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A game theoretic model of governance mechanisms coordination in combating accounting fraud

AUTHORS

Adrien B. BONACHE a, Karen MORIS a, b,*

a CRCGM (EA 3849), Clermont Université, Bâtiment Extension, 3ième étage, 28 place Henri-Dunant, 63000 Clermont-Ferrand, France.

b LaRGE (EA 2364), EM Strasbourg, 61 avenue de la Foret Noire, 67085 Strasbourg Cedex, France.

* Corresponding author. Address: Ecole Universitaire de Management, 26 avenue Léon Blum, 63 000 Clermont-Ferrand, France. Telephone: + 33 4 73 17 77 34. E-mail address: karenmoris@yahoo.fr.

ABSTRACT

The present study aims at explaining the divergence between the results of empirical studies and theory on the effectiveness of the corporate governance mechanisms in combating fraud. The demonstration is based on a game theoretic model with three agents: a top manager choosing the level of fraud to maximize its utility, a statutory auditor and a journalist selecting their levels of effort to minimize the cost of fraud detection. This model demonstrates and simulations show that the independence of mechanisms is a sufficient but not necessary condition, and the best way, to decrease top manager fraud. Increasing the effort of substitutable agents decreases the level of top manager agent’s fraud, but with a decreasing rate. Lastly, the effectiveness of complementary agents playing the role of corporate governance mechanisms is indeterminate if they do not coordinate their efforts.

KEYWORDS

Fraud, corporate governance, independence, complementarity, substitutability, game theoretic model

1. INTRODUCTION

Fraud is a breach of a country’s legislative and regulatory frameworks. A study

conducted by PricewaterhouseCoopers (2011) on a worldwide sample of companies revealed

that 34% had been victims of fraud in 2011, compared to 30% the previous year. In France,

the figures for the same period rose from 29% to 49%. These consequences are not only

financial in nature. They also affect employee motivation, company reputations, relations with

stakeholders (clients, suppliers, shareholders, banks, insurers, etc.) and levels of trust in the

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business world. In the United States, over a period of around 10 years, the cost of white-collar

crime is thought to have risen from $200 billion (Touby, 1994) to $600 billion (Association of

Certified Fraud Examiners, 2002). The poor allocation of capital, which results from instances

of fraud, can lead to lower levels of wealth production and ultimately slower economic

growth (Yeung, Morck, & Wolfenzon, 2004).

Corporate governance is a key lever for combating fraud. It involves a great many

agents and institutions which contribute directly (when it is their primary purpose) or

indirectly (when it is a consequence of their activities but not necessarily intended) to the fight

against fraud. The first category essentially includes financial regulatory authorities (French

regulator of markets1 in France, Securities and Exchange Commission in the US), judicial

authorities (courts), statutory auditors, and the Association of Certified Fraud Examiners

(ACFE)2, while the second includes financial analysts, the media, employees, clients, etc.

Each of these agents acts as corporate governance mechanism. In combination, these actors

constitute a governance system, which “effectively demarcates powers and influence top-level

decision makers, in other words which ‘govern’ their conduct and define their discretionary

space” (Charreaux, 1997: 421). By limiting and controlling the room of latitude of managers,

the governance system contributes to the prevention and detection of fraud. When it is

effective, it can lead to a reduction of the negative social and economic consequences of

fraud, thus helping to improve the value created by companies.

Corporate governance mechanisms as key levers for combating fraud involve several

economic, managerial, operational and political grand challenges. The challenge that is the

focus of the present paper is the coordination of agents playing the role of governance

mechanisms in combating accounting fraud. The way these agent coordinate their actions

leads to suboptimal value creation relative to the objective of maximizing corporate value

creation.

The literature on corporate governance does not address this grand challenge. First,

some authors restrict themselves to measure the effectiveness of one of the agents, for

instance the media (Dyck, Volchkova, & Zingales, 2008; Miller, 2006; Moris, 2011). Second,

others focus on comparing the effectiveness of several governance mechanisms (Beasley,

1996; Borden, 2007; Dyck, Morse, & Zingales, 2010; Fama and Jensen, 1983; Schnatterly,

1 “Autorité des marchés financiers”. 2 The ACFE is a worldwide association involved in the combat against fraud and provides a large amount of information and training in this regard. See: http://www.acfe.com.

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2003). These comparisons raise the question of the complimentary usage of several different

governance mechanisms to improve efforts to combat fraud. Third, according to Dyck, Morse

and Zingales (2010), and Bowen, Call and Rajgopal (2010), the detection of fraud only really

seems possible by weaving a dense web of mechanisms and agents. Yet, the studies by Gerety

and Lehn (1997), and Agrawal and Chadha (2005) raise issues about the better effectiveness

of a dense web of mechanisms and agents.

Hence, the link between governance mechanisms and fraud is empirically quite

ambiguous, even in the case of studies that try to test several mechanisms together. The

importance of complementarity or substitutability among some corporate governance

mechanisms and the methods used in these tests might explain why there is no consensus on

the results (Aguilera, Filatotchev, Gospel, & Jackson, 2008; Becht, Bolton, & Roëll, 2003;

Coles & Hesterly, 2000). This brings us to the following research question: in what way does

a combination of governance mechanisms make the fight against fraud more efficient and,

thus, can improve value creation?

The current article uses a game theoretic approach to study the way in which corporate

governance mechanisms can coordinate to improve their effectiveness in combating fraud.

The key idea is that the nature of the relations among mechanisms (complementarity,

independence or substitutability) influences the effectiveness of their joint efforts. As such,

our analysis addresses the following questions.

• Does a dense web of complementary mechanisms and agents improve the

effectiveness of the fight against fraud?

• Does a dense web of substitutable mechanisms and agents improve the effectiveness

of the fight against fraud?

• How can mechanisms and agents acting as corporate governance coordinate to limit

the level of fraud?

Addressing these issues is important to gain a deeper understanding of the link among

several corporate governance mechanisms combating fraud. As far as we know, previous

literature has still not made formalization of such questions. Thus, we hoped to develop a

model advancing our understanding of the effects of the complementarity and substitutability

of corporate mechanisms in the fight against fraud. Our model describes some results of the

interactions between two agents. Both are considered as corporate governance mechanisms

being able to combat fraud committed by top managers.

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By doing so, we hoped to provide a model which could be adapted and changed to study

coordination problems in combating fraud. Future research can use this model to address

other issues on this subject.

The literature review and our model have merit to show practitioners the challenges to

understand the effects on the level of top manager’s fraud of the combinations of two

corporate governance mechanisms, namely a journalist and a statutory auditor. Under

conditions of independence or substitutability, mix of corporate governance mechanisms can

improve the effectiveness of corporate governance system by combatting top manager’s

fraud, and, thus, potentially enhances the creation value of firm. The model presented in the

current paper help to understand that the result of complementary governance mechanism

combination is difficult to predict. Thus, implementing a new policy or practice, which are

complementary to others mechanisms, may paradoxically lead to worse efficiency.

To address these questions, we first explain and illustrate the importance of governance

mechanisms in the context of fraud. Then, we develop our model. Lastly, before to conclude,

we present the result, that is the propositions derived from the model.

2. CORPORATE GOVERNANCE IN THE FIGHT AGAINST FRAUD

This section provides the background on corporate governance, on value destruction

resulting from fraud (2.1), and on the effectiveness of corporate governance mechanisms (2.2)

that is needed for the rest of the present paper. In order to understand the fight against fraud,

we need first to define it precisely. Yet definitions vary from one study to another3 and cover

different actions. In this paper, fraud is a breach of a country’s legislative and regulatory

frameworks. In other words, where there is fraud there is a transgression of a source of law4.

This definition points to the fact that the fight against fraud covers several steps: prevention,

detection, public disclosures, and the implementation of curative measures.

