关系社群，并利用部分可观测的二值选择模型进行了实证检验。实证检验结果表明，在上市公司社会关系社群中，违法违规行为具有同伴遮掩效应、惩处具有同伴揭示效应，但未发现违法违规行为的同伴学习效应或惩处的替代惩罚效应：同伴遮掩效应意味着，对于拥有更多且更亲密的违法违规同伴时，目标公司实施违法违规行为后被检举的概率较低；同伴揭示效应意味着，对于拥有更多且更亲密的被惩处的同伴时，目标公司在实施违法违规行为后被检举的概率较高。因此，本文深化了对公司违法违规行为如何在社会网络社群中传播的理解，为利益相关者及监管部门提供了参考。

Introduction

Corporate fraud poses a significant threat to the economy (Zhang, Xu, Chen, & Jing, 2020) and society (Holzman, Miller, & Williams, 2021), and is a worldwide concern (Gabbioneta, Greenwood, Mazzola, & Minoja, 2013; Li, Shi, Connelly, Yi, & Qin, 2022; Ren, Zhong, & Wan, 2021; Zhong, Ren, & Song, 2021). Although Chinese corporations endeavor to pursue international governance standards, legislation and enforcement are still lacking (Liu, Heugens, Wijen, & van Essen, 2022). In emerging markets such as China, characterized by the development of internal governance and external regulation, social networks are widely recognized as an important factor influencing fraud (Free & Murphy, 2015; Kuang & Lee, 2017). Within the entire social network, the social network community is argued to play a more influential role in the process of fraud (Jaspers, 2020). The social network community of corporations refers to dense subgraphs based on social connections (Bao, Zhao, Tian, & Li, 2019), in which peers are more closely connected, interact more, and share more information (Clement, Shipilov, & Galunic, 2018).

However, few agreements have been reached on how fraud transmits within a social network community. Some argue that fraud tends to be more easily committed within the core group (Suh, Sweeney, Linke, & Wall, 2020), and hardly detected within well-connected groups (Phiri & Guven-Uslu, 2019). For example, Luckin, the fast-growing coffee retailer which opened more stores than Starbucks in China within 3 years, suffered an 80% stock price cut and was required to delist after financial manipulation around RMB 22 billion was found; it is reported that Luckin COO Liu (who used to be a colleague of Luckin founders) committed this manipulation with relating firms controlled by Luckin founders, thus this manipulation seems to be previously known while acquiesced by Luckin founders. Another famous case is Kuailu, which affected 40,000 investors with losses about RMB 15.2 billion due to illegal fundraising in 2016; it is reported that Kuailu learned illegal fundraising under the name of peer-to-peer internet finance during the expedition to the founder's social relationships, and made use of the founder's friends and colleagues during its illegal fundraising. Even in the less well-known instances, like the No. 0108(2988) sentence of punishment in Beijing, fraud (issuing false invoices) is found to be taught, learned, and committed by social connections, with social connections also trying to conceal the crimes.

However, others argue that social network communities govern fraud through vicarious punishment and regulatory contagion, taking effect among industrial peers (Agarwal & Muckley, 2022; Yiu, Xu, & Wan, 2014) and social network community peers (Bao et al., 2019). Kangmei, one of the largest traditional Chinese medicine suppliers, was found guilty of financial manipulation, cumulatively about RMB 27 billion revenue (around 40% of revenue reported in the same period) and RMB 4 billion profit (around 30% of profit in the same period). Kangmei was fined RMB 2,459 million, and each of its five independent directors was fined more than RMB 123 million, which can be paid off in 3,504 years based on the average disposable income in China in 2021 (about RMB 35,100). Panic diffused quickly after this punishment, and 24 independent directors resigned for personal reasons from 23 listing firms.

Moreover, the corporate fraud transmission mechanism becomes more complicated once partial observability of the fraud process is introduced. Many existing studies draw conclusions based on the assumption that corporate fraud is fully observable (Bai, Shang, Wan, & Zhao, 2021; Bao et al., 2019), while partial observability of fraud is a considerable problem, leading to estimation bias (Cao & Zhang, 2021; Khanna, Kim, & Lu, 2015; Kuang & Lee, 2017; Wang, Winton, & Yu, 2010).

Thus, we attempt to investigate the abovementioned problems, namely, how corporate fraud and its punishment are transmitted among peer corporations within social network communities, under the assumption that fraud is partially observable. To do so, we first construct a theoretical framework that mainly applies fraud triangle and trust triangle theories. Second, based on the interlocked network of Chinese listed corporations from 2008 to 2018, we applied the Clauset–Newman–Moore (CNM) algorithm to detect social network communities following Bao et al. (2019). Third, following the most recent industry standards of assuming fraud as partially observable (Cao & Zhang, 2021; Khanna et al., 2015; Kuang & Lee, 2017; Li et al., 2022; Yiu, Wan, & Xu, 2018), we divide the fraud process into three parts (unobservable fraud commission, unobservable fraud detection, and observable fraud), and accordingly adopt a bivariate probit regression with partial observability (Cao & Zhang, 2021; Khanna et al., 2015; Kuang & Lee, 2017; Li et al., 2022; Yiu et al., 2018). Fourth, we examined peer-contagion and peer-concealing effects during the fraud commission process, and investigated vicarious-punishment and peer-hinting effects during the fraud detection process.

Following the abovementioned main studies, we divided fraud into several subtypes and tested the mechanism of each. We also tested the influence of fraudulent peer existence and scale as well as the influence of fraudulent peer proximity. Furthermore, we applied several robustness tests, including an alternative community-detection algorithm and error assumption of estimations, possible variable omission, and endogeneity.

Based on the above data and methodologies, within social network communities, we mainly find that the peer-concealing effect exists within social network communities, which decreases the likelihood of being detected after committing fraud, for those having more and closer fraudulent peers; the peer-hinting effect after punishment on peers also exists within social network communities, which increases the likelihood of being detected after committing fraud, for those having more and closer punished peers; however, we did not find evidence supporting the peer-contagion effect and vicarious-punishment effect.

We make several contributions to the literature, including the aforementioned studies and findings. First, we enrich the literature on corporate fraud and governance by testing how corporate fraud is transmitted within a social network community. Second, we examine the vicarious-punishment theory under specific conditions (Yiu et al., 2014, 2018), and extend the defection against alliance partners’ misbehavior to a more specific reaction (Lee & Zhong, 2020a), namely the peer-hinting effect. Third, we not only verify the effectiveness of the fraud triangle theory and trust triangle theory in developing countries (Cao & Zhang, 2021; Gu, Hasan, & Lu, 2022), but also explain how their pillars possibly interact. Fourth, we contribute to the social network literature by investigating how closely connected social network subgroups, namely communities, react to fraud and punishment (Bao et al., 2019). We also verify the applicability of the CNM and GN algorithms to social networks in emerging markets. Finally, we also provide insights into practical implications, emphasizing the focus of attention on fraudulent social connectors due to the peer-concealing effect, and the appeal of utilizing vicarious punishment in social network communities due to the peer-hinting effect.

Theoretical Background and Hypotheses Development

Fraud Triangle Theory and Trust Triangle Theory

The fraud triangle theory and trust triangle theory are two of the most widely accepted theories for investigating how fraud is generated. Schuchter and Levi (2016, 2019) revisited and extended the fraud triangle theory based on several interviews. Huang, Lin, Chiu, and Yen (2017) attempted to identify financial statement factors using the fraud triangle theory, and Cao and Zhang (2021) constructed a fraud triangle to study a Chinese case. The trust triangle is a rather new concept (Dupont & Karpoff, 2020) and has drawn much attention (Cumming, Hornuf, Karami, & Schweizer, 2021; Gu et al., 2022; Karpoff, 2021).

Fraud commission and fraud triangle theory

Fraud triangle theory is constructed of three pillars (Schnatterly, Gangloff, & Tuschke, 2018): (1) Incentive, also called ‘pressure’, refers to the benefit of fraud. The main incentives are divided into two categories (Amiram, Bozanic, Cox, Dupont, Karpoff, & Sloan, 2018): capital-market incentives, which include manipulating stock prices (Call, Kedia, & Rajgopal, 2016) or insider trading (Peng & Röell, 2008), and contract incentives, such as manipulating accounting reports (Burns & Kedia, 2006; Dechow, Sloan, & Sweeney, 1995). (2) Opportunity refers to the ability to commit fraud with the expectation of avoiding detection. Opportunity is also divided into two dimensions: traditional internal governance, such as directors (Kong, Xiang, Zhang, & Lu, 2019; Kuang & Lee, 2017) and auditors (Krishnan & Peytcheva, 2019); the other is external governance, including delisting pressure (Zhou, Zhang, Yang, Su, & An, 2018) and analyst coverage (Ren et al., 2021). (3) Rationalization refers to moral justification after committing fraud. Rationalization is argued to be the most common pillar (Schuchter & Levi, 2016, 2019) and is mainly determined by managers’ characteristics (Huang et al., 2017), such as overconfidence (Cao & Zhang, 2021).

