Laurent Germain

Université de Toulouse, Toulouse Business School

Université de Toulouse, Toulouse Business School

[email protected]

[email protected]

April 2012

Abstract The aim of this paper is to study what are the e¤ects of Board monitoring and incentive compensation on the …rm performance in a framework with asymmetric information and uncertainty about the optimal projects for the …rm. We also analyze how collusion between the Board and the CEO may in‡uence both parties’behavior. In particular, we examine the optimal intensity with which the Board monitors the CEO and show that it depends on the incentive contract o¤ered. We also provide empirical predictions about the relationship between the intensity of monitoring, incentive compensation and …rms’characteristics. Keywords: Collusion, Corporate Governance, Asymmetric Information, Uncertainty. JEL Classi…cation: D81, D82, G34.

1

Introduction

Collusion between Boards of Directors’ members and the CEO may be a major problem for the governance of …rms. Indeed, most of the recent corporate scandals in the US or in Europe have emphasized the importance of corporate governance in the management of …rms. For instance, a signi…cant proportion of Board members of the Vinci Group in Europe or Worldcom and Home Depot in the US proved to be ever loyal to their CEO. An example of such a behavior is highlighted in The Boston Globe (January 6, 2007): "Despite his failure to increase the value of Home Depot’s stock, chief executive o¢ cer Robert Nardelli left the company this week with a $210 million farewell We thank Gilles Chemla, Francesca Cornelli, Mara Faccio, Daniel Ferreira, Urs Peyer, Charu Raheja, Silvia Rossetto, David Thesmar and participants to the Toulouse Business School Corporate Governance workshop, the EEA-ESEM 2011 conference in Oslo and to the CASS Business School, EM Lyon and Rouen Business School seminars for helpful comments. All remaining errors are ours.

1

package, the result of an agreement he negotiated with the board of directors in 2000. Across America, a culture of collusion between board members and prospective CEOs in‡ates executive pay and needs to be checked by greater shareholder involvement." Those "collusive" directors (some of them referred to as the "Bernie’s Boys" for Worldcom) vote in favor of the CEO’s propositions and allow her to get among other things generous bonuses, severance packages and golden retirement pensions. In many of those cases of "bad governance," one of the main issues was an explicit or implicit collusion between Directors of the Board and the CEO. The aim of this paper is to study what are the e¤ects of Board monitoring and incentive compensation on the …rm’s performance. The Sabarnes-Oxley Act, the NYSE and the NASDAQ regulations in the US request that independent directors, who are supposed to supervise more e¢ ciently …rms’ top executives, play a more important role in boards of directors. In order to study the e¢ ciency of such requirements, we examine what should be the optimal intensity with which the Board of Directors monitors the CEO from a shareholders perspective and show that it depends on the incentive compensation o¤ered. In our setting, the CEO has to choose between two projects that di¤er by their level of risk. The CEO’s ability to undertake projects (High or Low) is unknown by the shareholders. The level of risk of the projects and the CEO’s ability are her private information. Selecting a too risky project while it is not optimal for the …rm yields a private bene…t to the CEO. This private bene…t may represent her utility from deriving various advantages such as perks, or building empires. In order to limit the CEO’s discretion, shareholders have the opportunity to select the intensity with which the CEO will be monitored by the Board. In practice, this may result in increasing the number of independent directors, limiting the number of interlocked directors and the number of mandates held by each director, separating the role of Chairman and CEO, increasing the power and ensuring the independence of the main committees, or strengthening the internal audit process.1 We also allow for the possibility of collusion between the board and the CEO. Collusion takes place through a bribe o¤ered by the CEO to some Directors in order to induce them not to reveal to shareholders that she has made a bad decision for the …rm. Such a bribe may be a monetary or a non monetary transfer (e.g. future salary increases, perks, insurance to stay in the Board,...). Consequently, the collection of information from the CEO by shareholders may be more di¢ cult and more costly because collusion reduces the toughness of monitoring by directors. Monitoring of the CEO by the Board of Directors in‡uences the CEO’s behavior.2 Indeed, the lower is the intensity of monitoring, the more the Board’s information about the type of the project is precise, but also the more the Board is prone to engage in collusion with the CEO, both due to his relationships with the CEO (degree of con…dence, local networking, bargaining power) and his executive role in the …rm for instance.3 1

See Faleye, Hoitash and Hoitash (2011) or Ferreira, Ferreira and Raposo (2011). Notice that in our model, even though the Board may report information about the type of the project that has been advised by the CEO, we focus on his monitoring role. 3 See Ferreira, Ferreira and Raposo (2011) for instance. 2