2.1 CORPORATE GOVERNANCE FACED WITH VALUE DESTRUCTION AS A RESULT OF FRAUD

3 For example, Miller (2006) and Farber (2005) based their work on the Accounting, Auditing, and Enforcement Releases (AAERs), extreme violations of US accounting standards in respect of the rules of the Securities and Exchange Commission (SEC); Dyck, Morse and Zingales (2010) drew on the Stanford Securities Class Action Clearinghouse (SSCAC), also a failure to respect SEC rules but which leads to collective trials; Beasley (1996) relied on the AAERs and the Wall Street Journal Index (WSJ Index) which indexes white-collar crime; and Schnatterly (2003) is based solely on the WSJ Index, etc. 4 This implies that the manipulation of accounting data does not constitute fraud as it is based on an opportunistic usage of legislative or regulatory frameworks that are incomplete or imperfect, rather than on a deliberate breach.

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In the context of agency theory (Jensen & Meckling, 1976), company managers are

expected to maximise the value creation on behalf of shareholders. This theory is based on a

contractual vision of companies which supposes that conflicts of interest and information

asymmetries can arise between agents, shareholders and top managers, for example. These

can lead to agency costs that result in a reduction of value creation. In theory, the corporate

governance system makes it possible to improve value creation by reducing these phenomena.

A governance system is the combination of corporate governance mechanisms. There are

many such mechanisms: laws, boards of directors, the media, financial markets, etc.

(Charreaux, 1997). Through various mechanisms (stock options, internal audits, etc.),

managers are encouraged to defend the interests of shareholders. The aim of these

mechanisms is to generate a convergence between managers’ interests and those of the

shareholders.

From this perspective, an instance of fraud within a company is thought to go against

the interests of shareholders5. Fraud can lead to value destruction by generating financial or

extra-financial costs. These are the costs borne by the company during the fraud

(embezzlement of assets, abuse of trust, theft, etc.) but also those that arise when the fraud is

uncovered (fines, reputational damages, etc.). Schnatterly (2003) emphasises the very high

cost of white-collar fraud, the impact it has on company performance and the resulting need to

prevent or detect fraud: this cost is said to represent between 1% and 6% of annual sales

among US companies.

Therefore, an effective governance system should avoid not only opportunistic6 but

also fraudulent7 behaviour of managers. This makes it a key factor in the fight against fraud.

Governance systems can prevent fraud, detect it, denounce it publicly and encourage the

implementation of curative measures. For example, mechanisms play a preventive role in

companies whose managers are fearful of the negative repercussions on their reputation or the

profitability of the company (ex ante role). They play a curative role when they help sanction

fraud and provide a remedy for its consequences. In this way they can improve a company’s

profitability (ex post role).

5 Except in a short term vision, where they would be the beneficiaries. 6 For example, by increasing the personal wealth of a manager who exploits information asymmetries or his discretionary powers without necessarily breaking any laws. 7 Here, the personal wealth increase stems directly from the unlawful nature of one’s actions (abuse of company assets, insider trading, forgery or the use of forgery, etc.).

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When combined, these mechanisms make it possible to combat fraud through their

respective roles and capacities. Laws and regulations mark the boundary between what is

legal and illegal. Statutory auditors provide a link between companies and laws, regulations

and standards by certifying accounts or providing companies with advices. The media also

play an important role in this regard as a front-line information intermediary (Bushee, Core,

Guay, & Hamm, 2010).8 This role allows them to collect and communicate information about

fraud, but also to prevent it. They activate certain levers in terms of the law and/or corporate

reputations, and base their publications on the legal framework when encouraging companies

to respect the law. Companies which fail to do so can be denounced by the media if a

journalist becomes aware of the breach. Such publications can also allow the authorities to

initiate prosecutions and can allow stakeholders to better evaluate a particular company.

Corporate reputations are based on the same principle: by communicating certain information

about fraudulent companies or companies likely to commit fraud, the media can damage their

reputation. This can have repercussions on profitability and ultimately on value creation. The

media can also draw on other governance mechanisms to detect and denounce instances of

fraud or look to other intermediaries who do not have the same ability to make information

publicly available (lawyers, financial analysts, employees, etc.).

Having outlined the role of governance systems in value creation through the fight

against fraud, let us now look at certain studies to better understand this role.

2.2 ILLUSTRATIONS OF GOVERNANCE MECHANISMS IN COMBATING FRAUD

So as to better understand the role of governance mechanisms in combating fraud, we

have provided an overview of research findings in this area. This overview demonstrates that

corporate governance mechanisms can be effective (2.2.1). We then offer a comparison of

their respective levels of effectiveness (2.2.2) before reaching the conclusion that there are

limitations to this effectiveness (2.2.3).

2.2.1 Effectiveness of corporate governance mechanisms in combating fraud

Prior to the detection of fraud, the media are in a position to prevent it by exerting

pressure on company managers, for example by monitoring their behaviour or actions and the

performance of their companies. When they feel something is newsworthy, they can release it

8 The media represent a means of combating fraud spontaneously. They contribute to this by pursuing their interests, which may mean maximizing their profit in economic terms. It is not their raison d'être to combat fraud.

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into the public domain. This is the case of fraud (Jamieson & Campbell, 2001). Company

managers who wish to commit fraud must therefore weigh up the gains if their actions are not

uncovered against the losses suffered if they are.

In this regard, several studies have shown the importance of the media in detecting

fraud and publicly denouncing it. The media as a kind of “watchdog” governance mechanism

have been studied in France and in the US. Moris (2011) reports that 10% of all cases of fraud

committed in France between 2004 and 2007 were revealed by the press before being

sanctioned by the authorities. Miller (2006) shows that 29% of the accounting, auditing, and

enforcement releases published on the SEC Web site are identified by the press prior to the

SEC’s or firm’s public announcement.

The media also serve a role in amplifying certain information. They report information

that comes from other sources. According to Borden (2007), the accounting and financial

scandals at Enron were uncovered thanks to the work of journalists who encouraged lawyers

and the authorities to take an interest, while the financial markets and their intermediaries

were ineffective. Also, by examining the relations between financial analysts and the media,

the author found that these two mechanisms work in tandem to improve their effectiveness in

terms of surveillance and denunciation. In the Dirks-SEC affair at the beginning of the 1980s,

a manager in an investment firm informed the SEC that his company had committed fraud.

When the SEC failed to react, he informed a financial analyst named R. Dirks who, having

verified the information, gave the story to the Wall Street Journal. It was only then that the

scandal was able to break. The power of the media is confirmed in some studies (e.g., Dyck,

Volchkova, & Zingales, 2008).

Audit firms are also very important actors to combat fraud. Combatting fraud is a

significant issue to their tasks. Empirical studies provide evidence that the Big Five public

accounting firms are associated with higher quality financial statements (Francis, 2004) thus

confirming the quality of audit depends on the size of the audit firm (DeAngelo, 1981). But

some recent high-profile financial reporting failures that roiled the US capital markets can

question these results. Some indications show audit quality may have declined in the 1990s,

(Coffee, 2002; Cox 2003; Zeff, 2003; Francis, 2004). Despite criticisms that the Big Five

accounting firms received since the scandals and the frauds of the 2000s, they consistently

supplied rather higher-quality external monitoring: their clients are less likely to orchestrate

accounting fraud (Lennox & Pittman, 2010).

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2.2.2 Comparing the effectiveness of governance mechanisms

Before presenting literature on the relative effectiveness of different governance

mechanisms, we exposed some theoretical reasons explaining these differences.