Fraud detection and trust triangle theory

Trust triangle theory is recently being put forward along with fraud triangle theory, which aims to answer how trust is built or how fraud is eliminated (Dupont & Karpoff, 2020). Trust is thought to be the opposite of fraud, which is essential for both corporations (Amiram, Huang, & Rajgopal, 2020; Bao et al., 2019) and markets (Cole, Johan, & Schweizer, 2021). The trust triangle is also built upon three factors (Dupont & Karpoff, 2020; Karpoff, 2021): (1) Third-party enforcement refers to laws and regulations. (2) Second-party enforcement refers to societal judgments. For example, social connections imply more reputational capital and, thus, suppress fraud (Cumming et al., 2021). (3) First-party enforcement refers to individual demand for dignity. For example, directors with higher career concerns were found to be more related to corporate misconduct (Zaman, Atawnah, Baghdadi, & Liu, 2021).

Social–Network–Community Transmission of Peers’ Fraud

Peer-contagion effect of social network community fraud

The peer-contagion effect refers to the spillover of fraud from one peer to another. The peer-contagion effect is found through geography (Holzman et al., 2021; Parsons, Sulaeman, & Titman, 2018), workmates (Chan, Chen, Pierce, & Snow, 2021; Dimmock, Gerken, & Graham, 2018), and social networks (Chahine, Fang, Hasan, & Mazboudi, 2021). Corporations tend to commit fraud under the influence of a deviant subculture and with the support of deviant subcultural groups as observing fraudulent behavior allows individuals to rationalize their own misconduct (Holzman et al., 2021). Corporations operating in the context of widespread fraud could view fraud as a necessary strategy (Schnatterly et al., 2018). In addition, corporations also commit fraud under the strain of maintaining social connections (e.g., to obtain support) with fraudulent but important peers in the social network community. The deviant subculture in each social network community gradually forms as the number of deviant peers increases. Once formed, deviant subcultural groups provide illicit assistance (Colvin, Cullen, & Ven, 2002; Van Akkeren & Buckby, 2017). Corporations can also learn the technical skills necessary to commit fraud as well as attendant attitudes and rationalizations in intimate social groups (Van Akkeren & Buckby, 2017).

A social network community is a densely connected group in which peers pay great attention to each other (Knoke, 2009). Prior studies have also suggested that distance and number of relationships have an impact on peer interactions (Gronum, Verreynne, & Kastelle, 2012; Kuang & Lee, 2017). Interaction with fraudulent peers facilitates information sharing between peers (Bao et al., 2019), resulting in cognitive changes among individuals, thus making the offending conduct more attractive. Thus, close relationships give corporations a greater willingness to interact with fraudulent peers, and this increased interaction strengthens social influence (Dimmock et al., 2018), making corporations more likely to be persuaded to join the fraudulent group. Interactions within a community intensify social learning between peers (Clement et al., 2018), thereby resulting in fraudulent commission learning, namely fraud contagion (Kuang & Lee, 2017; Xiao, Dong, & Zhu, 2019).

Clearly, every pillar of the fraud triangle can be observed if peers’ fraud is embedded in a social network community: incentives (by showing illegal benefits), opportunity (by offering fraudulent experience), and rationalization (by forming a deviant subculture). Therefore, we propose the following hypotheses:

Hypothesis 1 (H1): Corporations with more and closer fraudulent peers are more likely to commit fraud.

Peer-concealing effect of social network community fraud

The trust triangle is built upon second-party enforcement, which is represented by social connections (Cumming et al., 2021). Peers within the same social community have stronger ties than those outside, thus providing more social support to each other. Once these connections are infected by immorality, peers tend to assist each other by concealing fraud because consequent punishments on detected fraud not only hurt the fraudster but also spill over to the connectors (Agarwal & Muckley, 2022; Lee & Zhong, 2020a). Therefore, second-party enforcement of the trust triangle tends to collapse if more social connections are fraudulent and lead to an unethical atmosphere. More specifically, the peer-concealing effect comes from the destruction of second-party enforcement, either forced by fraudulent social connectors or encouraged by the unethical atmosphere.

On the one hand, the peer-concealing effect comes from the destruction of second-party enforcement forced by fraudulent social connectors. This peer-concealing effect on fraud detection can be attributed to empathy (van de Weijer, Leukfeldt, & Van der Zee, 2020) between closer partners. During this process, the negative emotions of concealing fraud can be buffered by social belonging (Kaakinen, Keipi, Räsänen, & Oksanen, 2018) and embeddedness (Jaspers, 2020). Another direct motivation for peer-concealing behaviors is the fear of potential reprisal, which may come either directly from fraud-hinting peers or indirectly from the community (Tolsma, Blaauw, & Te Grotenhuis, 2012; van de Weijer et al., 2020).

On the other hand, the peer-concealing effect comes from the destruction of second-party enforcement, which is encouraged by the unethical atmosphere. It is argued that the expected likelihood of reporting crime is low given that the triad (victim, advisor, and offender) know each other, according to social support theory (De Kimpe, Ponnet, Walrave, Snaphaan, Pauwels, & Hardyns, 2020) and extended social balance theory (Knoth & Ruback, 2016). Usually, a trusted friend without judgment might be consulted about whether to report fraud, and their suggestion is often accepted (De Kimpe et al., 2020). However, the presence of friendships between consultants and offenders suppresses the probability of reporting fraud (Knoth & Ruback, 2016). That is, it is more likely that consultations occur within a community where the offender, consultant, and observer are connected, while the probability of reporting fraud is suppressed because of the connectedness between the offender and consultant. Thus, the peer-concealing effect emerges.

Furthermore, according to the theory of social identity (Bruner, Boardley, & Côté, 2014; Chiu, Huang, Cheng, & Sun, 2015), peers within the same fraudulent community tend to conceal each other's fraud. Corporations gain an additional identity by committing fraud, which provides access to a small social group of fraudulent peers. According to social support theory, peers with the same fraudulent identity (i.e., from the same fraudulent community) show a higher propensity to support each other. Given the corporate fraud situation, this stronger identity-caused social support leads to a higher propensity to conceal each other.

From these arguments, we hypothesize that immorality and fraud among peers in the social network community damages the second-party enforcement of trust triangles. Moreover, according to social support theory, it is noteworthy that the difference in fraud reporting is not only made by the number, but also by the closeness of social connections (De Kimpe et al., 2020). Thus, we draw the following hypothesis, assuming that observers tend to conceal peer fraud:

Hypothesis 2 (H2): Corporations with more and closer fraudulent peers are less likely to be detected.

Social–Network–Community Transmission of Peers’ Punishment

Vicarious-punishment effect of social network community punishment

Vicarious punishment refers to the indirect deterrence effect of punishment imposed upon peers’ fraud (Yiu et al., 2014), and is also called the regulatory contagion effect (Agarwal & Muckley, 2022). Given regulatory and punishing threats, observing peers tend to respond strategically, namely, to commit less fraud in the time window of the monitoring investigation (Chan et al., 2021). Vicarious punishment has been proven between peers within the same industry (Agarwal & Muckley, 2022; Yiu et al., 2014), strategic alliances and business affiliations (Yiu et al., 2018), supply chains (Xiao et al., 2019), and social network communities (Bao et al., 2019).

Vicarious punishment informs observers that detection is ongoing and fraud is costly, thus suppressing the propensity to commit fraud (Yiu et al., 2014). This is due to the inhibitive learning effect, where the observer witnesses the punishment on fraudulent peers and thinks of punishment as a potential fraudulent cost for himself (Xiao et al., 2019; Yiu et al., 2014). Another stronger deterrence is the regulatory contagion effect, which spills the lawbreaker's negative capital market reactions over its peers (Agarwal & Muckley, 2022).

Considering information sharing in social network communities (Sytch & Tatarynowicz, 2014), it has been argued that vicarious punishment (or regulatory contagion) is also effective within the same social network community (Bao et al., 2019). Similar to vicarious punishment within the same industry (especially between following corporations and benchmark corporations, or between similar corporations) (Agarwal & Muckley, 2022; Yiu et al., 2014), punishment on fraudulent peers within the same community also produces inhibitive learning effects among other observing peers (Bao et al., 2019; Xiao et al., 2019).

In summary, we conclude that punishment for fraudulent peers in the social network community damages observers’ every pillar of the fraud triangle: incentives (by showing the cost of fraud), opportunity (by signaling the existence of regulation), and rationalization (by deterring reputation and legitimacy). Thus, we propose the following hypothesis:

Hypothesis 3 (H3): Corporations with more and closer punished peers are less likely to commit fraud.

Peer-hinting effect of social network community punishment

The trust triangle is built on third-party enforcement, which refers to laws and regulations. However, most fraud remains unreported (Knoth & Ruback, 2016), even in the cyber era (De Kimpe et al., 2020; van de Weijer, Leukfeldt, & Bernasco, 2018; van de Weijer et al., 2020), especially in the case of seemingly less serious fraud, and the wrongdoer might not be caught (Knoth & Ruback, 2016). This fact hinders the effective operation of laws and regulations, destroying the third-party enforcement of the trust triangle, leaving few hints and a low detection likelihood of corporate fraud.

The punishment of fraud signals that laws and regulations are watching (Tolsma et al., 2012), manifesting the existence and strength of third-party enforcement, thus fixing the trust triangle. The punishment of fraudsters within the social network community leads to a peer-hinting effect through two channels: one from regulators and the other from peers.

