Fraud commission and fraud triangle theory

Fraud triangle theory is constructed of three pillars (Schnatterly, Gangloff, & Tuschke, Reference Schnatterly, Gangloff and Tuschke2018): (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, Reference Amiram, Bozanic, Cox, Dupont, Karpoff and Sloan2018): capital-market incentives, which include manipulating stock prices (Call, Kedia, & Rajgopal, Reference Call, Kedia and Rajgopal2016) or insider trading (Peng & Röell, Reference Peng and Röell2008), and contract incentives, such as manipulating accounting reports (Burns & Kedia, Reference Burns and Kedia2006; Dechow, Sloan, & Sweeney, Reference Dechow, Sloan and Sweeney1995). (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, Reference Kong, Xiang, Zhang and Lu2019; Kuang & Lee, Reference Kuang and Lee2017) and auditors (Krishnan & Peytcheva, Reference Krishnan and Peytcheva2019); the other is external governance, including delisting pressure (Zhou, Zhang, Yang, Su, & An, Reference Zhou, Zhang, Yang, Su and An2018) and analyst coverage (Ren et al., Reference Ren, Zhong and Wan2021). (3) Rationalization refers to moral justification after committing fraud. Rationalization is argued to be the most common pillar (Schuchter & Levi, Reference Schuchter and Levi2016, Reference Schuchter and Levi2019) and is mainly determined by managers’ characteristics (Huang et al., Reference Huang, Lin, Chiu and Yen2017), such as overconfidence (Cao & Zhang, Reference Cao and Zhang2021).

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, Reference Dupont and Karpoff2020). Trust is thought to be the opposite of fraud, which is essential for both corporations (Amiram, Huang, & Rajgopal, Reference Amiram, Huang and Rajgopal2020; Bao et al., Reference Bao, Zhao, Tian and Li2019) and markets (Cole, Johan, & Schweizer, Reference Cole, Johan and Schweizer2021). The trust triangle is also built upon three factors (Dupont & Karpoff, Reference Dupont and Karpoff2020; Karpoff, Reference Karpoff2021): (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., Reference Cumming, Hornuf, Karami and Schweizer2021). (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, Reference Zaman, Atawnah, Baghdadi and Liu2021).

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., Reference Holzman, Miller and Williams2021; Parsons, Sulaeman, & Titman, Reference Parsons, Sulaeman and Titman2018), workmates (Chan, Chen, Pierce, & Snow, Reference Chan, Chen, Pierce and Snow2021; Dimmock, Gerken, & Graham, Reference Dimmock, Gerken and Graham2018), and social networks (Chahine, Fang, Hasan, & Mazboudi, Reference Chahine, Fang, Hasan and Mazboudi2021). 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., Reference Holzman, Miller and Williams2021). Corporations operating in the context of widespread fraud could view fraud as a necessary strategy (Schnatterly et al., Reference Schnatterly, Gangloff and Tuschke2018). 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, Reference Colvin, Cullen and Ven2002; Van Akkeren & Buckby, Reference Van Akkeren and Buckby2017). 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, Reference Van Akkeren and Buckby2017).

A social network community is a densely connected group in which peers pay great attention to each other (Knoke, Reference Knoke2009). Prior studies have also suggested that distance and number of relationships have an impact on peer interactions (Gronum, Verreynne, & Kastelle, Reference Gronum, Verreynne and Kastelle2012; Kuang & Lee, Reference Kuang and Lee2017). Interaction with fraudulent peers facilitates information sharing between peers (Bao et al., Reference Bao, Zhao, Tian and Li2019), 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., Reference Dimmock, Gerken and Graham2018), making corporations more likely to be persuaded to join the fraudulent group. Interactions within a community intensify social learning between peers (Clement et al., Reference Clement, Shipilov and Galunic2018), thereby resulting in fraudulent commission learning, namely fraud contagion (Kuang & Lee, Reference Kuang and Lee2017; Xiao, Dong, & Zhu, Reference Xiao, Dong and Zhu2019).

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:

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., Reference Cumming, Hornuf, Karami and Schweizer2021). 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, Reference Agarwal and Muckley2022; Lee & Zhong, Reference Lee and Zhong2020a). 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, Reference van de Weijer, Leukfeldt and Van der Zee2020) between closer partners. During this process, the negative emotions of concealing fraud can be buffered by social belonging (Kaakinen, Keipi, Räsänen, & Oksanen, Reference Kaakinen, Keipi, Räsänen and Oksanen2018) and embeddedness (Jaspers, Reference Jaspers2020). 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, Reference Tolsma, Blaauw and Te Grotenhuis2012; van de Weijer et al., Reference van de Weijer, Leukfeldt and Van der Zee2020).