According to Dyck, Morse and Zingales (2010), three theories could explain who

should detect fraud when boards fail, namely the legal, the private litigation, and the financial

risk views. The legal view holds that auditors and security regulators (e.g., SEC) have to

detect them. The private litigation view states that, for instance, lawyers will find fraud while

searching for lucrative class-action lawsuit. Finally, the financial risk view asserts the firm’s

owners and their delegates (analysts, rating agencies, and bankers) will catch fraud because

shareholders have the most to lose if fraud is not detected. Beyond these three, a fourth

category could be added: the other whistleblowers whose aims and private interests may be

less clear. This last category includes employees, industry regulators, short term investors

(that is investors who saw the fraud and bet against the firm), and journalists. In sum,

combatting fraud involves a great many agents, as no group of actors has enough information

and incentives to detect and report alone fraud consistently.

In their study of the board of directors as a corporate governance mechanism, Fama

and Jensen (1983) highlighted the effectiveness of outside over inside directors in monitoring

the actions of company managers. Beasley (1996) later confirmed this by demonstrating that

the inclusion of a higher proportion of outside directors on the board reduces the likelihood of

financial fraud being committed. However, the presence of an audit committee has no

significant impact on this likelihood. Schnatterly (2003) offers a broader comparison by

studying the effectiveness of a range of mechanisms designed to prevent and detect fraud.

According to his findings, operational governance mechanisms (internal monitoring and

procedures, codes of conduct, incentive compensation system for all employees, etc.)

dominate more traditional mechanisms (independence of board members, compensation

systems for top managers, etc.). Dyck, Morse and Zingales (2010) also carried out a study on

the effectiveness of various governance mechanisms in terms of corporate fraud committed

between 1996 and 2004, but focused on those who initially denounced these actions.

According to their findings, the most effective sources of denunciation are as follows:

employees (17%), financial analysts (14%), the sector’s regulatory authorities (13%) and the

media (13%). They emphasise the significant role played by governance mechanisms that

have received little attention in the literature, such as the media. Adopting a similar systemic

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approach, Farber (2005) focused on the link between the quality of a corporate governance

system and the instances of fraud associated with financial information. Fraudulent companies

were found to have poor-quality governance: few outside directors on the board, few financial

experts present at audit committee meetings, such meetings occur infrequently, and the roles

of Chairman and CEO are often combined in one person. These findings confirm the earlier

results of Dechow, Sloan and Sweeney (1996).

In less developed countries, efficient corporate governance mechanisms are almost

non-existent. For instance, in Russia, laws are regularly broken by firms and effective

legislative and judicial mechanisms seem to not exist. Such weaknesses of corporate

governance mechanisms result in diversion of assets by managers of many privatized firms

(Boycko, Shleifer, & Vishny, 1995). On this matter, Dyck, Volchkova and Zingales, (2008)

observed Russian companies make efforts to improve their performances in proportion to

their coverage and control by Anglo-Saxon newspapers. This kind of press has a higher level

of credibility than the Russian press. For example, Khodorkovsky, the Russian ex-manager of

Yukos laughed at the media during the time the activities of his firm taken place only in

Russia. But when he turned towards international business he changed completely his

behavior because international press was watching him. He paid attention to his management

and his reputation. Generally speaking, the media pressures placed on companies and the level

of press independence in a country favours the detection of management-related fraud, thus

limiting the gains to be made.

This comparison raises the question of the complimentary usage of several different

governance mechanisms to improve efforts to combat fraud.

2.2.3 Much-needed but inadequate complementarity among mechanisms

As observed by Dyck, Morse and Zingales (2010), the detection of fraud only really

seems possible by weaving a dense web of mechanisms and agents. An effective governance

system cannot be based on just one or two mechanisms. Bowen, Call and Rajgopal (2010)

confirmed this result. According to them, a company faces a greater risk of being denounced

by its employees if they have access to an external mechanism which can transmit their

information to the public domain and denounce acts of fraud witnessed by the employees. The

media is an example of such a mechanism.

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By contrast, Agrawal and Chadha (2005), who based their study not on cases of fraud

that had been sanctioned by the SEC9 but rather on inaccurate accounting statements made by

US firms, found no significant link between the mechanisms studied above and these

erroneous statements that led to earnings figures being reprocessed. In an earlier study, Gerety

and Lehn (1997) also failed to find any significant link between traditional governance

mechanisms (the percentage of insider and outsider directors on the board, the presence of an

audit committee, a compensation system, the reputation of auditors, etc.) and instances of

fraud.

Moreover, some studies interpret the steep upward trend during the late 1990s and

early 2000s in fraud or in accounting misstatements by companies despite auditor firms as

evidence that the services of these firms have deteriorated over time (e.g., Coffee, 2002; Zeff,

2003). In which case, there could be merit in recent reforms such as the Sarbanes-Oxley Act

of 2002 in the US. Law, another corporate governance mechanism, could be employed to

compensate some weaknesses of the auditors (Francis, 2004).

In summary, the findings on the link between governance mechanisms and fraud are

quite ambiguous, even in the studies trying to test several mechanisms together. Beyond the

methods used in these tests, the relations among these mechanisms (complementarity,

substitutability or independence) might explain why there is no consensus. Hence, the focus

of this paper is to understand these complex relations and the effectiveness of mechanism

joint efforts using a game theoretic model.

3. MODEL

This section summarizes the model that underpins the resulting propositions in

section 4. Wilks and Zimbelman (2004) provide an overview of game theoretic models to

study the behaviors of actors committing or combating accounting fraud. A game theoretic

model permits to consider the interdependencies among agents and their strategies. This type

of model is a simplification of reality. Thus, the developing of hypotheses is bound to be a

simplification of the governance problem presented in section 2.

To study the complex coordination of governance mechanisms in combating

accounting fraud, we used a game theoretic model with three agents � ∈ {��, �, }: the top

9 The two previous studies were based on the AAERs (Accounting and Auditing Enforcement Releases). The SEC publishes these when a company violates certain important rules.

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manager � = �� and two agents playing the role of governance mechanisms. The first one, a

statutory auditor � = �, aims at detecting frauds. In contrast to the previous agent, the primary

purpose of the second agent acting as a governance mechanism, a journalist � = , is not fraud

combating. This second one can publicly reveal a fraud detected by the auditor agent. The

journalist agent may also uncover frauds to reach his or her primary goal (to sell more

newspapers, for instance). The three agents of this model are presented, namely a top manager

(3.1), an auditor (3.3) and a journalist (3.4). Before to present the auditor’s and the journalist’s

problems, the choice of a statutory auditor and a journalist as corporate governance

mechanisms and their possible interactions are exposed (3.2). The effectiveness of combining

corporate governance mechanisms’ efforts flows from the nature of their interactions, that is

their complementarity, independence, or substitutability.

3.1 THE TOP MANAGER AS A FRAUDSTER

As we study the effectiveness of combining corporate governance mechanisms’ efforts

on the behavior of the top manager, the model includes this agent. Marris (1964) asserts that

top managers maximize their utility by managing a firm. Their behavior may lead to conflicts

of interest regarding the other stakeholders of the firm. For instance, they do not always

maximize the shareholder value. As regards the issue of combatting fraud, their self-seeking

attitudes may lead them to commit frauds to maximize their short- and medium-term

objective.

According to top managers tradeoff between committing fraud and not committing

one (Becker, 1968), top managers seek to maximize their benefit by choosing a level of fraud.

In other words, Becker’s decision rule makes it possible to understand to which extent a top

manager frauds according to his or her private benefits resulting from this illegal act, and to

the risk to be caught and subject to sanctions. These sanctions include financial costs and non-

financial ones, such as a loss of reputation and legal sanctions.

The following tradeoff helps to understand to what point a top manager is willing to

accept to cultivate his or her reputation and to honor laws.