On the one hand, fraud within a community may be actively investigated by regulators, and passively and unintentionally hinted at by peers. Once a fraudster was caught and punished, the intuition of regulators was to further investigate, following the vine of social connections, especially those closest connectors. This intuition comes from possible peer conformity (Fotaki, Voudouris, Lioukas, & Zyglidopoulos, 2021; Miller, Le Breton-Miller, & Lester, 2013) and ethical spillover (Pierce & Snyder, 2008), which refers to stronger social learning among peers within the inner core of social networks, namely communities, including the inter-organizational convergence of ethics. Additionally, given the higher likelihood of being investigated, the social community, a dense social network where information flows frequently and quickly, makes it easier to identify peers’ fraud commission (Bai et al., 2021). Thus, the peer-hinting effect comes from third-party enforcement, taking advantage of better sharing information within the social network community.

On the other hand, fraud within the community may be actively and intentionally hinted at by peers. Within the cost–benefit framework (Tolsma et al., 2012; van de Weijer et al., 2020), the decision to hint at fraud depends on how laws and regulations operate. The whistleblowing triangle theory argues that three main components (pressure/incentive, opportunity, and rationalization) explain the reporting of wrongdoings (Latan, Chiappetta Jabbour, & Lopes De Sousa Jabbour, 2021; Smaili & Arroyo, 2019). Punishment for peers’ fraud strengthens pressure/incentive and opportunity to hint at peers’ fraud. Furthermore, punishment signals the seriousness of fraud and promotes the intrinsic motivation to report on any wrongdoing (Andon, Free, Jidin, Monroe, & Turner, 2018). Signaled by the punishment of the fraudulent peer, potential regulatory contagion effect haunts the community because the performance of others might be negatively affected once a fraudulent partner in the same strategic alliance is caught (Lee & Zhong, 2020b). This spillover effect of regulations is also found within similar corporate groups (Agarwal & Muckley, 2022). Due to the negative impact of the regulatory contagion effect, including threats to identity and efficiency (Lee & Zhong, 2020a), fraud might be hinted at by observers to save legitimacy (Zhang et al., 2020). Regarding the opportunity for whistleblowing, punishment shows the existence of third-party enforcement as an accessible reporting channel. Thus, the peer-hinting effect comes from peers observing third-party enforcement, boosting the whistleblowing incentive and opportunity, or by deterring the potential regulatory contagion effect.

In summary, we conclude that punishment for fraudulent peers in a social network community consolidates the trust triangle by showing the existence and strength of third-party enforcement and strengthening the trust triangle. Thus, we hypothesize that observers of peers punished by regulators tend to protect trust by hinting at peer fraud:

Hypothesis 4 (H4): Corporations with more and closer punished peers are more likely to be detected.

To summarize the above hypotheses, the general framework of this study is shown in Figure 1.

Figure 1. Theoretical framework

Research Design

Model and Estimation

A bivariate probit regression with partial observability was applied in this study, according to the literature on corporate fraud, such as Li et al. (2022), Kuang and Lee (2017), Wang et al. (2010), and Wang (2013). Moreover, the variable selection of the partially observable bivariate probit (POBi probit) model in this study was adjusted to the Chinese context based on Li et al. (2022), Kong et al. (2019), Yiu et al. (2018), and Zhang (2018), as well as the local study of Meng, Zou, and Hou (2019).

The POBi probit model was applied because of the inherent problem of partial observability of fraudulent samples (Khanna et al., 2015). That is, the commission of fraud is unobservable and only cases of fraud commission being detected can be observed. More specifically, the process of fraud can be divided into the following three phases: (1) fraud commission, when fraud is committed by a corporation and is unobservable, denoted as Commit _it; (2) fraud detection, when the regulator detects a corporation with an unobservable probability, denoted as Detect _it; and (3) observed fraud, until the regulator reports the detected fraud commission, denoted as Fraud _it. During the above process, only the final reported fraud is observed; that is, the detected fraud commission.

We denote the detected fraud commission by Fraud _it = Commit _it × Detect _it. We define Fraud _it = 1 if corporation i has been detected as committing fraud (Commit _it = 1 and Detect _it = 1) in year t. Fraud _it = 0 if it has not committed any fraud, or if it has not been detected even though it has committed fraud (Commit _it = 0 or Detect _it = 0) in year t.

To summarize and clarify the partial observability problem, following Morais, Serrasqueiro, and Ramalho (2020), the relationships among unobservable committing propensity, unobservable detection probability, and final observable fraud in this research are shown in Figure 2.

Figure 2. Partial observability problem of fraud

For each corporation i in year t, $Commit_{it}^{\rm \ast }$ and $Detect_{it}^{\rm \ast }$ denote the latent variables determining the propensity of the fraud commission Commit _it and the likelihood of detection Detect _it, respectively, as follows:

$$Commit_{it}^\ast{ \, = \,} {\boldsymbol A} \times {\boldsymbol ExCommi}{\boldsymbol t}_{it} + {\boldsymbol C} \times {\boldsymbol ExShar}{\boldsymbol e}_{{\boldsymbol it}} + \mu _{it}, \;$$

$$Detect_{it}^\ast{ \, = \,} {\boldsymbol B} \times {\boldsymbol ExDetec}{\boldsymbol t}_{{\boldsymbol it}} + {\boldsymbol D} \times {\boldsymbol ExShar}{\boldsymbol e}_{{\boldsymbol it}} + \vartheta _{it}.$$

Here, ExCommit_it is a vector of ex ante variables that explains the propensity of fraud commission, ExDetect_it is a vector of ex ante variables that explains the possibility of being detected, and ExShare_it is a vector of ex ante variables that influence both the propensity of fraud commission and the possibility of being detected. A, B, C, and D are the coefficient vectors. μ _it and $\vartheta _{it}$ are zero-mean disturbances with a bivariate normal distribution whose deviation is equal to 1, and their correlation is denoted as ρ.

The rule for defining $Commit_{it}^\ast$ and Commit _it is as follows: Commit _it = 1 if $Commit_{it}^\ast > 0$, and Commit _it = 0 if $Commit_{it}^\ast \le 0$. The rules defining $Detect_{it}^\ast$ and Detect _it were similar. The definitions are as follows.

$$Commit_{it} = \left\{{\matrix{ {0, \;} & {\vert Commit_{it}^\ast \le 0} \cr {1, \;} & {\vert Commit_{it}^\ast > 0} \cr } } \right.$$

$$Detect_{it} = \left\{{\matrix{ {0, \;} & {\vert Detect_{it}^\ast \le 0} \cr {1, \;} & {\vert Detect_{it}^\ast > 0} \cr } } \right.$$

Accordingly, the empirical model for Fraud _it can be written as follows:

$$P( {Fraud_{it} = 1} ) = P( {Commit_{it}Detect_{it} = 1} ) = P( {Commit_{it}^\ast > 0, \;Detect_{it}^\ast > 0} ) $$

$$P( {Fraud_{it} = 0} ) = P( {Commit_{it}Detect_{it} = 0} ) = 1-P( {Commit_{it}^\ast > 0, \;Detect_{it}^\ast > 0} ) $$

Here, $P\{ {Commit_{it}^\ast > 0, \;Detect_{it}^\ast > 0} \} = \phi ( {{\boldsymbol A} \times {\boldsymbol ExCommi}{\boldsymbol t}_{{\boldsymbol it}}, \;{\boldsymbol B} \times {\boldsymbol ExDetec}{\boldsymbol t}_{{\boldsymbol it}}, \;\rho } )$, where ϕ denotes the bivariate standard normal cumulative distribution function and ρ denotes the correlation between commission and detection of fraud.

Thus, the log-likelihood function for the POBi probit model is

$$L( {A_{it}, \;B_{it}, \;\rho } ) = \sum log[ {P( {Fraud_{it} = 1} ) } ] + \sum log[ {P( {Fraud_{it} = 0} ) } ] .$$

As per Khanna et al. (2015), maximum likelihood estimation was applied, and industrial-clustered robust standard errors were introduced to account for any possibility of industrial correlations.

However, the POBi probit model may not converge if it includes too many variables (Yiu et al., 2018; Zhang, 2018). Thus, the selection of ex ante variables is one of the most difficult parts of applying the POBi probit model, and different variables are included in different studies. We initially set the POBi probit model based mainly on Khanna et al. (2015) and then adjusted the control variables for Chinese features according to recent studies on Chinese corporate fraud (Kong et al., 2019; Meng et al., 2019; Yiu et al., 2018; Zhou et al., 2018). For example, government ownership was introduced following Kong et al. (2019), Yiu et al. (2018), and Zhang (2018), and shareholding centrality was introduced following Meng et al. (2019).

Dependent Variable: Corporate Fraud

According to existing empirical studies on corporate fraud (Khanna et al., 2015; Yiu et al., 2018; Zhang, 2018), the fraud occurrence of Chinese listed corporates is applied as a proxy for detected fraud in this study. However, corporate fraud has several definitions (Amiram et al., 2018), and a comprehensive database is needed to alleviate sample selection bias. Thus, we introduce the local corporate fraud recorded by the China Regulatory Enforcement Research Database (CRSR) in the China Stock Market and Accounting Research Database (CSMAR), according to existing studies of fraud in China, such as Zhang (2018) and Yiu et al. (2018). As for valuing the detected fraud variable, if listed corporate i is announced to commit fraud in year t, Fraud _it is denoted as 1; otherwise, Fraud _it is denoted as 0.