2

This framework allows us to derive the optimal compensation contract of the CEO which consists of a …xed and a variable part. More precisely, our results are the following. First, we consider as a benchmark the case of no board of directors (or equivalently the case of no CEO’s monitoring by the directors). In this setting, we show that the variable part of the CEO’s wage is higher for a high ability CEO than for a low ability CEO. Then, we allow shareholders to recruit a Board of Directors in order to monitor the CEO, assuming that collusion cannot emerge. An interesting result is that the Board behaves as a perfectly honest Board. The contract takes the same form as the one with no monitoring i.e. no informational rent for a low ability CEO and a positive informational rent for a high ability CEO. Those informational rents correspond to the surplus a CEO can extract from the shareholders thanks to her informational advantage. However, informational rents are lower in this case than when there is no monitoring from the Board. This implies that it is less costly for shareholders to obtain information from the CEO when the Board monitors him. This enables us to characterize a threshold wage such that if the Board’s wage is lower than this threshold, recruiting a Board of Directors in order to monitor the CEO is always bene…cial for the shareholders. Allowing for the possibility of collusion between the board and the CEO, we show that the optimal contract is collusion proof: it is optimal for the shareholders to o¤er a contract preventing collusion to emerge. The optimal contract is designed such that shareholders have to concede to the CEO the same informational rents as in the presence of a perfectly honest board. However, they also have to ensure that the coalition Board-CEO does not collude which is costly in terms of informational rents. We also prove that there exists a degree of independence of the Board above which it is not pro…table for the coalition Board-CEO to engage in collusion. In this case, shareholders do not have to care about preventing collusion when designing the optimal contract. The Board will therefore behave as a perfectly honest Board. To our knowledge, our paper is the …rst theoretical model to consider the possibility of explicit collusion between the Board of Directors and the CEO. However, collusion has received a large attention in the Mechanism Design literature. The seminal paper of Tirole (1986) studies a threetier organization with a principal, a supervisor and an agent in a moral hazard framework. In Tirole (1986), the agent and the supervisor can collude. Tirole (1986) derives the optimal collusion-proof contract. In our model and in another context with adverse selection, we also tackle this problem and derive the optimal collusion-proof contract.4 Faure-Grimaud, La¤ont and Martimort (2003) also study, in an adverse selection model, the optimal design of organization and the value of delegation when the supervisor and the agent can collude against the principal. We also derive the optimal intensity with which the Board monitors the CEO. Notice that this intensity corresponds to the most e¢ cient incentive compensation contract that allows shareholders to pay the lowest informational rents to the CEO. Contrary to the usual idea that an optimal Board should be strongly monitored, we …nd that shareholders may prefer to select a low intensity 4

Our paper di¤ers from Tirole (1986) as we introduce the possibility that the CEO (the agent) chooses between di¤erent projects of investments and that the possibility of collusion is a¤ected by the composition of the board. Moreover, we study what would be the optimal supervisor (board of directors) in the context of corporate governance.

3

of monitoring. Indeed, when designing the optimal compensation contract, shareholders face a trade-o¤ between the information that they may extract from the Board and the costs from both extracting it and avoiding collusion. We then characterize conditions under which it is optimal to select a low intensity of monitoring. Those conditions are the following: the risk of both projects have to be close and the intensity of monitoring necessary to have a perfectly honest Board should be high enough. However, when project 2 is too risky compared to project 1 or when the intensity of monitoring necessary to have a perfectly honest Board is low enough, it is optimal to select a low intensity of monitoring. In this case, the shareholders should not care about collusion because collusion is not pro…table for such Boards. Indeed, when the level of relative risks of the two projects is high, it is of great importance to monitor the CEO and prevent him to choose too a risky and non pro…table project for the shareholders. In this case, shareholders should select a high intensity of monitoring. The problem is less acute when the risks of the two projects are close. This is consistent with empirical results. In particular, Demsetz and Lehn (1985) and Ferreira, Ferreira and Raposo (2011) show respectively that more monitoring is needed in riskier environments and in more complex …rms. This …nally allows us to provide empirical predictions about the relationship between the intensity of monitoring, incentive compensation and …rms’characteristics. There is a large literature in corporate governance about the composition of Boards of Directors (Boone, Field, Karpo¤ and Raheja, 2007, Dahya and McConnell, 2007, Harris and Raviv, 2006, Linck, Netter and Yang, 2008, Raheja, 2005), the relationship between the structure of Boards of Directors and the CEO compensation (Chhaochharia and Grinstein, 2009) as well as the monitoring role (Hermalin and Weisbach, 1998, or Cornelli, Kominek and Ljungqvist, 2010) and the advisory role of the boards of directors (Adams and Ferreira, 2007). Nevertheless, the problem of potential collusion between the CEO and the board has received little attention.5 Our paper is closely related to Adams and Ferreira (2007) work. In their model, there is a continuum of projects but the projects do not di¤er with their level of risks. The CEO is reluctant from transmitting information to the Board of Directors because of the Board’s monitoring role. The composition of the board of directors in‡uences the behavior of the CEO as the more independent is the board of directors the more the CEO is monitored and the less the CEO is inclined to share information with the board. We share their result stating that it may be optimal for the shareholders to choose a Board who is reluctant to monitor the CEO . However, the force driving our result is di¤erent from theirs. In Adams and Ferreira, when the Board’s independence level is low, there is a low probability for the CEO to lose control. This makes revelation of information less costly for him and implies that choosing such a Board may be optimal for the shareholders. In our article, shareholders choose a Board with a low level of CEO’s monitoring because of its greater ability to collect information which allows them to make a better investment decision. Moreover, they do not explicitly model collusion between the CEO and the board members. Another related paper is Hermalin and Weisbach (1998) who analyze the role of independent 5