� ��������������� = � ������������������������� + � ����������������������� (1)

where E(.) is the mathematical expectation operator. The top manager seeks to draw

maximum benefit from his or her position. In this aim, this agent commits frauds to the level

equaling the mathematical expectation of the private benefits, and the sum of the

mathematical expectations of the costs due to loss of reputation and to legal sanctions for

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failing to comply with the law. The mathematical expectations of the costs increase with the

efforts of each corporate governance mechanism, as their individual efforts in combatting

fraud raise the probability of fraud detection. Hence, as recommended by Fellingham and

Newman (1985), we supposed that the top manager behaviour both is influenced by, and

influences, the actions of the two other agents: �� and �� are the efforts of the auditor and of

the journalist in combating accounting fraud, respectively.

Taking into account the auditor’s and the journalist’s efforts, in our setting, the top

manager chooses a level of fraud � maximising his or her objective function !" ��, �� , ��. The level of fraud depends on the type and the importance of fraud. This function is the

difference between the probable gains # �� resulting from covered fraud, and the probable

losses $ �� resulting from uncovered fraud: #’ �� > 0and#’’ �� < 0, and$’ �� > 0

and$’’ �� > 0.

Top manager problem:

)*+,-./ = 01 − 3456, 57, ,89: ,� − 3456, 57, ,8; ,� (2)

In this configuration, through its corporate governance mechanisms, governance

system may lead to reduce the conflicts of interest. This reduction may result in lower agency

costs and thus in improving corporate value creation.

3.2 THE AUDITOR AND JOURNALIST AS INVESTIGATORS

In their combat against fraud, the corporate governance mechanisms may be

considered as whistleblowers. That is to say, they are informers or raise the alarm bell. There

are a great many whistleblowers (e.g., the financial regulatory authorities, the financial

analysts, journalists, auditors). To justify our choice to include in our model a journalist and a

statutory auditor, the motivations of the different whistleblowers are exposed.

Dyck, Morse and Zingales (2010) wonder what motivates different actors to detect and

expose management fraud. They identified two broad factors: incentives and access to

information. Several categories of whistleblowers could be discerned.

First, stockholders, law firms, short sellers, and the SEC, for example, all have the incentive

to expose publicly fraud, but not the necessary information (especially when corrupt managers

typically hide their actions).

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Second, some potential whistleblowers, however, may lack both information and incentive.

To do such a mission, stock analysts and journalists depend on managers for information and

revealing a fraud could penalize their careers. For example Dyck, Morse and Zingales (2010)

found that stock analysts who did report management fraud tended to be “all-stars” whose

positions were secure and who had a good reputations and high credibility. Likewise,

whistleblowing journalists tended to come from big, credible media outlets that can withstand

pressure and threats from firms, often landing more future promotions after “scooping” a

fraud case.

Third, some other whistleblowers have access to information but could lack incentive to use

it, specifically, whistleblowing auditors. A distinction should be made, depending on the

respect of codes of ethics and laws by these whistleblowers (e.g., Earley, Odabashian, &

Willenborg, 2003). Foremost, in respect to codes or laws, these whistleblowers have to reveal

a fraud to the justice system, but not publicly. Information is thus kept confidential.

Sometimes, they could even prefer to hide certain frauds at all because these whistleblowers’

managers ask them to cover these frauds, or because these whistleblowers fear to lose a

customer. But some changes appear after passage of the Sarbanes-Oxley (SOX) Act and other

legislation in 2002 that increased auditors’ incentives to act in respect to law and codes of

ethics and reveal fraud. These whistleblowers could thus uncover a fraud publicly, but against

the law. In the case of public revelation of fraud, they act for prestige or because they think

scandal must be brought to light in accordance with their own understanding of justice and

social equity. Information is not kept confidential.

Finally, employees often have easy access to information. But employees are often pressured

to be complicit with managers. They have a strong incentive to keep quiet. According to

Dyck, Morse and Zingales (2010), 37% hid their identity. Of those who went public, 82%

were fired or reassigned, or quitted their company under pressure. Many former employees

fled their industries or moved away to escape personal harassment.

Among all these agents, combating fraud may be either the main mission or not. For

instance, it is the main motivation of whistleblowers as a statutory auditor or authorities (e.g.,

the SEC). Contrariwise, the main mission of other whistleblowers, namely journalists or

employees, does lead them to uncover frauds.

Hence, we chose a statutory auditor and a journalist as agents combatting fraud in our

model for at least two reasons. First, the inclusion of two agents differing in their motivations,

access to information and their incentives and goals makes it possible to enrich the analysis.

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Second, journalist and statutory auditor may be complementary, independent, or substitutable,

in the compliance or the noncompliance of the ethical, legal or regulatory standards governing

the profession.

3.3 THE STATUTORY AUDITOR ’S ROLE IN FRAUD PREVENTION , DETECTION AND REVELATION

In our setting, we assume the statutory auditor seeks to maximize his or her utility

through a costs-benefits comparison (Dyck, Morse, & Zingales, 2010). As his or her main

mission is the detection of fraud, the utility of the statutory auditor may depend positively on

the advantages from target-based bonuses, private benefits, prestige and reputation gains, and

negatively on the costs from employability and reputation losses, distrust on the part of the

customers and a loss of independence in his or her relation with the investigated top manager.

Hence, the statutory auditor agent may detect the top manager’s fraud according to this

cost-benefit tradeoff, and also helps to uncover publicly the fraud due to, voluntary or

involuntary, links, which may occur. By the detection and the public revelation of top

manager’s fraud, the agent playing the role of statutory auditor increases the possible costs

incurred by the top manager, and decreases the risk of fraud commission by the top manager.

The auditor investigates and looks for evidence in databases, internal or public

corporate documents to combat the top manager’s fraud. These investigations have a cost

< ��� that is positively correlated to the auditor’s efforts with increasing rate (<′ ��� > 0 and

<′′ ��� > 0). When the top manager’s fraud is not detected, the auditor suffers a penalty > �� increasing with the level of fraud. This penalty might be a loss of reputation, a reduction in

salary, a loss of market share, etc. Hence, the auditor chooses a level of effort to minimise his

or her objective function: � �, ��, ���.

Auditor problem:

)?@56 -64,, 56, 578 = A 56� + 01 − 3456, 57, ,89B ,� (3)

3.4 THE JOURNALIST ’S ROLE IN COMBATING FRAUD

Like the agent playing the role of statutory auditor, the journalists are supposed to seek

for maximizing his or her utility following neoclassical economic theory. Their utility

depends on their reputation, wages, bonuses, incentives, employability, sources of

information, advertising revenues, capabilities, and independence from journalistic sources,

15

etc. Unlike the statutory auditors, the journalists’ mission is to provide information, not to

detect fraud. Journalists serve as informational intermediaries (Bushee, Core, Guay, & Hamm,

2010; Bushee & Miller, 2007; Healy & Palepu, 2001). Yet, within their mission, journalists

may be incited to detect and/or publicly uncover frauds. Journalists may reveal firsthand

information, which has been detected by them. Journalists might also uncover secondhand

information, frauds discovered by other corporate governance mechanisms such as employees

(Bowen, Call, & Rajgopal, 2010) or, in our setting, statutory auditors.

In practical terms, the agent playing the role of journalist has two levers to influence

the top manager’s behavior. First, the journalist revelations may influence the top manager’s

reputation. Second, these disclosures may result in legal action.

In the right-hand side of Becker’s equation (1), the journalist agent’s efforts thus

influence the costs due to reputation loss and legal sanctions in at least three ways, namely, by

disseminating information, exposing scandals, and increasing the costs related to reputation

loss.

The journalist investigates and looks for evidence in databases, internal or public

corporate documents, and by interviewing his or her informants. These investigations have a

cost <4��8 that is positively correlated with increasing rate to the journalist’s level of effort.

When the top manager’s fraud is not uncovered, the journalist suffers a penalty > �� rising

with the level of fraud. This penalty might be a loss of reputation, a reduction in salary, a loss

of information sources. Hence, the journalist decides a level of effort to minimise his or her

objective function: � �, ��, ���.