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, Reference De Kimpe, Ponnet, Walrave, Snaphaan, Pauwels and Hardyns2020) and extended social balance theory (Knoth & Ruback, Reference Knoth and Ruback2016). Usually, a trusted friend without judgment might be consulted about whether to report fraud, and their suggestion is often accepted (De Kimpe et al., Reference De Kimpe, Ponnet, Walrave, Snaphaan, Pauwels and Hardyns2020). However, the presence of friendships between consultants and offenders suppresses the probability of reporting fraud (Knoth & Ruback, Reference Knoth and Ruback2016). 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, Reference Bruner, Boardley and Côté2014; Chiu, Huang, Cheng, & Sun, Reference Chiu, Huang, Cheng and Sun2015), 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., Reference De Kimpe, Ponnet, Walrave, Snaphaan, Pauwels and Hardyns2020). Thus, we draw the following hypothesis, assuming that observers tend to conceal peer fraud:

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., Reference Yiu, Xu and Wan2014), and is also called the regulatory contagion effect (Agarwal & Muckley, Reference Agarwal and Muckley2022). 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., Reference Chan, Chen, Pierce and Snow2021). Vicarious punishment has been proven between peers within the same industry (Agarwal & Muckley, Reference Agarwal and Muckley2022; Yiu et al., Reference Yiu, Xu and Wan2014), strategic alliances and business affiliations (Yiu et al., Reference Yiu, Wan and Xu2018), supply chains (Xiao et al., Reference Xiao, Dong and Zhu2019), and social network communities (Bao et al., Reference Bao, Zhao, Tian and Li2019).

Vicarious punishment informs observers that detection is ongoing and fraud is costly, thus suppressing the propensity to commit fraud (Yiu et al., Reference Yiu, Xu and Wan2014). 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., Reference Xiao, Dong and Zhu2019; Yiu et al., Reference Yiu, Xu and Wan2014). Another stronger deterrence is the regulatory contagion effect, which spills the lawbreaker's negative capital market reactions over its peers (Agarwal & Muckley, Reference Agarwal and Muckley2022).

Considering information sharing in social network communities (Sytch & Tatarynowicz, Reference Sytch and Tatarynowicz2014), it has been argued that vicarious punishment (or regulatory contagion) is also effective within the same social network community (Bao et al., Reference Bao, Zhao, Tian and Li2019). Similar to vicarious punishment within the same industry (especially between following corporations and benchmark corporations, or between similar corporations) (Agarwal & Muckley, Reference Agarwal and Muckley2022; Yiu et al., Reference Yiu, Xu and Wan2014), punishment on fraudulent peers within the same community also produces inhibitive learning effects among other observing peers (Bao et al., Reference Bao, Zhao, Tian and Li2019; Xiao et al., Reference Xiao, Dong and Zhu2019).

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:

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, Reference Knoth and Ruback2016), even in the cyber era (De Kimpe et al., Reference De Kimpe, Ponnet, Walrave, Snaphaan, Pauwels and Hardyns2020; van de Weijer, Leukfeldt, & Bernasco, Reference van de Weijer, Leukfeldt and Bernasco2018; van de Weijer et al., Reference van de Weijer, Leukfeldt and Van der Zee2020), especially in the case of seemingly less serious fraud, and the wrongdoer might not be caught (Knoth & Ruback, Reference Knoth and Ruback2016). 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., Reference Tolsma, Blaauw and Te Grotenhuis2012), 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, Reference Fotaki, Voudouris, Lioukas and Zyglidopoulos2021; Miller, Le Breton-Miller, & Lester, Reference Miller, Le Breton-Miller and Lester2013) and ethical spillover (Pierce & Snyder, Reference Pierce and Snyder2008), 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., Reference Bai, Shang, Wan and Zhao2021). 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., Reference Tolsma, Blaauw and Te Grotenhuis2012; van de Weijer et al., Reference van de Weijer, Leukfeldt and Van der Zee2020), 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, Reference Latan, Chiappetta Jabbour and Lopes De Sousa Jabbour2021; Smaili & Arroyo, Reference Smaili and Arroyo2019). 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, Reference Andon, Free, Jidin, Monroe and Turner2018). 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, Reference Lee and Zhong2020b). This spillover effect of regulations is also found within similar corporate groups (Agarwal & Muckley, Reference Agarwal and Muckley2022). Due to the negative impact of the regulatory contagion effect, including threats to identity and efficiency (Lee & Zhong, Reference Lee and Zhong2020a), fraud might be hinted at by observers to save legitimacy (Zhang et al., Reference Zhang, Xu, Chen and Jing2020). 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:

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

Figure 1. Theoretical framework

Interlocked community

Following Bao et al. (Reference Bao, Zhao, Tian and Li2019), the fast greedy algorithm was applied to detect communities based on an interlocked network. The algorithm proposed by Clauset, Newman, and Moore (Reference Clauset, Newman and Moore2004) is one of the most accepted community-detection algorithms based on optimization and is called the CNM algorithm (Fortunato & Hric, Reference Fortunato and Hric2016). 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., Reference Clauset, Newman and Moore2004). 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. (Reference Bao, Zhao, Tian and Li2019) and Chan et al. (Reference Chan, Chen, Pierce and Snow2021), we first replaced the punished node number used by Bao et al. (Reference Bao, Zhao, Tian and Li2019) with fraudulent node numbers. Bao et al. (Reference Bao, Zhao, Tian and Li2019) 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. (Reference Chan, Chen, Pierce and Snow2021), 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 (Reference Xiong, Ouyang, Tong and Zhang2021), 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., Reference Chan, Chen, Pierce and Snow2021), because a closer relationship might bring more loyalty which is argued to be a critical requirement of fraud conspiracy (Khanna et al., Reference Khanna, Kim and Lu2015).