For reviews of the Corporate Governance literature, see Adams, Hermalin and Weisbach (2010), Bebchuk and Weisbach (2010),or Tirole (2001).

4

directors in boards and the intensity of monitoring and show that a bad CEO is more likely to be replaced when the board is independent. Independent directors are therefore a mean for controlling the performance of the …rm and a threat for bad CEOs. While we also examine the optimal intensity of monitoring, we focus on Board’s monitoring of the relative risk of the …rm’s projects and not on Board’s monitoring of the CEO’s ability. Moreover, we also characterize the optimal incentive compensation for the CEO and the role of collusion on the Board’s monitoring role. Hermalin (2005) studies the decision of hiring an internal vs an external CEO. Less is known about the external CEO. The model he develops determines whether it is optimal to keep an existing CEO or to replace him at a certain cost. While we do not address the question of the replacement of the CEO, monitoring of the CEO by the directors may entail a high …ne for him which may be interpreted as his dismissal. Raheja (2006) studies the question of the optimal composition and the ideal size of Boards of Directors. In the model, the optimal board structure is determined by the trade-o¤ between insiders’ incentives to reveal their private information and the outsiders’ costs to verify projects. We also derive the optimal intensity of monitoring of the CEO, which may be interpreted by the Board’s composition in Raheja’s model, taking into account the collusive behavior of CEO and directors. The article is organized as follows. Section 2 describes the model. Section 3 analyzes the benchmark case of no monitoring of the CEO by the Board while section 4 introduces Board monitoring. Section 5 studies the impact of collusion on our results. The optimal intensity with which the Board monitors the CEO is characterized in section 6. Finally, section 7 o¤ers conclusions.

2 2.1

The Model The CEO and the Projects of the Company

A …rm can undertake a project which yields an uncertain payo¤. The …rm is run for the shareholders by a CEO, i.e. the CEO’s task is to select the project that will be undertaken by the …rm. The CEO’s ability to succeed in the projects may be either low, = ; with probability ( ) or high, = with probability (1 ): As corresponds to a low CEO’s ability and to a high ability, we have . We assume that the …rm can undertake two kinds of projects that di¤er with their level of risk. The implementation of those projects initially require a …xed investment I by the …rm’s shareholders. The characteristics of those projects are the following: Project 1 either succeeds, that is, yields veri…able income R > 0 or fails, that is, yields no income. The probability of success is denoted by (q1 ): Moreover, this project may have a low probability of success, that is, q1 =p i with probability ( ) or may have a high probability of 5

success q1 = p i with probability (1 in the projects.

) where

i

2

;

is the CEO’s ability to succeed

In the same way, Project 2 either succeeds, that is, yields veri…able income R > 0 or fails, that is, yields no income. The probability of success is denoted by (q2 ): Moreover, this project may have a low probability of success, that is, q2 = (p ") i with probability ( ) or may ) where i 2 ; have a high probability of success q2 = (p + ") i with probability (1 is the CEO’s ability to succeed in the projects. The success and the failure of both projects are assumed to be perfectly correlated i.e. ( ) represents the probability that the economic context is bad for the type of projects considered by the …rm while (") represents the relative volatility of project two compared to project one. As the Net Present Value of the riskiest project has to be at least higher than the NPV of the other project, we have: (p

")

i

+ (1

) (p + ")

i

R

I

p

i

+ (1

)p

i

R

I:

This is equivalent to: 1 : 2 The CEO perfectly knows both her ability’s type and the probability of success of the projects while shareholders only know their prior probability distributions. The CEO may therefore send signals to shareholders about her type and the project she advises to select: 8 > " and q1 = p > L;L = ( = ; Project 1) ) q2 = p > > < L;H = ( = ; Project 2) ) q2 = p + " and q1 = p > " and q1 = p H;L = ( = ; Project 1) ) q2 = p > > > : H;H = ( = ; Project 2) ) q2 = p + " and q1 = p