Journalist problem:

)?@57 -74,, 56, 578 = A4578 + 01 − 3456, 57, ,89B ,� (4)

Finally, the statutory auditor and the journalist can be complementary, substitutable or

independent. The form of the probability function depends on the nature of their interactions.

Their efforts are complementary when the auditor detects the top manager’s fraud and

the journalist publicly uncovers publicly this fraud for example. Their personal efforts are

combined together enhancing the effectiveness of the fight against fraud. In this case, the

probability for the top manager to be uncovered is supposed to be of the form: �4��, �� , �8 =

16

�CD��4��, ��8. If the journalist’s effort level is lower than the one of the other agent, this

probability function depends positively on the efforts of the journalist with constant rate and

on the level of fraud with increasing rate: EFEGH = 0, EIFEGHI = 0, EF

EGJ > 0, EIFEGJI= 0, EFEK > 0, EIFEKI > 0.

If the effort level of the journalist is higher than the one of the other agent, this probability

does not depend on his or her efforts with constant rate and on the level of fraud with

increasing rate: EFEGH > 0, E²FEGHI = 0, EFEGJ = 0, E²FEGJI

= 0, EFEK > 0, E²FEK² > 0. Moreover, in the case of

complementary agents, the mixed second-order partial derivative of the probability EIF

EGHEGJ is

null. Lastly, the mixed second-order partial derivatives of the probability EIFEGHEK is positive and

EIFEGJEK is null, if the effort level of the journalist agent is higher than the one of the other agent,

and conversely.

Their efforts are substitutable when each of the two agents playing the role of

governance mechanisms endeavours to both detect and uncover the fraud. In contrast to the

previous situation, efforts of one agent could overlap or duplicate efforts of the other one and,

thus, decreases the efficiency of their effort in combating fraud. Yet, efforts of one agent can

compensate the weakness of the efforts of the other and, so, increase the efficiency of their

join efforts. Therefore, determining a priori the result of the fight against fraud seems to be

difficult. In this case, the probability � ��, �� , �� for the top manager to be uncovered is

supposed to be of the form: �4��, �� , �8 = �C��M��N. This probability function depends

positively on the efforts with decreasing rate and on the level of fraud with increasing rate:

EFEGH > 0, E²FEGHI < 0, EF

EGJ > 0, E²FEGJI< 0, EFEK > 0, E²FEK² > 0. Moreover, in the case of substitutable

agents, the mixed second-order partial derivatives of the probability function are strictly

positive.

The independence of their effort is a limit case. In this limit case, the agents follow

their own goal independently of one another. There is no interaction between the agents. In

this limit case, the probability � ��, �� , �� for the top manager to be uncovered is supposed to

be linear in �� and ��: �4��, �� , �8 = �C + O�� + P��. This probability function depends

positively on the efforts with constant rate, and on the level of fraud with increasing rate:

17

EFEGH > 0, E²FEGHI = 0, EF

EGJ > 0, E²FEGJI= 0, EFEK > 0, E²FEK² > 0. Moreover, in the case of substitutable

agents, the mixed second-order partial derivatives of the probability function are null.

In sum, for these theoretical and practical reasons, the agent playing the role of

journalist or the one of statutory auditor, in our model, may detect itself and publicly reveal

frauds. In this case, the journalist and statutory auditor agents are substitutable or

independent. If they are complementary, the journalist agent reveals publicly the frauds

detected by the statutory auditor agent.

4. RESULTS

This section presents the propositions derived from the model presented above. We

adopted three assumptions to study the influence of the efforts by two agents playing the role

of corporate governance mechanisms on the level of fraud.

4.1 ASSUMPTION 1: THE TWO AGENTS ARE INDEPENDENT

In this case, the total derivative of the first order condition of the top manager’s problem is

QR� + SR�� + T. R�� = 0, where A, B and D are negative. The total derivative of the first

order condition of the auditor’s problem is �R� + VR�� + W. R�� = 0, where � < 0, V > 0

and W = 0.

PROPOSITION 1. Given assumption 1, for any level of auditor’s effort, the increase in the

journalist’s effort decreases the level of top manager’s fraud: XKXGJ =

YZ[\]^][_Z < 0.

Proof of this proposition is provided in Appendix 1. Proposition 1 suggests that the

independence of corporate governance mechanisms justify the claims that the revelation of

fraud is improved by “densifying” the web of mechanisms and agents committed in

combating fraud. Figure 1 displays the simulated level of fraud resulting from a change in the

level of journalist effort in case of independent mechanisms.

18

Figure 1: Simulated effect of independent journalist effort ej on the level of fraud x

This proposition 1 also justifies the two following additional assumptions to study

what relation between the two mechanisms is sufficient to improve the revelation of fraud by

“densifying” the web of agents committed in combating fraud. Assumption 2 makes it

possible to study the case where the statutory auditors’ and the journalists’ efforts are

substitutable.

4.2 ASSUMPTION 2: THE TWO AGENTS ARE SUBSTITUTABLE

In this case, the total derivative of the first order condition of the top manager’s problem is

QR� + SR�� + T. R�� = 0, where A < 0, B < 0 and D < 0. Moreover, the total derivative of

the first order condition of the auditor’s problem is �R� + VR�� + W. R�� = 0, where E < 0, F

> 0 and H < 0.

Proposition 2. If assumption 2 holds, for any level of auditor’s effort, the effect of the increase

in the journalist’s effort on the level of manager’s fraud is negative: XKXGJ =

YZ[\]^][_Z < 0.

Proof of this proposition is provided in Appendix 2. Proposition 2 suggests that the

substitutability of corporate governance mechanisms is sufficient to justify the claims that the

revelation of fraud is improved by “densifying” the web of mechanisms and agents committed

in combating fraud. Figure 2 displays the simulated level of fraud resulting from a change in

the level of journalist effort in case of substitutable mechanisms.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0 0,2 0,4 0,6 0,8 1

Leve

l of t

he to

p m

anag

er a

gent

's f

raud

, x

Level of the journalist agent's effort, ej

19

Figure 2: Simulated effect of substitutable journalist effort ej on the level of fraud x

The higher the journalist effort, the lower is the level of fraud (Figure 2). However, in

the case of substitutable corporate governance mechanisms for high level of effort by the

journalist, increasing this effort further seems to be useless. Assumption 3 permits to study the

case where the statutory auditors’ and the journalists’ efforts are not substitutable, but

complementary.

4.3 ASSUMPTION 3: THE TWO AGENTS ARE COMPLEMENTARY

In this case, the relation between the level of fraud and the effort of the journalist agent is

contingent. This relation depends on the relative effort of the two agents.

If the effort level of the journalist is higher than the one of the statutory auditor, total

derivative of the first order condition of the top manager’s problem is QR� + SR�� +T. R�� = 0, where A < 0, B < 0 and D = 0. And the total derivative of the first order condition

of the auditor’s problem is �R� + VR�� + W. R�� = 0, where E < 0, F > 0 and H = 0.

Proposition 3a. If assumption 3 holds, for any level of the auditor’s effort lower than the

journalist’s effort level, the effect of an increase in the journalist’s effort on the level of

manager’s fraud is null: XKXGJ =

YZ[\]^][_Z =

`^][_Z = 0.

If the effort level of the journalist is lower than the one of the statutory auditor, total

derivative of the first order condition of the top manager’s problem is QR� + SR�� +

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,2 0,4 0,6 0,8 1

Leve

l of t

he to

p m

anag

er a

gent

's f

raud

, x

Level of the journalist agent's effort, ej

20

T. R�� = 0, where A < 0, B = 0 and D < 0. And the total derivative of the first order condition

of the auditor’s problem is �R� + VR�� + W. R�� = 0, where E = 0, F > 0 and H = 0.