Furthermore, according to the fraud categories by Khanna et al. (2015) and local research (Meng et al., 2019), fraud can be divided into three categories (as shown in Table 1): informative (Info _it), operating (Oprt _it), and executive fraud (Exct _it). The definitions of fraud type, ID, and category are listed in Table 1.

Table 1. Fraud type subdivision

Notes: The major type is subdivided following Kong et al. (2019). CSRC Type and Type ID come from CSRC and CSMAR.

The fraud data collected by CRSR are based on each corporate fraud announcement officially released by Chinese securities and exchange regulators (the China Securities Regulatory Commission [CSRC], the Shanghai Stock Exchange [CSHSE], and the Shenzhen Stock Exchange [CSZSE], respectively). Specifically, CSBC defines announced fraud as illegal acts (violations) in information disclosure, corporate operations, or executive behaviors that are publicly condemned, criticized, or punished by the CSRC, law and enforcement authorities, or stock exchanges (Chen, Cumming, Hou, & Lee, 2016).

Independent Variable: Fraud and Punishment in an Interlocked Community

To measure the social network of corporations, an interlocked network of chained directors was constructed following mainstream corporate social network studies (Bao et al., 2019; Chahine et al., 2021; El-Khatib, Fogel, & Jandik, 2015; Kuang & Lee, 2017). Two corporations are interlocked if they share the same director in a specific year, and this interlock is assumed to exist until one of the nodes dies (El-Khatib et al., 2015; Tao, Li, Wu, Zhang, & Zhu, 2019). Subsequently, both network centrality and communities were calculated based on the interlock network panel, following Bao et al. (2019).

Interlocked community

Following Bao et al. (2019), the fast greedy algorithm was applied to detect communities based on an interlocked network. The algorithm proposed by Clauset, Newman, and Moore (2004) is one of the most accepted community-detection algorithms based on optimization and is called the CNM algorithm (Fortunato & Hric, 2016). The CNM algorithm is a hierarchical agglomeration algorithm for community detection, whose running time on a network with n nodes and m edges is O(mdlog n), where d denotes the depth of the dendrogram (Clauset et al., 2004). Because the social network of interlocked directors is sparse and hierarchical, the CNM algorithm performs even better. The insight behind the CNM algorithm is that a community is detected when the influence of adding a new node diminishes below a certain threshold.

Peer contagion and peer concealing: Fraud within the interlocked community

To capture potential peer contagion and peer concealing within the social network community, we measured using the number of fraudulent nodes within interlock communities weighted by their social distance (denoted as CommunityFraud _it) after community detection. Weighted community fraud (CommunityFraud _it) is used as the proximity of peer contagion when testing fraud commission (H1) and as the proximity of peer concealing when testing fraud detection (H2).

Referring to Bao et al. (2019) and Chan et al. (2021), we first replaced the punished node number used by Bao et al. (2019) with fraudulent node numbers. Bao et al. (2019) measured the vicarious punishment within interlocked network communities with the number of punished nodes in the community; the operation of counting fraudulent node numbers in this step is similar to that of Chan et al. (2021), who measured the peer-contagion effect considering theft count.

We then developed our measure further by introducing social distance, motivated by Xiong, Ouyang, Tong, and Zhang (2021), who emphasized the importance of proximity in corporate fraud studies and found a negative relationship between geographic proximity and corporate fraud. The rationale behind introducing social distance is that a closer relationship might be a critical requirement of peer contagion (Chan et al., 2021), because a closer relationship might bring more loyalty which is argued to be a critical requirement of fraud conspiracy (Khanna et al., 2015).

Generally, CommunityFraud _it is calculated as the number of fraudulent nodes within the community weighted by the social distance between the observing corporation and each fraudulent peer. The calculation is as follows:

$$CommunityFraud_{it} = \mathop \sum \limits_j \displaystyle{{Fraud_{\,jt}} \over {ShortestPathLength_{ijt}}}{\rm , \;}$$

where i denotes the target node, j denotes the fraudulent node of the same community as node i, and t is the year. Fraud _jt denotes whether node j is detected as committing fraud in year t. ShortestPathLength _ijt denotes the length of the shortest path between node i and node j in year t. By introducing social distance (ShortestPathLength _ijt), this weighted fraud measures the peer-contagion effect between corporations more precisely by hinting at the fact that influence diminishes when nodes are more remote.

Vicarious punishment and peer hinting: Punishment within the interlocked community

Similar to the measures of peer contagion and peer concealing, vicarious punishment and peer hinting are measured by the punishment number within the community weighted by the distance between a specific corporation and the punished corporation, denoted as CommunityPunish _it. Weighted community punishment (CommunityPunish _it) is used as the proximity of vicarious punishment when testing fraud commission (H3) and is used as the proximity of peer hinting when testing fraud detection (H4).

Weighted community punishment (CommunityPunish _it) also refers to Bao et al. (2019), Chan et al. (2021), and Xiong et al. (2021), while we introduce social distance to weight the influences of punished peers. The rationale behind this is also alike: individuals learn the cost of committing fraud from a larger number of punished peers, which results in vicarious punishment. Proximity lowers information acquisition costs, improves governance efficiency (Xiong et al., 2021), and facilitates the social learning of punishment.

The calculation is as follows.

$$CommunityPunish_{it} = \mathop \sum \limits_j \displaystyle{{Punish_{\,jt}} \over {ShortestPathLength_{ijt}}}, \;$$

where i denotes the target node, j is the punished node of the same community as node i, t is the year. Punish _jt denotes whether node j has been punished, as mentioned above. ShortestPathLength _ijt denotes the length of the shortest path between nodes i and node j in year t.

Control Variables for Estimating Latent Variables

The POBi probit model requires two sets of variables, one for modelling the fraud commission and the other for estimating the fraud detection equations. According to Khanna et al. (2015), Yiu et al. (2018), and Zhang (2018), and the local study of Meng et al. (2019), three sets of control variables are divided into (1) ex ante factors of both commission and detection, (2) ex ante factors of fraud commission propensity, and (3) ex ante factors of fraud detection likelihood.

The first set of sharing variables considers punishment directly on the observing individual, its centrality within the interlocked director network, and the financial information that is open to both the insider and the public, such as stock price volatility and turnover. The second set of commission variables considers private information related to the internal characteristics of corporations, such as tenure, age, and gender of the CEO. The third set of detection variables considers monitoring factors, such as the size and independence of the director board.

Ex ante factors of both committing and the detecting processes

The first set sharing variables considers three parts of potential factors:

The first part is punishment directly for the individual. According to previous research (Gong, Huang, Wu, Tian, & Li, 2021), punishment refers to whether a corporation has been punished by securities regulators. Punishment is denoted as Punish _it, and is set as 1 if corporation i has been punished in year t. Punishment is controlled because it directly suppresses the propensity to commit fraud, and a punished corporation draws more attention from both stakeholders and regulators (Wang, Ashton, & Jaafar, 2019a), thus it is more likely to be detected. Another widely accepted measure of punishment is the penalty amount (Yiu et al., 2014; Zhang et al., 2020). However, considering the small sample size of the penalty, too many zero outcomes might lead to a Poisson distribution with a bias of the zero-inflated Poisson distribution (Greene, 1994).

The second part is social network capital. Social network capital influences fraudulent activity by lowering coordination costs (Bao et al., 2019) and concealing fraudulent activity (Khanna et al., 2015). The interlocked network centrality is measured using a more comprehensive index than the simple eigenvector used by Bao et al. (2019). A comprehensive index (NetAvgPCAStd_it) was constructed following the methods described by El-Khatib et al. (2015) and Tao et al. (2019). First, based on the interlocked network, four network centralities of directors were calculated: betweenness, closeness, degree, and eigenvector. Second, each corporate centrality was measured by averaging the corresponding centralities of its directors. Third, an initial comprehensive index is constructed using principal component analysis (PCA) with four corporate network centralities. Finally, the final comprehensive index was calculated with min–max scaling, using the initial comprehensive index to maintain comparability.

The third part of the sharing variables is public information on a corporation's finances and capital market, referring to Meng et al. (2019). For corporations, pressure from internal finances and outside capital is one of the main reasons for committing fraud. For monitors, information accessibility comes first, and then abnormal information draws attention. This assumption of information accessibility is the main difference between this study and Khanna et al. (2015).

(1) Corporation size (lnAsset), which is measured by assets in logarithmic form, is considered negatively related to a corporation's incentives because larger corporations face heightened monitoring and public attention (Kong et al., 2019; Yiu et al., 2018; Zhang, 2018). (2) Corporation performance, which is measured by the return on assets (ROA), and its effect is still unclear as to whether it has a positive or negative effect due to the contrary results of Dechow, Ge, Larson, and Sloan (2011) and Khanna et al. (2015). (3) Corporation leverage (Leverage), which is measured by debt on assets, is believed to be an important fraud-inducing factor (Zhang, 2018). (4) Corporation growth (Growth), which is measured by sales growth, is a controlling variable because corporations with higher growth can attract more attention from regulators and investors (Wang, Ashton, & Jaafar, 2019b). (5) State ownership (SOE), which is a dummy variable that equals 1 if a corporation is controlled by the state and 0 otherwise. SOE draws a lot of research attention; some have concluded that SOE weakens monitoring (Wang et al., 2019b; Yiu et al., 2018), and has a lower enforcement incidence (Hou & Moore, 2010), while others argue that SOEs are less likely to be involved in fraud such as bribes (Shaheer, Yi, Li, & Chen, 2019). (6) Tobin's Q (TobinQ) was measured using the well-known corporate value index Tobin's Q (Yiu et al., 2018; Zhang, 2018). (7) Stock returns, which are measured by earnings per share (EPS), are regulators that may trigger investigations once a manager manipulates financial statements to mislead investors (Wang et al., 2019b). (8) Stock price volatility (Volatility), measured by the annual average standard deviation of stock price changes, is introduced because corporations with higher stock return volatility have a greater probability of being complained of by investors because the likelihood of a large investment loss is higher (Wang et al., 2019b). (9) Stock turnover (Turnover), which is measured by annual stock turnover, is considered because a corporation with a higher turnover tends to draw more publicity, which may raise its litigation risk (Zhou et al., 2018).