The CEO’s compensation is composed by a …xed part i;j and a variable part i;j that depends on the pro…ts from the project ( ) where i 2 fL; Hg corresponds to the CEO’s signal about her ability (called hereafter the CEO’s type) and j 2 fL; Hg corresponds to the CEO’s signal about the probability of success of the project (called hereafter the best project’s type). We assume that CEO’s compensation is designed by the …rm’s shareholders or equivalently by a compensation committee whose members’objectives are in line with shareholders’ones6 . When Project 2 is selected while it has a low probability of success q2 = (p "), the CEO receives a private bene…t B which represents his private compensation for choosing a project that poorly performs. In this state of nature, the CEO should rationally choose Project 1 but this private bene…t may induce him to misbehave. The CEO’s reservation wage is w. 6

Bizjack, Lemmon, and Naveen (2008) document that most …rms in the US use a compensation committee that relies on recommendations from outside consultants, peer groups and competitive benchmarking in order to structure the CEO’s compensation. They show that total compensation is usually anchored to the peer group.

6

2.2

The Board of Directors

Shareholders also have the opportunity to hire a Board. Even though the Board may report information about the type of the project that has been advised by the CEO, his main role is to monitor the information communicated by the CEO. Monitoring of the CEO by the Board of Directors is endogenous, in the sense that shareholders choose it. Lower is this intensity of monitoring, more the Board’s information about the type of the project is precise, but also more the Board is prone to engage in collusion with the CEO. Indeed, a low level of monitoring by the Board, because of close relationships with the CEO, a high degree of con…dence between both parties, their repeated interaction, or local networking for instance, may induce the CEO to share more information about the projects with the Board7 but also makes collusion more easily enforceable. In practice, increasing the intensity with which the Board monitors the CEO would correspond to an increase in the number of independent directors, a limited number of interlocked directors and mandates held by each director, a separation of the role of Chairman and CEO, an increase in the power and in the independence of the main committees, or an improvement of the internal audit process. We model monitoring of the CEO by the Board of Directors by a variable 2 [ min ; +1]; with 1; that acts as a discount factor for the collusion’s rents. When this intensity of monitoring, min ; increases, the amount of information hold by a Board decreases while his willingness to engage in collusion decreases. can also be interpreted as the shareholders’ willingness to increase the degree of toughness and also the enforceability of the Corporate Governance regulations and the laws against collusion. Tougher are those laws, more di¢ cult it is for the coalition Board-CEO to engage in collusion. Let ( ) = 1 be the probability that a Board with an intensity of monitoring has gathered the true information about the economic context for the type of projects considered by the …rm. When increases, Board monitoring increases and Board members are less prone to collusion. However, as they have less information about the …rm, their probability of knowing the truth is lower. We also assume that the CEO incurs a …ne F when the Board reveals to the shareholders that she has announced that the project has a high probability of success while it is a project with a low probability of success, i.e. the case in which she gets the bonus B. We are particularly interested in determining the value of the intensity of monitoring such that the Board is completely honest and never accepts to engage in collusion with the CEO (this however means that he has a less precise information about the type of the project). When collusion takes place, we assume that the CEO shares the collusive pro…ts with the Board. As it is usually the case in practice, the Board’s wage is the total amount of the directors’fees which is constant and equals to w0 . Notice that, as in Hermalin and Weisbach (1998), Hermalin (2005) or Adams and Ferreira (2007), we assume that the objectives of Board members can be aggregated. This implies that the Board behaves as if he was a single agent. 7

See Adams and Ferreira (2007) for instance.

7

2.3

Multidimensional Screening Model

This model is a multidimensional screening model. Solving this kind of model is usually very complex (see Rochet and Chone, 1998). However, the structure of the model allows us to reduce this problem’s complexity. Indeed, as the CEO’s program can be speci…ed as a function of only one parameter, i;j , we can rewrite the model as a usual four types unidimensional screening model. In this case, i;j is de…ned in the following way: 8 > > L;L = p > > < L;H = (p + ") > H;L = p > > > : H;H = (p + ")

Moreover, we assume that p " (p + ") ; i.e. a high ability CEO undertaking a project with a low probability of success is more likely to succeed than a low ability CEO undertaking a project with a high probability of success. This assumption highlights the positive role of the CEO in her management of projects. Denote the …rm’s pro…ts j ( i;j ) = i;j R I: The shareholders maximize their expected pro…ts: W = + (1

3

)

1 1

1

L;L 1

H;L

(

(

L;L )

+ (1

L;L

H;L )

H;L

)

+ (1

1

)(1

)

2

L;H

1

H;H

(

L;H ) 2

(

L;H

H;H )