Proposition 3b. If assumption 3 holds and the journalist’s effort is lower than the level of the

auditor’s effort, the effect of an increase in the journalist’s effort on the level of manager’s

fraud is negative: XKXGJ =

YZ[\]^][_Z = − \

^ < 0.

Proof of these propositions is provided in Appendix 3. Proposition 3a suggests that

neither the independence nor the substitutability of corporate governance mechanisms is

necessary to justify the claims that the revelation of fraud is improved by “densifying” the

web of mechanisms and agents committed in combating fraud. This could also be the case

where the mechanisms and agents combating fraud are complementary. However, proposition

3b suggests that the complementarity of corporate governance mechanisms is not sufficient to

justify this claims. Figure 3 displays the simulated level of fraud resulting from a change in

the level of journalist effort in case of complementary mechanisms.

Figure 3: Simulated effect of complementary journalist effort ej on the level of fraud x

The higher the journalist effort, the lower is the level of fraud, for low level of the

journalist’s effort (Figure 3). However, in the case of complementary mechanisms, higher

level of the journalist’s effort seems to have an unpredictable effect, since a bifurcation exists.

The upper part of the bifurcation displays that increasing the journalist’s effort could be

useless in combating fraud if the effort of this agent is higher than the one of the statutory

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,2 0,4 0,6 0,8 1

Leve

l of t

he to

p m

anag

er a

gent

's f

raud

, x

Level of the journalist agent's effort, ej

21

auditor. The lower part shows that increasing the journalist effort maybe effective with

decreasing rate when this effort is lower or equal to the statutory auditor’s effort.

Note that the three propositions focus on the effect of a marginal increase of the

journalist’s efforts on the level of top manager’s fraud. In the case of a marginal increase of

the statutory auditor’s efforts, the three propositions remain unchanged (Appendix 4).

5. DISCUSSION AND MODEL LIMITATIONS

Level of fraud and efforts of the agents playing the role of governance mechanisms are

bound. The effectiveness of combining agents’ efforts in combating accounting fraud is linked

to their independence or, under some conditions, to their substitutability or complementarity

(Table 1).

Relation Substitutable Independent Complementary R�R�� < 0 < 0 = 0, if ea < ej < 0, if ej < ea

Effect Less and less

effective Effective Ineffective

Less and less effective

Table 1: Effectiveness of densifying the web of mechanisms

The current research makes significant theoretical, methodological and managerial

implications.

5.1 IMPLICATIONS FOR THEORY

First of all, the present research identifies the condition of the effectiveness of a dense

web of mechanisms and agents. The results drawn from the current paper’s model partially

confirmed the claims of Dyck, Morse and Zingales (2010), and Bowen, Call and Rajgopal

(2010). Moreover, this model permits to explain the results of the studies by Gerety and Lehn

(1997), and Agrawal and Chadha (2005), which challenged corporate governance theory. Our

results thus improve our understanding of the joint effectiveness of corporate governance

mechanisms by offering a critical redirection of existing views and by offering an entirely

new point of view on this joint effectiveness. Thus, we addressed important questions

research which enables us to enhance our understanding of the links among corporate

governance mechanisms combatting fraud. To that end, we developed a model that helps us to

22

understand more precisely the effect on fraud level of the complementarity, the independence,

and the substitutability which could exist among such mechanisms.

If the assumptions of our model hold, when they independently combat top-manager’s

fraud, journalist and statutory auditor improve the effectiveness of one another as corporate

governance mechanisms. Otherwise, the complementarity among governance mechanisms

could improve the effectiveness of corporate governance systems, and value creation of firms

if and only if the agents playing the role of corporate governance mechanisms coordinate their

efforts. Such coordination seems to be unnecessary in the case where these agents are

substitutable, since increasing individual effort is effective but with decreasing rate. Thus, our

model could also advance our understanding of the heterogeneity among the results of

previous studies on the effectiveness of corporate governance mechanisms on value creation

(Aguilera, Filatotchev, Gospel, & Jackson, 2008; Becht, Bolton, & Roëll, 2003 ; Coles &

Hesterly 2000).

Moreover, our study is also important to gain a deeper understanding that doing

research in the field of corporate governance may require a systemic approach (Beatty &

Zajac, 1994; Coles & Hesterly, 2000; Zajac & Westphal, 1994). A systemic approach

necessitates studying together several corporate governance mechanisms and not only one or

two.

5.2 IMPLICATIONS FOR PRACTICE

Several managerial implications flow from these findings. First, if some agents want to join

their efforts to combat fraud, they know they should be independent to improve the

effectiveness of their fight and, finally, to enhance the performance of firms. Second, they

should hence replace a dependent mechanism by another independent mechanism (e.g., the

board and the compensation committee or employee media). In this context, each actors

combating fraud could restrain its role to the domain where it has a relative competitive

advantage. Third, the authorities could have a better understanding, if they actually would

effectively fight against fraud. More generally, to improve the effectiveness of corporate

governance system, the authorities have to take account of the combination of independent

corporate governance mechanisms. To do so, they should not just change a law. Fourth, the

results of this article could help the practitioners and stakeholders to understand the difficulty

to determine the outcomes of a mix of corporate governance mechanisms. Therefore, if they

adopt a new practice they should be aware that the consequences may be not what they

23

anticipated, especially in the case of complementary between this new practice and other

corporate governance mechanisms already used. A new law could cause significant adverse

effects. In the line of the previous idea, a corporate governance system is specific to each

firm. So, thinking that some corporate governance mechanism called “best practices” could be

implementing in each firm in the same way is a mistake. It is important to consider the

specificity of each firm and the evolution of its environment before implementing new

policies or practices.

5.3 IMPLICATIONS FOR METHOD

Lastly, the current paper introduces an original model which could be adapted to study

other issues on the effectiveness of governance mechanisms. This model can be modified to

extend research on the effectiveness of corporate governance system in combatting fraud. For

instance, the agents involved or their goal could be changed and the model could include

more than three agents.

But the current study presents also some limitations. First limitations concern the

modeling approach. To clarify the issue we simplify the reality by including only the efforts

of two agents combating top-manager’s fraud. More agents may have provided other deeper

results. Moreover, we do not consider the contingency factors like environment or evolution

of the firm.

The second limitations concern the study of the coordination between the two agents

playing the role of governance mechanisms. The sign of the mixed second-order partial

derivative of the probability of fraud detection was supposed to be constant. However, in real

setting, the sign of this mixed second-order partial derivative could be dependent on agents’

behaviours.

Considering these two types of limitations, at least two avenues for further research

may be suggested. First, an agent based model may be used to study the case where more than

two agents play the role of governance mechanism. Resulting from an agent based model,

simulations will make it possible to study the sensitivity of our propositions to the inclusion

of other agents. In this agent based model, further study might also add contingency factors to

assess the robustness of our results to endogenous or exogenous events.

24

Second, numerical experiments will permit to assess the propositions presented in

more complex setting. For instance, graphics of these numerical experiments may be used to

display the effect of a marginal increase of the journalist’s or statutory auditor’s efforts on the

level of top manager’s fraud in the case where the sign of the mixed second-order partial

derivative of the probability of fraud detection is not constant.

REFERENCES

Agrawal, A., & Chadha, S. (2005). Corporate governance and accounting scandals. Journal of Law and Economics, 48(2), 371–406.

Aguilera, R. V., Filatotchev, I., Gospel, H., & Jackson, G. (2008). An organizational approach to comparative corporate governance: Costs, contingencies, and complementarities. Organization Science, 19(3), 475–492. Association of Certified Fraud Examiners. (2002). available at: http://www.acfe.com (accessed 11 January 2013).

Beasley, M. (1996). An empirical analysis of the relation between the board of director composition and financial statement fraud. Accounting Review, 71(4), 443–465.

Beatty, R. P., & Zajac, E. J. (1994). Top management incentives, monitoring, and risk sharing: A study of executive compensation, ownership and board structure in initial public offerings. Administrative Science Quarterly, 39, 313–336.