Considering the Chinese context, this study includes political connections, as several studies have pointed out, which is a representative Chinese characteristic that influences corporate fraud and detection. According to a recent study by Kong et al. (2019), political connections are a considerable factor that suppresses the incidence of fraud. Thus, political connection is included as a dummy variable in this study, denoted as PC, and it is set to 1 if there is any political connection and 0 otherwise.

Industry average performance (EPSIndAve) is included to control for fixed effects instead of the other 19 and 7 yearly industrial dummy variables, because too many variables may prevent the POBi probit model estimation from converging (Yiu et al., 2018; Zhang, 2018). EPSIndAve was measured as the annual average EPS per industry.

Ex ante factors of fraud commission propensity

Referring to the local study of Meng et al. (2019), the characteristics of the CEO constitute this part of the fraud commission propensity control variables. This study applies CEO characteristics as the ex ante factor of fraud commission propensity because these characteristics are more private information than financial reports and capital market indexes. When considering fraud commission and detection, private information plays a larger role, while monitors and investors can observe financial information.

(1) CEO tenure (CEOTenure) is included, based on O'Reilly, Doerr, and Chatman (2018), who showed that CEO tenure is related to the number and duration of lawsuits. (2) The CEO's age (CEOAge) was considered according to Conyon and He (2016). (3) Gender of CEO (CEOMale), which is measured by a dummy variable (equal to 1 if the CEO is male and 0 otherwise), is introduced based on Liu (2021) and Zhou et al. (2018). (4) Shareholding of CEO (lnCEOShare), which is measured by the logarithmic form of CEO shareholdings, is considered an important equity-based incentive to commit fraud (Kong et al., 2019; Yiu et al., 2018). (5) CEO duality, in which the CEO is also the chairman of the board (Duality), which is measured by a dummy variable (equal to 1 if the CEO is the board chairman at the same time and 0 otherwise), is widely accepted as enhancing the CEO's controlling power in his corporation, allowing more managerial discretion and impeding effective monitoring (Zhang, 2018). (6) Shareholding centrality (Shrcr1), measured by the percentage of shares held by the largest shareholder, is considered based on Conyon and He (2016) and Zhou et al. (2018).

Ex ante factors of fraud detection likelihood

Referring to Khanna et al. (2015) and Meng et al. (2019), the monitoring factors are mainly considered among the detecting control variables, including five control variables related to internal monitoring and two control variables related to external monitoring.

(1) The size of the director board (lnDrct), measured by the logarithmic form of director board size, is believed to influence fraud detection (Hass, Tarsalewska, & Zhan, 2016; Wu, Johan, & Rui, 2016; Zhang, 2018). (2) The independence of the director board (IndDrctRatio), which is measured by the ratio of independent directors, is widely accepted to detect fraud (Yiu et al., 2018; Zhou et al., 2018). (3) The frequency of meetings held by the director board (DBM), which is measured by the number of board meetings held in a year, is considered to reflect internal monitoring effectiveness (Wang et al., 2019b). (4) The number of auditors (AuditNo), which is measured by the number of auditors, is believed to have a significant effect on corporate fraud detection (Zhang, 2018). (5) Qualification of auditors (BigFour), which is measured by whether the auditor is one of the Big Four internationally known accounting corporations (PwC, DTT, KPMG, and EY); if the auditor is one of the Big Four, BigFour = 1, otherwise, BigFour = 0. BigFour is included as external auditing is believed to benefit the detection of corporate fraud (Zhou et al., 2018). (6) Analyst coverage (Analyst), which is measured by the number of analysts following it, is considered because security analysts scrutinize a corporation's financial disclosure (Zhang, 2018) and thus help detect corporate fraud. (7) Institutional ownership (InstOwn), measured by the ratio of institutional shareholding, is believed to effectively monitor a corporation's management (Wu et al., 2016).

Data and Sample

Primary data were obtained from the CSMAR database, which is a resource for several relevant studies (Conyon & He, 2016; El-Khatib et al., 2015; Kong et al., 2019; Tao et al., 2019; Yiu et al., 2018; Zhang, 2018; Zhou et al., 2018). The data used in this study were from A-share corporations listed on the CSHSE and CSZSE from 2008 to 2018. After removing missing data and winsorization by 1% at both tails, a sample of 15,610 corporation-year observations was obtained. The descriptive statistics are presented in Table 2.

Table 2. Summary statistics

The sample started in 2008 for two main reasons: (1) China's share structure reform around 2006 significantly changed the reporting of some accounting data. Thus, some financial indicators are not easily comparable with those prior to the reform (Zhou et al., 2018); (2) the Chinese property law reform around 2007 also significantly influenced corporate fraud (Kong et al., 2019). Additionally, the 2008 global crisis was another considerable event that caused structural changes.

Table 2 presents a summary of our sample. Chinese listed corporations are found to commit fraud 4,399 times (28.2% of the total observations), while they are punished 3,348 times (21.5% of the total observations). As a result, around 76.1% of fraud was punished, and the reason for 23.9% away from 100% might be twofold: on the one hand, serial fraudulent incidences were punished together; on the other hand, some cases of fraud might slip from detection and punishment.

After dividing fraud into categories, 20.6% of the observations are announced for informative fraud, 18.2% observations are announced for operating fraud, and 6.7% observations are announced for executive fraud.

Moreover, the most frequent fraud subtypes are classified as operating fraud, the most frequent subtype being P2599 (22.1%), which is other operating fraud (besides listing, capital, unauthorized fund use, embezzlement, and illegal guarantees). Except for the unobserved subtype in our sample (P2508, capital fraud), the least frequent subtype was P2507 (0.05%), which is listing fraud.

If we turn our attention to the social network community defined by the interlocked director network based on the CNM algorithm, there are 1,194 nodes on average in each community, and 1,883 nodes in the largest community. There are 344 fraudulent peers on average in each community and 535 peers in the community with most nodes committing fraud. There were 255 punished peers on average in each community and 385 peers in the community, with most of the nodes being punished.

Empirical Analysis

Hypotheses 1–4 are tested in the main results of the baseline models, while the sub-hypotheses are tested in the further analysis section. The baseline models considered the total effects of weighted community fraud and weighted community punishment. Further analyses divide these possible factors and separately test their effects (e.g., certain types of fraud and punishment, existence and number of community fraud, and punishment).

Main Results of Baseline Models

Table 3 presents the results of fraud commission and fraud detection estimated using the POBi probit model. The results of fraud commission are shown in Models (1)–(3), and those of fraud detection are shown in Models (4)–(6). Models (3) and (6) are the whole models, Models (2) and (5) exclude fixed effects of industry and year, and Models (1) and (4) further exclude constants.

Table 3. Main results of fraud commission and detection

Notes: [1] *, **, and *** denote significant at a confidence level of 10, 5, and 1%. [2] t-value in parentheses. [3] Fixed effect of corporation is considered. [4] FE denotes whether includes fixed effects of industry and year. [5] Cons denote whether include constants. [6] Independent and control variables lag one period.

The main results listed in Table 3 are presented in Figure 3.

Figure 3. Main results of baseline models

Results about fraud commission

Models (1), (2), and (3) report the results for the fraud committing process. Model (1) considers community fraud and community punishment, as well as control variables, but excludes fixed effects (of industry and year) and constants. Model (2) introduces the fixed effects of industry and year based on Model (1). Model (3) introduces constants based on Model (2).

According to the results of Models (1)–(3) in Table 3, the coefficients of CommunityFraud _it and CommunityPunish _it are not statistically significant in Models (1)–(3); namely, no evidence supporting H1 or H3 is found. Thus, we cannot provide direct evidence of either the peer-contagion effect or the vicarious-punishment effect.

The result of no peer-contagion effect differs from the contagion effects argued by Kuang and Lee (2017) and Chahine et al. (2021). The reason might be the different measurement: Kuang and Lee (2017) prove the fraud contagion effect by measuring the number of connections to fraudulent corporations; Chahine et al. (2021) use the F-Score, which is calculated by several CEO characteristics, while we considered not only the number but also the distance between the connections.

The result of no vicarious-punishment effect differs from that of Yiu et al. (2014), who found vicarious punishment within an industry. The reason might be the different samples and the assumption of fraud observability. Yiu et al. (2014) assume fraud to be fully observable and apply conditional logit regression based on Chinese listing corporations from 2002 to 2008, while we assume fraud to be partially observable and apply a bivariate probit model with partial observability based on Chinese listing corporations from 2008 to 2017.