H;H

No CEO’s Monitoring by the Board

When they do not induce the Board of Directors to monitor the CEO, shareholders maximize their expected pro…ts under the usual Participation and Incentive constraints. P Cij is the Participation constraint of a CEO with ability i 2 fL; Hg when the project is of type j 2 fL; Hg. The Participation constraints ensure that the CEO will earn at least her reservation wage w. ICij!kl is the Incentive constraint of a CEO who reveals that her ability is k 2 fL; Hg and the project is of type l 2 fL; Hg while her true ability is i and the true type of the best project is j. The Incentives constraints ensure that the CEO earns a higher wage revealing the truth than lying to the shareholders. Through this process, shareholders induce the CEO to reveal her true type. Those constraints are stated here: i;j HH HH

+

HH

HH

+

+

(p + ") R HH

(

HH

+

HH )

I

(p + ") R

j

i;j

(

i;j )

HL

LH

+

+

LH

LL

+

I

8

w

(P Cij )

HL

p R

I

(p + ") R LL

p R

I

(ICHH!HL ) I

(ICHH!LH ) (ICHH!LL )

+

HL HL

HL

+

HL

p R

I

p R

I

HL LH

+

LH

LH

+

LL

LH

HH

p

"

R

I +B

(ICHL!HH )

LH

+

LH

p

"

R

I +B

(ICHL!LH )

p R

I

I

HH

I

(p + ") R

I

+

LH

+

LL

p R

LL

+

(p + ") R

LH

+

HL

(p + ") R

LL LL

+

HH

I +

HH

p R

LL

p R

+

I

LH

p R

I

(ICHL!LL )

(p + ") R

I

(ICLH!HH )

LL

+

HH

HL

+

HL

p R

I

(ICLH!HL )

LL

+

LL

p R

I

(ICLH!LL )

p

"

HH

I +

+

LL

+

HL

p

LH

R HL

"

I +B p R

R

(ICLL!HH )

I

(ICLL!HL )

I +B

(ICLL!LH )

Moreover, the Spence Mirrlees condition has to be satis…ed, that is: HH

HL

LH

LL

By assumption, we know that the following condition is satis…ed: p

"

(p + ")

0

(1)

As usual in this kind of problem, the binding constraints are8 : LL

LH

+

(p + ") R

LH

+

LL

p R

I

=

LL

+

LL

p R

I

=

LL

+

LL

p R

I +

I =w

= w+

HL

+

HL

p R

I

=

LH

+

LH

=

LH

+

LH

= w+

HH

+

HH

(p + ") R

I

LL R

p

"

LL R

R

LH R

+

HL

p R

I

=

HL

+

HL

p R

I +

p+

p

LH R

(ICHL!LH )

LH R

p

HL

LL R

LL R

p

I

=

= w+

(ICLH!LL )

I +B

(p + ") R p+

(P CLL )

p

(p + ")

"

+

p

"

+B

+B (ICHH!HL )

HL R

p

p

p "

+

+

HL R

p+B

Then we can characterize the optimal contract when there is no monitoring from the Board in the …rm’s organization. This is stated in the following Proposition: 8

We check that all constraints are satis…ed in the Appendix.

9

Proposition 1 When they do not induce the Board of Directors to monitor the CEO, shareholders must concede the following informational rents to a CEO ULL = w ULH

= w

UHL = w +

UHH

=

B p " [ p + 2"]

8 < w+ :

B (p ")p(

)2

if "

[ p+2"][p p ] (p+") w + B [ p+2"]

Moreover, the shareholders’ expected pro…ts are 8 (1 )B (p ") > < E( ) w ( p+2") WN M = > : E( ) w (1 ) (p + "

if "

p

+p

"nb

p+p p

if "

2 ")

B ( p+2")

p

p

p

"nb =

"nb if "

"nb

A low ability CEO does not receive any rent whatever the type of project she advises to select. However, when her signal pushes shareholders to select the project with the highest volatility (Project 2), she receives a variable wage while she only gets a …xed wage when shareholders are induced to select Project 1. A high ability CEO receives an informational rent which is higher when her signal induces shareholders to select the project with the highest volatility (Project 2) than when shareholders are induced to select Project 1. Moreover, the variable part of her wage is higher when project 2 is selected than when it is Project 1. But, in any case, the variable part of a high ability CEO is higher that the one of a low ability CEO. Finally, this highest informational rent when Project 2 is selected takes di¤erent forms depending on the projects’ relative volatility. Indeed, in order to induce the CEO to reveal the truth, the variable part of her wage has to be set as high as possible. If the relative volatility between both projects is low, a high ability CEO only has low incentives to lie about her type. However, when this relative volatility increases, the relative weight of the CEO’s ability in i;j decreases. This reduces the CEO’s loss when lying about her ability. It is then necessary to ensure that she will not misreport her ability. This is made in increasing a high ability CEO’s variable wage when the relative volatility between both projects exceeds some threshold.

4

Board Monitoring

In this section, we assume that the Board has the ability to monitor the CEO but that collusion is not possible between both parties9 . When shareholders hire a Board, the CEO may incur a loss 9

We examine the case of collusion in the next section.