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. (Reference Bao, Zhao, Tian and Li2019), Chan et al. (Reference Chan, Chen, Pierce and Snow2021), and Xiong et al. (Reference Xiong, Ouyang, Tong and Zhang2021), 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., Reference Xiong, Ouyang, Tong and Zhang2021), 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.

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, Reference Gong, Huang, Wu, Tian and Li2021), 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, Reference Wang, Ashton and Jaafar2019a), thus it is more likely to be detected. Another widely accepted measure of punishment is the penalty amount (Yiu et al., Reference Yiu, Xu and Wan2014; Zhang et al., Reference Zhang, Xu, Chen and Jing2020). 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, Reference Greene1994).

The second part is social network capital. Social network capital influences fraudulent activity by lowering coordination costs (Bao et al., Reference Bao, Zhao, Tian and Li2019) and concealing fraudulent activity (Khanna et al., Reference Khanna, Kim and Lu2015). The interlocked network centrality is measured using a more comprehensive index than the simple eigenvector used by Bao et al. (Reference Bao, Zhao, Tian and Li2019). A comprehensive index (NetAvgPCAStd_it) was constructed following the methods described by El-Khatib et al. (Reference El-Khatib, Fogel and Jandik2015) and Tao et al. (Reference Tao, Li, Wu, Zhang and Zhu2019). 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. (Reference Meng, Zou and Hou2019). 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. (Reference Khanna, Kim and Lu2015).

(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., Reference Kong, Xiang, Zhang and Lu2019; Yiu et al., Reference Yiu, Wan and Xu2018; Zhang, Reference Zhang2018). (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 (Reference Dechow, Ge, Larson and Sloan2011) and Khanna et al. (Reference Khanna, Kim and Lu2015). (3) Corporation leverage (Leverage), which is measured by debt on assets, is believed to be an important fraud-inducing factor (Zhang, Reference Zhang2018). (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, Reference Wang, Ashton and Jaafar2019b). (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., Reference Wang, Ashton and Jaafar2019b; Yiu et al., Reference Yiu, Wan and Xu2018), and has a lower enforcement incidence (Hou & Moore, Reference Hou and Moore2010), while others argue that SOEs are less likely to be involved in fraud such as bribes (Shaheer, Yi, Li, & Chen, Reference Shaheer, Yi, Li and Chen2019). (6) Tobin's Q (TobinQ) was measured using the well-known corporate value index Tobin's Q (Yiu et al., Reference Yiu, Wan and Xu2018; Zhang, Reference Zhang2018). (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., Reference Wang, Ashton and Jaafar2019b). (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., Reference Wang, Ashton and Jaafar2019b). (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., Reference Zhou, Zhang, Yang, Su and An2018).

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. (Reference Kong, Xiang, Zhang and Lu2019), 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., Reference Yiu, Wan and Xu2018; Zhang, Reference Zhang2018). 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. (Reference Meng, Zou and Hou2019), 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 (Reference O'Reilly, Doerr and Chatman2018), 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 (Reference Conyon and He2016). (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 (Reference Liu2021) and Zhou et al. (Reference Zhou, Zhang, Yang, Su and An2018). (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., Reference Kong, Xiang, Zhang and Lu2019; Yiu et al., Reference Yiu, Wan and Xu2018). (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, Reference Zhang2018). (6) Shareholding centrality (Shrcr1), measured by the percentage of shares held by the largest shareholder, is considered based on Conyon and He (Reference Conyon and He2016) and Zhou et al. (Reference Zhou, Zhang, Yang, Su and An2018).

Ex ante factors of fraud detection likelihood

Referring to Khanna et al. (Reference Khanna, Kim and Lu2015) and Meng et al. (Reference Meng, Zou and Hou2019), 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, Reference Hass, Tarsalewska and Zhan2016; Wu, Johan, & Rui, Reference Wu, Johan and Rui2016; Zhang, Reference Zhang2018). (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., Reference Yiu, Wan and Xu2018; Zhou et al., Reference Zhou, Zhang, Yang, Su and An2018). (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., Reference Wang, Ashton and Jaafar2019b). (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, Reference Zhang2018). (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., Reference Zhou, Zhang, Yang, Su and An2018). (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, Reference Zhang2018) 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., Reference Wu, Johan and Rui2016).

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.

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., Reference Wang, Ashton and Jaafar2019a). Thus, according to the fraud categories by Khanna et al. (Reference Khanna, Kim and Lu2015) and local research (Meng et al., Reference Meng, Zou and Hou2019), 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., Reference Khanna, Kim and Lu2015). 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. (Reference Yiu, Wan and Xu2018) 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. (Reference Xiong, Ouyang, Tong and Zhang2021), 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.