Control variables in Models (1)–(3). Punish _it, EPS _it, EstDrtn _it, ListDrtn _it, and CEOTenure _it were statistically significant and positive. These results show that punishment, financial market profitability, establishment duration, listing duration, and CEO tenure induce corporate fraud. Meanwhile, ROA _it, SOE _it, and Shrcr1_it were statistically significant and negative. These results indicate that accounting profitability, state ownership, and shareholding centrality suppress corporate fraud.

Results about fraud detection

Models (4), (5), and (6) report the results of fraud detection. Model (4) considers community fraud and community punishment, as well as control variables, but excludes fixed effects (of industry and year) and constants. Model (5) introduces the fixed effects of industry and year based on Model (4). Model (6) introduces constants based on Model (5).

According to the results of Models (5) and (6) in Table 3, CommunityFraud _it and CommunityPunish _it are both statistically significant with fraud detection, where the coefficient of CommunityFraud _it is negative, while coefficients of CommunityPunish _it are positive. In other words, the peer-concealing effect (H2) and peer-hinting effect (H4) were proved. To be more specific:

A peer-concealing effect is found, according to the statistically significant and negative coefficients of CommunityFraud _it in Models (5) and (6). Though CommunityFraud _it is found to be insignificant in Model (4), once considering the fixed effects of industry and year, CommunityFraud _it becomes statistically significant in Models (5) and (6), at −0.0139 and −0.0140 at the 5% confidence level, respectively. These results indicate that, with more and closer fraudulent peers, fraud is less likely to be detected. The result of finding a peer-concealing effect differs from the conclusion of Kuang and Lee (2017) that directors’ connections to fraudulent corporations increase the likelihood of being detected. The reason for this is twofold: (1) concealing may be involuntary. That is, although relationships within the community are stronger than those outside the community, information is still partial and may not hint at seriousness. (2) Concealing may be voluntary. Given a less serious fraud, it may be unworthy of the time spent summoning the police, or the small probability that the offenders will be caught and the lost benefits returned, peers tend to protect friends, and the peer-concealing effect comes into being (Knoth & Ruback, 2016). Moreover, the additional privacy led by closer relationships balances the governance effectiveness and efficiency of norms and institutions and augments the peer-concealing effect (Hullenaar & Ruback, 2021).

The peer-hinting effect is found according to the statistically significant and positive coefficients of CommunityPunish _it in Models (5) and (6). Similar to CommunityFraud _it, CommunityPunish _it is insignificant in Model (4) but becomes significant and positive in Models (5) and (6), at 0.0186 and 0.0186 at the 5% confidence level, respectively. These results indicate that fraud is more likely to be detected with more and closer punished peers. The peer-hinting effect is found when a greater number and more closely connected peers are punished, which partly supports relational governance in the vicarious-punishment theory by Yiu et al. (2018). The reason is threefold: (1) for involuntary concealing, punishment hints at committing fraud, and peers informed by this information may realize that fraud is being committed. (2) For voluntary concealing, punishment hints at the seriousness of fraud, and peers who have this information may realize the importance of involving regulators. (3) For regulators, more connected or more closely connected peers would face more suspicion and inspection.

The existence of both peer-concealing effect of community fraud and peer-hinting effect of community punishment extends the conclusion of Gu et al. (2022), arguing a possible substitute between legal and cultural forces in disciplining misconduct in emerging markets: fraudulent cultural forces tend to conceal fraud, while legal forces rebuild the moral orientation through cultural force.

Control variables of Models (4)–(6) in Table 3. Punish _it, DrctAge _it, MDB _it, and MSH _it were statistically significant and negative. These results show that punishment, age of the director or board chairman, meetings of the director board, and meetings of shareholders facilitate corporate detection. Meanwhile, lnAsset _it, ROA _it, SOE _it, ListDrtn _it, Big4_it, and Analyst _it were statistically significant and negative. These results show that asset scale, profitability, state ownership, listing duration, auditing from the Big Four, and analyst following hinder corporate detection.

Marginal effect test

Regarding the marginal effects of CmntCNMCommit _it and CmntCNMPunish _it on fraud commission propensity and detection likelihood, we ran an average marginal effect test after estimating the whole-model regression set as Models (3) and (6) in Table 3. The results are presented in Table 4.

Table 4. Results of the average marginal effect test on baseline models

Notes: [1] *, ** and *** denote significant at confidence level of 10%, 5% and 1%. [2] Average marginal effect reported. [3] Z-value in brackets.

According to the results of the average marginal effect test in Table 4, the conditional probability P(Detect _it = 1|Commit _it = 1) is decreased by the community-weighted fraud CmntCNMCommit _it by −0.0060 at a 1% significance level. This result shows that, given having committed fraud, each additional social-distance-weighted fraudulent peer decreases the likelihood of being detected by 0.60% on average. Thus, this result supports the peer-concealing effect hypothesis (H2) and gives an average marginal effect of 0.60%.

Meanwhile, conditional probability P(Detect _it = 1|Commit _it = 1) is promoted by the community-weighted punishment CmntCNMPunish _it with 0.0083 at the 1% significance level. This result shows that, given having committed fraud, each additional social-distance-weighted punished peer increases the likelihood of being detected by 0.83% on average. Thus, this result supports the peer-hinting effect hypothesis (H4) and provides an average marginal effect of 0.83%.

The joint probability of P(Commit _it = 1, Detect _it = 0) is promoted by the community-weighted fraud CmntCNMCommit _it with 0.0019 at a 1% significance level and is suppressed by community-weighted punishment CmntCNMPunish _it with −0.0027 at a 1% significance level. However, no evidence was found that CmntCNMCommit _it and CmntCNMPunish _it affected P(Commit _it = 1) and P(Commit _it = 1, Detect _it = 1). Taking these results together (community-weighted fraud increases the probability of committing fraud without being detected by 0.19% but may not impact the fraud commission propensity), a possible conjecture is that these results are caused by the peer-concealing effect (H1). Similarly, another possible conjecture is the peer-concealing effect of community-weighted punishment. However, we cannot provide further evidence of the peer-concealing effect; thus, it remains worthy of further research.

Further Analysis

Subtypes of corporate fraud

Different fraud types might influence committing and detecting processes, and punishment for different fraud types might also make a difference (Wang et al., 2019a). Thus, according to the fraud categories by Khanna et al. (2015) and local research (Meng et al., 2019), fraud can be divided into the following three categories: informative, operating, and executive fraud. The results are presented in Table 5. Models (1) and (2) show the results of informative fraud, Models (3) and (4) show operating fraud, and Models (5) and (6) show executive fraud.

Table 5. Main results of subtypes of fraud

Notes: [1] *^, **^, and *** denote significant at a confidence level of 10, 5, and 1%. [2] t-value in parentheses. [3] Independent and control variables lag one period. [4] CV denotes whether include control variables same as the baseline models. [5] Fixed effect of corporation is considered. [6] FE denotes whether includes fixed effects of industry and year. [7] Cons denotes whether include constants. [8] Commit _it respectively denotes informative fraud commission in model (1), operating fraud commission in model (3), and executive fraud commission in model (5). [9] Detect _it respectively denotes observed informative fraud in model (2), observed operating fraud in model (4), and observed executive fraud in model (6). [10] CommunityFraud _it respectively denotes community-weighted informative fraud commission in model (1) and (2), community-weighted operating fraud commission in model (3) and (4), and community-weighted executive fraud commission in model (5) and (6). [11] CommunityPunish _it respectively denotes community-weighted observed informative punishment in model (1) and (2), community-weighted observed operating punishment in model (3) and (4), and community-weighted observed executive punishment in model (5) and (6).)

First, the subtype Punish _it was found to be statistically significant and positive, except in Model (4), and the subtype CmntCNMPunish _it was statistically significant and positive in Models (1) and (5). Accordingly, punishment for subtype fraud is not sufficiently effective to deter any subtype fraud commission.

Second, the subtype NetAvgPnsh _it was found to be statistically significant and negative in Models (1) and (5). Thus, the vicarious-punishment effect within the entire social network is found in informative and executive fraud.

Third, the subtype NetAvgPnsh _it was found to be statistically significant and negative in Models (2) and (6). Accordingly, the peer-hinting effect within the entire social network is found in informative and executive fraud.

Finally, the subtype CmntCNMPunish _it was statistically significant and positive in Models (4) and (6). Thus, peer-hinting effects within the social community are found in operating and executive fraud.

Existence of fraud and punishment in community

The empirical tests above consider the mixing effect of both fraud (or punishment) and social connections (i.e., proximity and number of interlocked directors). Thus, this section considers the effects of fraud (and punishment) in the community and puts aside the effects of social connections. This setting tests whether fraud or punishment is transmitted within the social community.

To do so, the following three dummy variables are constructed: (1) CCCmmtDm _it represents whether fraud is committed within the social community (divided using the CNM algorithm) of firm i in year t, and equals 1 if fraud is committed; CCCmmtDm _it substitutes CmntCNMCommit _it in the baseline models. (2) CCPnshDm _it represents whether fraud is punished within the social community (divided using the CNM algorithm) of firm i in year t, and equals 1 if fraud is punished; CCPnshDM _it substitutes CmntCNMPunish _it. (3) NetPnshDm _it represents whether fraud is punished within the whole social network of corporation i in year t, and equals 1 if fraud is punished; NetPnshDm _it substitutes CmntCNMCommit _it.