10

F when the Board has found that she has announced that the Project has a high probability of success while it is a low probability of success project, i.e. the case in which she has the bonus B. The Participation and Incentive constraints are now: ij HH HH

+

+

HH

HH

+

HL

+

HL

p R

HL

+

HL

p R

LH

+

LL

(p + ") R

+

p R

I

I

LH

+

( ))

(p + ") R

I

HL

+

LH

LL

+

(p + ") R

I

(1

HH

I

+

( )) LL

( ))

p R LH

+

HH

I

LH

(1

HH

(p + ") R

LL LL + LL

LH

+

(P Cij ) p R

I

(p + ") R LL

p R

p

"

(ICHH!HL ) I

(ICHH!LH )

I

(ICHH!LL )

I + B + ( ) (w F ) (ICHL!HH ) I (1 ( )) LH + LH p " R I + B + ( ) (w F ) (ICHL!LH ) I I (ICHL!LL ) LL + LL p R HL + HL p R

LH

(1

HL

I

w

ij ij

I

(p + ") R

I

LH

p R

(p + ") R

HH

+

LH LL

HH

+

+

HH

+

HH

HL

+

HL

p R

I

(ICLH!HL )

LL

+

LL

p R

I

(ICLH!LL )

p

"

+

HH

I LH

R

HL

p

(p + ") R

+

"

HL

R

I

(ICLH!HH )

R

I + B + ( ) (w F ) (ICLL!HH ) (ICLL!HL ) p R I I + B + ( ) (w

F ) (ICLL!LH )

We also assume that the CEO faces a limited liability constraint, i.e., even if the Board found that the CEO has sent the wrong signal, she cannot get less than her reservation wage plus a …xed amount, K representing for instance the minimal compensation written in the CEO’s labor contract. This gives: (1

( )) fw + Bg + ( ) (w ,B

F)

w+K

(LL)

( ) F +K (1 ( ))

The binding constraints are: LL

LH

+

LH

(p + ") R

+

LL

p R

I

=

LL

+

LL

p R

I

=

LL

+

LL

p R

I +

= w+ 11

I =w

LL R

(P CLL )

p

(ICLH!LL ) LL R

p

HL

HH

+

+

p R

HL

HH

I

= (1

( ))

= (1

( ))

= (1

( )) w +

(p + ") R

I

LH

(

+

p

I + B + ( ) (w F ) ) I LH + LH (p + ") R + ( ) (w p " +B LH R (p + ") LH

"

p+

LL R

R

LH R

=

HL

+

HL

p R

I

=

HL

+

HL

p R

I +

= (1

( )) w +

+ ( ) (w

p

"

+

F)

+ B + ( ) (w (ICHH!HL )

HL R

p+

LL R

F) +

p

(ICHL!LH )

HL R

p

LH R

p

p

"

+

+B

p

The optimal contract when there is Board monitoring and when collusion is not achievable is characterized in the following Proposition: Proposition 2 When the Board of Directors is able to monitor the CEO and when collusion is not possible, shareholders must concede the following informational rents to a CEO ULL = w ULH

= w

UHL = w + (1

UHH

=

8 (p ")p( > < w+ [ > :

@

"

( )) p

)2 [(1

p

( )F ]

]h

B

(p+")

B

( ) (1 ( )) F

(p + ")

( ))B

p+2"][p

w+

h

0

(1

p

if " ( ) F ( ))

[(p+") (p ")]

i

A

"

"ib = i

1

if "

(1

p

( ))

( )p p

+p

"ib

Moreover, the shareholders’ expected pro…ts are 8 i h ( ) B (1 ( )) F > > < E( ) w w0 (1 )(1 ( ))(p ") + (1 ( p+2") h i WM = ( ) > B (1 ( )) F > : E( ) w w0 (1 ) (1 ( ))(p ") + (1 ( p+2")

) pp

if "

"ib

)(p + ") if "

"ib

p

In this case, the optimal contract has the same form than without monitoring, i.e. no rent for a low ability CEO and a positive rent for a high ability CEO which is higher when Project 2 is selected following her advice. However, it is worth to notice that the informational rents extracted by a CEO when there is a monitoring Board of Directors having no possibility to collude are lower than when there is no monitoring whatever the CEO’s type. Moreover, we can prove that "ib "nb . Indeed, "ib

"nb =

p (1

) () 2

p +

p p p

p 12

+ p

0:

p p

0;

F)

This also allows us to conclude that if the Board’s wage is low enough, inducing the Board to monitor the CEO is always bene…cial for the shareholders when collusion is not possible, i.e. WIB WN B for all w0 w f0 : Corollary 3 There exists a Board’s wage w f0 such that for all w0 w f0 ; inducing the Board to monitor the CEO is always bene…cial for the shareholders when collusion is not possible