Becht, M., Bolton, P., & Roëll, A. (2003). Corporate governance and control. In G. M. Constantinides, M. Harris, & R. M. Stulz (Eds.), Handbook of the economics of finance (pp. 1–109). Amsterdam: Elsevier.

Becker, G. S. (1968). Crime and punishment: An economic approach. Journal of Political Economy, 76, 169–217. Borden, M. (2007). The role of financial journalists in corporate governance. Fordham Journal of Corporate and Financial Law, 12(2), 311–369. Bowen, R., Call, A., & Rajgopal, S. (2010). Whistle-blowing: Target firm characteristics and economic consequences. Accounting Review, 85(4), 1239–1271. Boycko, M., Shleifer, A., & Vishny, R. (1995). Privatizing Russia. Cambridge: M.I.T. Press. Burgstahler, D., & Dichev, I. (1997). Earnings management to avoid earnings decreases and losses. Journal of Accounting and Economics, 24(1), 99–126.

Bushee, B., Core, J., Guay, W., & Hamm, S. (2010). The role of the business press as an information intermediary. Journal of Accounting Research, 48(1), 1–19.

Bushee, J., & Miller, G. (2007). Investor relations, firm visibility, and investor following. Accounting Review, 87(3), 867 – 897.

Charreaux, G. (1997). Vers une théorie du gouvernement des entreprises. In G. Charreaux (Ed.), Le gouvernement des entreprises : théories et faits (pp. 421–469), Paris: Economica.

Coffee, J. C., Jr. (2002). Understanding Enron: “It’s the gatekeepers, stupid.” Business Lawyer, 57(4), 1403–1420. Coles, J. W., & Hesterly, W. S. (2000). Independence of the chairman and board composition: Firm

choices and shareholder value. Journal of Management, 26, 195–214. Cox, J. D. (2003). Reforming the culture of financial reporting: The PCAOB and the metrics for accounting measurements. Washington University Law Review, 81(2), 301–327.

25

DeAngelo, L. E. (1981). Auditor size and audit quality. Journal of Accounting and Economics, 3(3), 183–199.

Dechow, P., Sloan, R., & Sweeney, A. (1996). Causes and consequences of earnings manipulation: An analysis of firms subject to enforcement actions by the SEC. Contemporary Accounting Research, 13(1), 1–36.

Dyck, A., Morse, A., & Zingales, L. (2010). Who blows the whistle on corporate fraud? Journal of Finance, 65(6), 2212–2253.

Dyck, A., Volchkova, N., & Zingales, L. (2008). The corporate governance role of the media: Evidence from Russia. The Journal of Finance, 63(3), 1093–1135.

Earley, C. E., Odabashian, K., & Willenborg, M. (2003). Some thoughts on the audit failure at Enron, the demise of Andersen, and the ethical climate of public accounting firms. Connecticut Law Review, 35(3), 1013–33.

Fama, E., & Jensen, M. (1983). Separation of ownership and control. Journal of Law & Economics, 26(2), 301–326.

Farber, D. (2005). Restoring trust after fraud: Does corporate governance matter? Accounting Review, 80(2), 539–561.

Fellingham, J. C., & Newman D. P. (1985). Strategic considerations in auditing. Accounting Review, 60(4), 634–650. Francis, J. R. (2004). What do we know about audit quality? The British Accounting Review, 36(4),

345–68. Gerety, M., & Lehn, K. (1997). The causes and consequences of accounting fraud. Managerial and

Decision Economics, 18(7-8), 587–599. Healy, P., & Palepu, K. (2001). Information asymmetry, corporate disclosure, and the capital markets:

A review of the empirical disclosure literature. Journal of Accounting & Economics, 31, 405–440. Jamieson, K., & Campbell, K. (2001). The interplay of influence: News, advertising, politics, and the

mass media. (5th ed.), Wadsworth: Belmont. Jensen, M., & Meckling, W. (1976). Theory of the firm: Managerial behavior, agency costs and

ownership structure. Journal of Financial Economics, 3(4), 305–360. Lennox, C. S., & Pittman, J. A. (2010). Big five audits and accounting fraud. Contemporary

Accounting Research, 27(1), 209–247. Marris, R. (1964). The economic theory of managerial capitalism. New York: Free Press. Miller, G. (2006). The press as a watchdog for accounting fraud. Journal of Accounting Research,

44(5), 1001–1033. Moris, K. (2011). La presse en tant que mécanisme de gouvernance disciplinaire. Finance Contrôle

Stratégie, 14(4), 21–66. PricewaterhouseCoopers (2011). http://www.pwc.fr/les-entreprises-ont-franchi-un-cap-en-matiere-de-

prevention-et-de-controle-des-fraudes-en-france-pres-dune-entreprise-sur-deux-declare-avoir-ete-touchee-par-la-fraude1.html (accessed 25 October 2013).

Schnatterly, K. (2003). Increasing firm value through detection and prevention of white-collar crime. Strategic Management Journal, 24(7), 587–614.

Touby, L. (1994). In the company thieves. Journal of Business Strategy, 15(3), 24–35. Wilks, J. T., & Zimbelman, M. F. (2004). Using game theory and strategic reasoning concepts to

prevent and detect fraud. Accounting Horizons, 18(3), 173–184. Yeung, B., Morck, R., & Wolfenzon, D. (2004). Corporate Governance, Economic Entrenchment and

Growth. working paper, available at: http://ssrn.com/abstract=1282564 (accessed 11 January 2013).

26

Zajac, E. J., & Westphal, J. D. (1994). The costs and benefits of managerial incentives and monitoring in large U.S. corporations: When is more not better? Strategic Management Journal, 15, 121–142.

Zeff, S. A. (2003). How the U.S. accounting profession got where it is today: Part II. Accounting Horizons, 17(4), 267–86.

Appendix. Mathematical Proofs

To prove the propositions, first, we calculated the first order condition of the top manager objective function in (2) and its total derivative.

First order condition:

a-./a, = :′ ,� − :′ ,�3456, 57, ,8 − a3

a,: ,� − ;′ ,�3456, 57, ,8 −a3a, ; ,� = b (5)

Total derivative of this first order condition:

d:ee ,� − :ee ,�. 3456, 57, ,8 − a3a, . :e ,� −

af3a,f . : ,� − :e ,�.

a3a, −

;ee ,�. 3456, 57, ,8 − a3a, . ;e ,� −

af3a,f . ; ,� −

a3a, . ;e ,�gh, + i−

a3a57 . :

e ,� −af3a,a57 . : ,� −

a3a57 . ;

e ,� − af3a,a57 . ; ,�j . h57 + d−

a3a56 . :

e ,� − af3a,a56 . : ,� −

a3a56 . ;

e ,� − af3a,a56 . ; ,�gh56 = b (6)

The total derivative of the first order condition of the top manager’s problem can be simplified:

kh, + lh56 +m.h57 = b (7)

Then, we derived the auditor objective function in (3).

First order condition:

a-6a56 = Ae 56� − a3

a56 . B ,� = b (8)

Total derivative of this first order function:

dAee 56� − af3a56f . B ,�gh56 + d−B

e ,�. a3a56 −af3a56a,B ,�g h, + i−

a²3a56a57 . B ,�j h57 = b

(9)

The total derivative of the first order condition of the auditor’s problem can be simplified:

nh, + oh56 +p.h57 = b (10)

APPENDIX 1: PROOF OF PROPOSITION 1.

In the case of independent mechanisms,

27

Q = #ee �� 01 − �4��, ��, �89 − EFEK . #e �� −

EIFEKI . # �� − #e ��.