The results are presented in Table 6. Model (1) represents the results of fraud commission and Model (2) represents the results of fraud detection. Except for the dummy variables, the models are set the same as those tested above, and the POBi probit estimation is applied as well.

Table 6. Main results of hierarchical measure of fraud and punishment in community

Notes: [1] *^, **^, and *** denote significant at a confidence level of 10, 5, and 1%. [2] t-value in parentheses. [3] Independent and control variables lag one period. [4] CV denotes whether include control variables same as the baseline models. [5] Fixed effect of corporation is considered. [6] FE denotes whether includes fixed effects of industry and year. [7] Cons denotes whether include constants. [8] Commit _it in model (1), (3), (5), and (7) respectively denotes whether fraud is committed within community, number of fraud commission within community, shortest path to closest fraudulent peer, and aggregate proximity effect of fraud committed within community. [9] Detect _it in model (2), (4), (6), and (8) respectively denotes whether fraud is punished within community, number of fraud punishments within network, shortest path to closest punished peer, and aggregate proximity effect of punishment within community.

According to the results of Model (1) in Table 6, the main findings were twofold. On the one hand, CCCmmtDm _it is found to be statistically significant for fraud commission, and the coefficient is negative. In other words, given any peer from the same social community committing fraud, the propensity to commit fraud is lower. This result implies the possibility of a peer-contagion effect because the effect of peer-committing fraud is indeed transmitted within the social community. However, this finding may be insufficiently robust.

On the other hand, CCPnshDm _it is found to be statistically significant for fraud commission, and the coefficient is positive. In other words, given that any fraudulent peer from the same social community is punished, the propensity to commit fraud is higher. This result implies the fact of a positive expecting return of committing fraud, namely the observers realize that fraud benefits exceed the punishment and thus tend to commit fraud. Thus, the punishment for fraud should be leveled up to set off the fraud benefit and deter the potential fraud commission. This result also implies the possibility of a vicarious punishing effect given a more severe punishment because the effect of punishment indeed transmits within the social community.

According to the results of Model (2) in Table 6, the main findings were twofold. On the one hand, CCCmmtDm _it is found to be statistically significant for fraud detection, and the coefficient is positive. In other words, given any peer from the same social community committing fraud, the likelihood of detection after committing fraud is higher. This finding contrasts with that of the baseline models, which might be due to the consideration of social distance. Social distancing indicates a different level of loyalty, which is important during the fraud process (Khanna et al., 2015). Thus, this result implies a peer-hinting effect within a social group in which information is shared, whereas loyalty is insufficient to cover each other.

On the other hand, CCPnshDm _it is found to be statistically significant for fraud commission, and the coefficient is negative. In other words, given that any fraudulent peer from the same social community is punished, the likelihood of being detected after committing fraud is lower. This finding contrasts with that of the baseline models, which might be due to the consideration of social distance. That is, punishment for fraudulent peer signals may result in detection and show the detection process, and this information may be shared within the social community. The signal alerts undetected fraudulent peers and the detection process is learned to conceal fraud. Thus, the likelihood of detection decreased.

Scale of fraud and punishment in community

After testing the existence effect of fraud (and punishment) in the social community, this section tests the scale effect. To do so, the following three variables are constructed: (1) CCCmmtNo _it represents the number of fraud commissions within the social community (divided using the CNM algorithm) of corporation i in year t; CCCmmtNo _it substitutes CmntCNMCommit _it in the baseline models. (2) CCPnshNo _it represents the number of fraud punishments within the social community (divided using the CNM algorithm) of corporation i in year t; CCPnshNo _it substitutes CmntCNMPunish _it. (3) NetPnshNo _it represents the number of fraud punishments within the entire social network of corporation i in year t; NetPnshNo _it substitutes CmntCNMCommit _it.

The results are presented in Table 6. Model (3) represents the results of fraud commission and Model (4) represents the results of fraud detection. Except for the scale-effect variables, the models were set the same as those tested above, and the POBi probit estimation was applied as well.

According to the results of Model (3) in Table 6, NetPnshNo _it is found to be statistically significant for fraud commission, and the coefficient is negative. In other words, given the more frequent punishment within the entire social network, propensity to commit fraud is lower. Thus, the scale effect of punishment on the entire social network was found, and this scale effect plays the role of vicarious punishment. This finding supports the vicarious-punishment theory of Yiu et al. (2018) and further verifies that vicarious-punishment theory works within social networks.

According to the results of Model (4) in Table 6, the findings were threefold. First, NetPnshNo _it was found to be statistically significant for fraud detection and the coefficient was positive. In other words, given the more frequent punishment within the whole social network, the likelihood of being detected after committing fraud is higher. Thus, this finding supports the peer-hinting effect found in the baseline models.

Second, CCCmmtNo _it is found to be statistically significant for fraud detection, and the coefficient is negative. In other words, given more fraudulent peers within the same social community, the likelihood of detection after committing fraud is lower. This finding supports H2 and the peer-concealing effects found in baseline models.

Third, CCPnshNo _it is found to be statistically significant for fraud detection, and the coefficient is positive. In other words, given more punished peers within the same social community, the likelihood of detection after committing fraud is higher. This finding supports H4 and the peer-hinting effects found in the baseline models.

Proximity of fraud and punishment in community

The empirical tests above put aside the effect of social connections (i.e., proximity of interlock directors), focusing on fraud and punishment. This section tests from the opposite direction, focusing on the proximity of fraudulent peers (and punishment), and puts aside the scale of fraud and punishment. The necessity of considering social proximity is motivated by Xiong et al. (2021), who investigate whether geographic proximity suppresses corporate fraud.

To do so, the closest relationships between the observers and their most intimate fraudulent peers (or punished peers) are considered, and two variables are constructed accordingly: (1) ShrPth2C _it represents the shortest path between corporation i and its closest fraudulent peer in year t; ShrPth2C _it substitutes CmntCNMCommit _it in the baseline models. (2) ShrPth2P _it represents the shortest path between corporation i and its closest punished peer in year t; ShrPth2P _it is to substitute CmntCNMPunish _it.

The results are presented in Table 6. Model (5) represents the results of fraud commission and Model (6) represents the results of fraud detection. Except for the shortest-path variables, the models were set the same as those tested above, and the POBi probit estimation was applied as well.

In general, there is no evidence of a close relationship. This contrasts with the baseline models, and the rationale behind this, may be the consideration of the scale of fraud and punishment. Essentially, the effect of the social community might not merely be represented by the most intimate relationships, but also by the joint force of the major peers.

Aggregate proximity of fraud and punishment in community

The empirical tests above focus mainly on the most intimate fraudulent (and punished) peers, while the results show that this simplification might be too aggressive. Thus, this section considers the aggregate proximity effect of social communities and attempts to eliminate the scale effect. To do so, the measures of the baseline models were applied as the basis of the aggregate effect of the social community, and the scale effect was eliminated by dividing the number of frauds (or punishments).

By doing so, two variables are constructed: (1) CCCmmtAvg _it represents the aggregate proximity effect of fraud committed within the social community (divided using the CNM algorithm) eliminating the scale effect, calculated as CmntCNMCommit _it divided by CCCmmtNo _it; CCCmmtAvg _it substitutes CmntCNMCommit _it in the baseline models. (2) CCPnshAvg_it represents the aggregate proximity effect of fraud punishment within the social community (divided using the CNM algorithm) eliminating the scale effect, calculated as CmntCNMPunish _it divided by CCPnshNo _it; CCPnshAvg_it substitutes CmntCNMPunish _it in the baseline models.

The results are presented in Table 6. Model (7) represents the results of fraud commission and Model (8) represents the results of fraud detection. Except for the aggregate-proximity-effect variables, the models are set the same as those tested above, and the POBi probit estimation is applied.

According to the results of Model (7) in Table 6, the main findings are twofold: on the one hand, CCCmmtAvg _it is found to be statistically significant with fraud commission, and the coefficient is negative. In other words, given intimate peers from the same social community committing fraud, the propensity to commit fraud is lower. This result implies the possibility of a peer-contagion effect because the effect of peer-committing fraud is indeed transmitted within the social community. This finding is consistent with that of existing effect tests. However, this finding may be insufficiently robust.

On the other hand, CCPnshAvg _it is found to be statistically significant for fraud commission, and the coefficient is positive. In other words, given that any fraudulent peer from the same social community is punished, the propensity to commit fraud is higher. This result implies a positive expected return of committing fraud; namely, the observers realize that fraud benefits exceed the punishment and thus tend to commit fraud. Thus, the punishment for fraud should be leveled up to set off the fraud benefit and deter the potential fraud commission. This result also implies the possibility of a vicarious punishing effect given a more severe punishment because the effect of punishment indeed transmits within the social community. These findings are generally consistent with those of existing effect tests.

According to the results of Model (8) in Table 6, the findings are twofold: on the one hand, CCCmmtAvg _it is found to be statistically significant with fraud detection, and the coefficient is negative. In other words, given more fraudulent peers within the same social community, the likelihood of detection after committing fraud is lower. This finding supports H2, namely, the peer-concealing effect found in the baseline models, and supports the findings of the scale-effect test.