To conclude this section, notice that when collusion is not achievable, it is optimal for the shareholders to choose the intensity of monitoring as low as possible. Indeed, if the Board has no incentives to hide the information he has gathered, it is in the shareholders’interest to choose the Board with the most precise information which corresponds to the lowest intensity of monitoring. Corollary 4 When collusion is not possible, it is optimal for the shareholders to select the intensity of monitoring as low as possible. This directly follows from the fact that WIB is decreasing in :

5

Collusive Board

We now examine a framework in which the CEO and the Board of Directors may collude when this is pro…table for them. In the following inequalities, wL is the income of a board that announces that the project has a low probability of success, wH is the income of a board that announces that the project has a high probability of success, w; is the income of a board that announces that it has no information regarding the project probability of success, w0 is the income of a board when collusion cannot emerge as in the previous section. The following constraints ensure that the CEO-Board coalition get more when telling the truth than colluding. [ULL

w + wL ] + (1 ULH

, wL

[ULH

) [UHL

w + wH ] + (1

w

ULL

, wH Since we have ULL

ULH

(ULL

) [UHH

ULH w

w

(ULL

w) + (1

)

w

w) + (1

)

UHH and w) + (1 13

w

w

UHH

w

UHH

)

(UHL

+ w; + (1

UHL

min

)

+ w; + (1

UHH

ULL

w + wH ]

(ULH UHL

ULH

w + wL ]

UHL

(UHL

w)

w

w) + w;

1, necessarily w

+ w;

w) + w;

)

(UHH

w

0

+ w;

. We then have 4 constraints to satisfy: wL wH

ULH

w

ULH

w

wL

w0 (3)

wH

w0 (4)

(ULL

w) + (1

)

(ULL

w) + (1

)

UHH

w

UHH

w

(UHL

w) + w; (1)

(UHL

w) + w; (2)

In the following, we will examine when it is in the shareholders’ interest to avoid collusion between the Board and the CEO. Indeed, avoiding collusion is costly because shareholders have to pay higher wages to the Board in order to induce him to reveal the gathered information. If those informational rents are too high, it may therefore be optimal for the Board to let collusion happen.

5.1

Collusion-Proof contract

We …rst analyze a situation in which shareholders want to ensure that collusion in the Board is avoided. The only case they have to take into account is when the Board tells that there is a low probability of success (the Board is more likely to lie when the project is of a low probability of success; there is no point in lying when it is of a high probability of success). We therefore always have wL wH . Shareholders can try to use wL to pay the Board into revealing the truth: if they set wL high enough, collusion might be avoided. The shareholders’expected pro…ts have the following form: WCP

= E( )

ULL

( )wL

(1

(1

) ULH

) ( )wH

(1 (1

) UHL

(1

) (1

) UHH

( )) w0

In that case, the constraint on wL is binding. Since they want to maximize their income, shareholders set wH = w; = w0 (because w0 is the lowest wage of the board). wL = = wH

ULH

w

ULH

ULL

(ULL +

1

w) + (1 (ULL

)

UHH

w) + (1

w

)

(UHL

UHH

UHL

w) + w; +

1

(UHL

w) + w;

= w; = w0

We can remark that there exists 0 such that wL w0 () 0 : This means that for 0, engaging in collusion is not bene…cial for the coalition Board-CEO and the optimal contract is the same as with a perfectly honest Board. Actually, when 0 , the Board will not collude whatsoever happens. Shareholders don’t need to induce the Board to say the truth because he will do it anyway. So, we have in this case wL = wH = w0 14

We are now characterizing wL

w0 ()

[ (ULL

()

UHH UHL

And then, as ( ) = 1 :

0

w) + (1 8 w < = : w 0

=

) (UHL p+" 1 1 ( 0) p " p if p p 8 < 1+ :

w)] if "

p

p

w) + (1

) (UHH

w)

"ib

"

p+" p "

p

(ULH

"ib

if "

"ib

if "

"ib

However, for an intensity of monitoring in the interval [ min ; 0 ], since shareholders have paid enough to avoid collusion, the CEO’s rents are the same as in the Board Monitoring section: ULL = w ULH

= w

UHL = w + (1

UHH

=

( )) p

8 (p ")p( > < w+ [ > :

w+

0

"

)2 [(1

@

( ))B

p+2"] h [p (p+") B (1

p

]

( ) F ( ))

[(p+") (p ")]

h

B

( ) (1 ( )) F

(p + ")

( )F ] i

if "

if "

p "ib

i

"

1 A

"ib

This is stated in the following Proposition. Proposition 5 Assume that collusion between the Board of Directors and the CEO is possible. In the optimal collusion proof contract, shareholders must concede the same rents to a CEO as in the presence of a monitoring Board. In this case, the shareholders’ expected pro…ts are 8 > E( ) w w0 > > # > h i" > ( ) > (1 ( )) B (1 ( )) F > < (1 )(1 ( ))(p ") if " "ib ( p+2") +(1 + ( ) ) pp p WCP = > # h i" > > ( ) 2 (p > B (1 ( )) F ") (1 ( )) > > ) if " "ib > : E( ) w w0 (1 ( p+2") +(1 + ( ) )(p + ")