EFEK − $ee ��. �4��, �� , �8 −

EFEK . $e �� −

EIFEKI . $ �� −

EFEK . $e �� < 0, as #′′ < 0, 1 − � > 0, �′K > 0, #′ > 0, # > 0,

�′′KK > 0, $′′ > 0, � > 0 and $′ > 0 ;

S = − EFEGH . #

e �� − EIFEKEGH . # �� −

EFEGH . $

e �� − EIFEKEGH . $ �� < 0, as �′GH > 0, #′ > 0,

�ee��� = 0, # > 0, $′ > 0, $ > 0 ;

T = − EFEGJ . #

e �� − EIFEKEGJ . # �� −

EFEGJ . $

e �� − EIFEKEGJ . $ �� < 0, as �′GJ > 0, #′ > 0, # > 0

�’’��� = 0, $′ > 0, $ > 0 ;

� = −>e ��. EFEGH −EIFEGHEK> �� < 0, as >′ > 0, �′GH > 0, �′′��� = 0, > > 0 ;

V = <ee ��� − EIFEGHI . > �� > 0, as <′′ > 0, �′′GHGH = 0, > > 0 ;

W = − EIFEGHEGJ . > �� = 0, as > > 0,

E²FEGHEGJ = 0.

To prove this proposition and to study the effect of the journalist’s effort on the level of fraud, we solved the system obtain using equations (7) and (10).

R�R�� =

WS − TVQV − �S

As A, B, D and E are strictly negative, F is strictly positive,QV − �S is strictly negative. And

as H is null, WS − TV is strictly positive and thus XKXGJ < 0. □

APPENDIX 2: PROOF OF PROPOSITION 2.

In the case of substitutable mechanisms,

Q = #ee �� 01 − �4��, ��, �89 − EFEK . #e �� −

EIFEKI . # �� − #e ��.

EFEK − $ee ��. �4��, �� , �8 −

EFEK . $e �� −

EIFEKI . $ �� −

EFEK . $e �� < 0, as #′′ < 0, 1 − � > 0, �′K > 0, #′ > 0, # > 0,

�′′KK > 0, $′′ > 0, � > 0 and $′ > 0 ;

S = − EFEGH . #

e �� − EIFEKEGH . # �� −

EFEGH . $

e �� − EIFEKEGH . $ �� < 0, as �′GH > 0, #′ > 0,

�ee��� > 0, # > 0, $′ > 0, $ > 0 ;

T = − EFEGJ . #

e �� − EIFEKEGJ . # �� −

EFEGJ . $

e �� − EIFEKEGJ . $ �� < 0, as �′GJ > 0, #′ > 0, # > 0

�’’��� > 0, $′ > 0, $ > 0 ;

28

� = −>e ��. EFEGH −EIFEGHEK> �� < 0, as >′ > 0, �′GH > 0, �ee��� > 0, > > 0 ;

V = <ee ��� − EIFEGHI . > �� > 0, as <′′ > 0, �′′GHGH < 0, > > 0 ;

W = − EIFEGHEGJ . > �� < 0, as > > 0,

E²FEGHEGJ > 0.

To prove the proposition 2 and to study the effect of the journalist’s effort on the level of fraud, we solved the system obtain using equations (7) and (10).

R�R�� =

WS − TVQV − �S

As A, B, D and E are strictly negative, F is strictly positive,QV − �S is strictly negative. And

as H is negative, WS − TV is strictly positive and thus XKXGJ < 0. □

APPENDIX 3: PROOF OF PROPOSITIONS 3A AND 3B.

In the case of complementary mechanisms, if �� < ��,

Q = #ee �� 01 − �4��, ��, �89 − EFEK . #e �� −

EIFEKI . # �� − #e ��.

EFEK − $ee ��. �4��, �� , �8 −

EFEK . $e �� −

EIFEKI . $ �� −

EFEK . $e �� < 0, as #′′ < 0, 1 − � > 0, �′K > 0, #′ > 0, # > 0,

�′′KK > 0, $′′ > 0, � > 0 and $′ > 0 ;

S = − EFEGH . #

e �� − EIFEKEGH . # �� −

EFEGH . $

e �� − EIFEKEGH . $ �� < 0, as �′GH > 0, #′ > 0,

�ee��� > 0, # > 0, $′ > 0, $ > 0 ;

T = − EFEGJ . #

e �� − EIFEKEGJ . # �� −

EFEGJ . $

e �� − EIFEKEGJ . $ �� = 0, as �′GJ = 0, #′ > 0, # > 0

�’’��� = 0, $′ > 0, $ > 0 ;

� = −>e ��. EFEGH −EIFEGHEK> �� < 0, as >′ > 0, �′GH > 0, �ee��� > 0, > > 0 ;

V = <ee ��� − EIFEGHI . > �� > 0, as <′′ > 0, �′′GHGH = 0, > > 0 ;

W = − EIFEGHEGJ . > �� = 0, as > > 0,

E²FEGHEGJ = 0.

To prove the proposition 3a and to study the effect of the journalist’s effort on the level of fraud, we solved the system obtain using equations (7) and (10).

R�R�� =

WS − TVQV − �S

29

As A, B and E are strictly negative, F is strictly positive,QV − �S is strictly negative. And as

H and D are null, WS − TV is null and thus XKXGJ = 0. □

In the case of complementary mechanisms, if �� < ��,

Q = #ee �� 01 − �4��, ��, �89 − EFEK . #e �� −

EIFEKI . # �� − #e ��.

EFEK − $ee ��. �4��, �� , �8 −

EFEK . $e �� −

EIFEKI . $ �� −

EFEK . $e �� < 0, as #′′ < 0, 1 − � > 0, �′K > 0, #′ > 0, # > 0,

�′′KK > 0, $′′ > 0, � > 0 and $′ > 0 ;

S = − EFEGH . #

e �� − EIFEKEGH . # �� −

EFEGH . $

e �� − EIFEKEGH . $ �� = 0, as �′GH = 0, #′ > 0,

�ee��� = 0, # > 0, $′ > 0, $ > 0 ;

T = − EFEGJ . #

e �� − EIFEKEGJ . # �� −

EFEGJ . $

e �� − EIFEKEGJ . $ �� < 0, as �′GJ > 0, #′ > 0, # > 0

�’’��� > 0, $′ > 0, $ > 0 ;

� = −>e ��. EFEGH −EIFEGHEK> �� = 0, as >′ > 0, �′GH = 0, �ee��� = 0, > > 0 ;

V = <ee ��� − EIFEGHI . > �� > 0, as <′′ > 0, �′′GHGH = 0, > > 0 ;

W = − EIFEGHEGJ . > �� = 0, as > > 0,

E²FEGHEGJ = 0.

To prove the proposition 3b and to study the effect of the journalist’s effort on the level of fraud, we solved the system obtain using equations (7) and (10).

R�R�� =

WS − TVQV − �S

As A and D are strictly negative, F is strictly positive, and B and E are null,QV − �S is

strictly negative. And as H is null, WS − TV is strictly positive and thus XKXGJ < 0. □

APPENDIX 4. STATUTORY AUDITOR’S MARGINAL EFFORT EFFECT ON THE LEVEL OF FRAUD

We derived the journalist’s objective function in (4).

First order condition:

a-7a57 = Ae4578 − a3

a57 . B ,� = b (11)

Total derivative of the first order function:

30

iAee4578 − af3a57f

. B ,�j h57 + i−Be ,�. a3a57 −af3a57a,B ,�jh, + i−

a²3a57a56 . B ,�jh56 = (12)

The total derivative of the first order condition of the auditor’s problem can be simplified:

neh, + oeh57 +pe. h56 = b (13)

To prove the propositions hold and to study the effect of the statutory auditor’s effort on the level of fraud, we solved the system obtain using equations (7) and (13).

XKXGH =

ZYr[\]e^]e[Z_e

As E’, F’ and H’ have the same signs as E, F and H respectively, the propositions 1, 2, and 3a and 3b remain unchanged. □