On the other hand, CCPnshAvg _it was found to be statistically significant for fraud detection, and the coefficient was positive. In other words, given more punished peers within the same social community, the likelihood of detection after committing fraud is higher. This finding supports H4, namely, the peer-concealing effect found in the baseline models, and supports the findings of the scale-effect test.

Robustness Tests

Several robustness tests are applied, considering (1) different community-detection algorithms, (2) different error assumptions during estimation, (3) whether corporations are listed for short sale to alleviate variable omission problems, and (4) regions where corporations are located to alleviate potential endogeneity problems. The main results are presented in Table 7, and the major results of the baseline models generally remain robust.

Table 7. Main results of robustness tests

Notes: [1] *, **, and *** denote significant at a confidence level of 10, 5, and 1%. [2] t-value in parentheses. [3] Independent and control variables lag one period. [4] CV denotes whether includes control variables same as the baseline models. [5] Fixed effect of corporation is considered. [6] FE denotes whether include fixed effects of industry and year. [7] Cons denotes whether include constants. [8] ShortSale _it denotes whether is qualified to securities margin trading and has a nonzero balance. [9] RgnEast _it, RgnMid _it, and RgnWest _it respectively denotes whether locates in east, middle, and west.

Different Community-Detection Algorithm: The Girvan–Newman Algorithm

Considering the possible bias hidden behind the CNM algorithm, another algorithm proposed by Girvan and Newman (2002) is widely used as a substitution for the CNM algorithm. The GN community-detection algorithm was recently applied by Kydros, Pazarskis, and Karakitsiou (2021), who introduced it as part of the network textual analysis method to detect falsified financial statements. The results are treated as a robustness test and presented in Table 7, Models (1) and (2). Based on the results, the main conclusions were robust.

Different Error Assumption: Clustered by Corporations

Different error assumptions were introduced to avoid estimation bias. In contrast to the baseline model, which is estimated with a robust error, the estimation clustered by corporations is used as the robustness test. The results are shown in Table 7, Models (3) and (4), indicating the robustness of the major conclusions.

Alleviating Variable Omission: Considering Short Sales

To alleviate the omitted variable problems, we introduce short sales into our model. The rationale behind this is that short sales, as a newly introduced and seldom-used institution in the Chinese financial market (Meng, Li, Chan, & Gao, 2020), is believed to decrease fraud commission propensity but increase fraud detection likelihood (Meng et al., 2019). To do so, we introduce the variable ShortSale _it, which equals 1 if corporation i is qualified for securities margin trading and has a nonzero balance (Hope, Hu, & Zhao, 2017; Porras Prado, Saffi, & Sturgess, 2016). The data were obtained from the Securities Margin Trading database in CSMAR. The other settings followed the baseline models. The results are shown in Table 7, Models (5) and (6), indicating the robustness of the major conclusions.

Alleviating Endogeneity: Considering Regions

To alleviating the endogeneity problems, we introduce the corporation locating regions into our model following the Chinese relating study of Meng, Li, and Cai (2018). The rationale behind this is that regions somehow reflect context factors (e.g., economic development, institutions, policies, and demanding markets), which influence corporate fraud instead of the opposite mechanism. To do so, we define corporate regions using their registered province, follow the four-region division provided by the National Bureau of Statistics of China (http://www.stats.gov.cn/ztjc/zthd/sjtjr/dejtjkfr/tjkp/201106/t20110613_71947.htm), and construct three dummy variables: (1) RgnEast _it, which equals 1 if the corporation is located in the eastern region; (2) RgnMid _it, which equals 1 if the corporation is located in the middle region; and (3) RgnWest _it, which equals 1 if the corporation is located in the west region; thus, the baseline is in the northeast region. The results are shown in Table 7, Models (7) and (8), which indicate the robustness of the major conclusions.

Discussion

To further explore the role of social networks in corporate fraud, attention has recently been paid to social network communities (Bao et al., 2019; Van Akkeren & Buckby, 2017). We investigated the effect of peer fraud and punishment transmission within the social network community under the partial observability assumption of fraud. Our results show that (1) the peer-concealing effect exists, which decreases the likelihood of wrongdoers being detected after committing fraud, especially for those with more and closer fraudulent peers. (2) Peer-hinting effect exists, which increases the likelihood of wrongdoers being detected after committing fraud, especially for those with more and closer punished peers. (3) There is no evidence supporting the peer-contagion effect. (4) No evidence supports the vicarious-punishment effect. (5) Different subtypes of fraud are influenced differently, with executive fraud being the most susceptible. (6) Both peer number and social distance critically influence the social network community's transmission of fraud and punishment. (7) The abovementioned conclusions hold according to the robustness tests, considering alternative community-detection algorithms, alternative error assumptions of estimations, variable omissions, or endogeneity.

Theoretical Implications

First, we extend the literature on corporate fraud and governance. The existing literature has inductively investigated how social network influences corporate fraud (Phiri & Guven-Uslu, 2019; Van Akkeren & Buckby, 2017), and what prevents learning from prior fraud in the social network community (Bao et al., 2019). We test how corporate fraud is transmitted within the social network community and interpret its mechanism, during which we further introduce social distance and relax the full observability assumption of fraud to a partial one.

Second, we test the specific conditions under which vicarious punishment is effective and transmitted within the social network community. Essentially, peers within the same community tend to conceal fraud commission, while punishment deters the peer-concealing effect and leads to the peer-hinting effect, where fraudulent peers tend to be detected. By doing so, we extend the vicarious-punishment theory (Yiu et al., 2014, 2018), and provide suggestions to regulators of business administration and exchange markets. We also extend the defection against alliance partners’ misbehavior (Lee & Zhong, 2020a), specify it to a more severe reaction, namely the peer-hinting effect.

Third, we not only verify the effectiveness of the fraud triangle theory and trust triangle theory in developing countries and corporate fraud studies but also explain how their pillars possibly interact. We apply fraud triangle theory and trust triangle theory with corporate social–network–community transmission in China, the largest developing country, extending the already developed applications (Cumming et al., 2021; Holzman et al., 2021; Schuchter & Levi, 2016, 2019), and support the emerging usage in developing areas (Cao & Zhang, 2021; Gu et al., 2022). During our application of fraud triangle theory and trust triangle theory, we interpreted their three pillars and three legs with specific concepts and explained the potential mechanisms using theories such as social learning and social support.

Fourth, we extend the social network literature by investigating how corporate fraud and punishment are transmitted within closely connected social network subgroups, namely communities. By investigating the communities of Chinese corporations, we extend the conclusions of connections on governmental officers (Phiri & Guven-Uslu, 2019), on CFOs (Suh et al., 2020), and on CEOs (Chahine et al., 2021) to more closely connected corporations. We also contribute to the few studies relating proximity to corporate fraud (Xiong et al., 2021), such as extend the geographic proximity to social one. Meanwhile, by applying the CNM and GN algorithms to Chinese corporations, we verify the algorithms’ reliability and availability on social network in emerging markets.

Practical Implications

First, corporations should attach importance to community network governance. Although social networks are very important in China as informal institutional support (Opper, Nee, & Holm, 2017; Park & Luo, 2001), peer fraud within community networks will lead to corporations’ unethical behaviors under the weight of various pressures. Thus, corporations need network governance in advance to prevent the occurrence of their own cognitive dissonance behavior, such as increasing their political connections (e.g., gaining investment by state-owned assets) and industry association connections.

Second, regulators need to pay attention to and use the transmission mechanism of fraud commission and detection in social network communities. An interesting finding similar to that of Bao et al. (2019) is that direct punishment on fraud does not suppress fraud propensity, which might be due to the soft intensity of the penalty for fraud (Schell-Busey, Simpson, Rorie, & Alper, 2016), warnings instead of fines (Hou, Wang, & Ma, 2021), or ease of wrongdoers regaining legitimacy (Cumming et al., 2021). Our findings also indicate a peer-concealing effect and peer-hinting effect. In view of social network identity, the purpose of gaining and showing social support, and avoiding retaliation, the corporation will conceal peer fraud. However, the decision to report fraud (and suggesting from consultant to report) is influenced by the signal (the cost of peer concealing and the benefit of peer hinting) hinted at by punishment. Therefore, on the one hand, regulators need to actively inspect and strictly supervise corporate behaviors to reduce fraud; on the other hand, regulators also need to timely detect and punish corporate fraud and encourage enterprises to report peers’ fraud.

Limitations and Future Research

We have to acknowledge several limitations of our study, which could be set as the future agenda. On the one hand, future studies can explore and test the boundary conditions of transmission mechanisms. In this study, we did not find robust empirical evidence to verify the peer-contagion effect of fraud commission and vicarious-punishment effect of fraud detection within the social network community. We suspect that this may also be related to the detection of the corporate social network community based on the interlocking director network. The transmission mechanism of corporate fraud commission and detection is affected by network situations. In different network situations, the four peer effects of fraud commission and punishment are different. Future studies can explore and test the deeper boundary conditions of the four effects; for example, a study in an analyst network community can consider that corporations in the same analyst network community are more similar in terms of industry, size, financial status, and so forth.

On the other hand, future studies can construct and apply a spatial regression model with a time-variable spatial matrix to test the transmission mechanisms, and more precisely measure and estimate the influence of different social proximities. Future studies can construct and apply a spatial regression model with a time-variable spatial matrix to test the transmission mechanism of corporate fraud commission and detection within a community network and, thus, more precisely measure and estimate the influence of different social proximities.