Moreover, there exists 0 such that for Boards of Directors with an intensity of monitoring 0 , it is not bene…cial to engage in collusion. The second part of this Proposition means that from some intensity of monitoring for the Board, it is so di¢ cult for the coalition Board-CEO to engage in collusion that they prefer not to collude without any shareholders’intervention. For such Boards, the shareholders should therefore not care about collusion. 15

5.2

Collusion Free contract

We now characterize the optimal collusion free contract. In this case, shareholders would have to pay too much to avoid collusion. They therefore decide to let it happen because avoiding collusion will be too costly for them in terms of informational rents paid to the Board. The shareholders’ expected pro…ts have the following form: WCF

= E( )

ULL

( )wL

(1

(1

) ULH

) ( )wH

(1 (1

) UHL

(1

) (1

) UHH

( )) w;

This is optimal to set wL = w0 . Inequalities (1) and (2) do not need to be satis…ed. Subsequently, we have: wL = wH = w; = w0 Since the Board is collusive, shareholders should not trust what it reports. Therefore, the CEO’s rents are the same as in the No Monitoring case. ULL = w ULH

= w

UHL = w +

UHH

=

B p " [ p + 2"]

8 < w+ :

w

B (p ")p(

)2

if "

[ p+2"][p p ] (p+") + B [ p+2"] if "

"nb "nb

Proposition 6 Assume that collusion between the Board of Directors and the CEO is possible. In the optimal collusion free contract, shareholders must concede the same rents to a CEO as without any CEO’s monitoring from the Board. In this case, the shareholders’ expected pro…ts are 8 B (p ") > < E( ) w0 w (1 ) + (1 ) pp p "nb ( p+2") if " WCF = > : E( ) w0 w (1 ) [(p + ") ( p + 2")] ( Bp+2") if " "nb

5.3

Optimal Contract with collusion

We will now use the speci…ed form for the probability that a Board with an intensity of monitoring has gathered the true information about the economic context for the type of projects considered by the …rm, i.e. ( ) = 1 . In order to …nd the optimal contract in presence of collusion, WCB ; we have to compare WCP and WCF and to …nd which one is the highest depending on . Indeed, the shareholders will choose to design the contract (Collusion Proof or Collusion Free) in order to maximize their objective. As "ib "nb we only have three cases: 16

1. "

"ib

2. "ib

"

3. "nb

"

"nb

The following Proposition characterizes the optimal contract when collusion is achievable. Proposition 7 For all

2[

min ; 0 ] ;

the optimal contract is the collusion proof contract for all ".

This allows us to state that the shareholders’s welfare, WCB that depends on 2 [ min ; 0 ] : WCB ( ) = max(WCP ; WCF ) = WCP ( )

is, for all

This is an important result as it means that when collusion is achievable and is pro…table for the coalition Board/CEO, it is always bene…cial for the shareholders to o¤er a contract preventing collusion to emerge. The optimal compensation contract therefore deters any attempt of collusion between the CEO and the Board members even though this is costly in terms of informational rents. However, the informational gains from monitoring always exceed the costs of those informational rents paid to the Board in order to induce him to monitor e¢ ciently and not to collude. This result and those of the previous sections allow us to characterize what is the optimal structure of the Board of Directors from the shareholders’perspective.

6

Optimal Structure of the Board

We are now able to …nd what is the optimal Board’s intensity of monitoring maximizing the piecewise continuous shareholders’s welfare WCB ( ): Notice that the optimal intensity of monitoring is related to the incentive compensation o¤ered to the CEO. Indeed, shareholders choose the intensity of monitoring that will allow them to pay the lowest informational rents to the CEO, i.e. the most e¢ cient incentive compensation contract. We also have to consider corner solutions as 2 [1; 0 ] : In order to be able to solve this problem, we assume that shareholders optimally set the penalty F: This implies that F h has to bei set as high as possible, i.e. such that the CEO limited liability 1 constraint binds, i.e. B 1 F = K: In order to simplify the computations, we rewrite the intervals of discontinuity of WCB ( ) in order to build them with respect to : This gives

"

"ib =

p (

1)

p

1

pp

p+p

p

17

,

p p

[p [p

p p

]

] (p+") (p ")

=b

Hence, when b and when b

0

0

or

p p

[p

(p+") (p ")

]

"

and

p p

[p

(p+") (p ")

]

p

0; () "

p

p+[p

p

"ib for all p

0; () "

"

"ib for

"

"ib for

p

p+[p

p

b; and

]

]

=b ";

=b ";

b

The shareholders thus have the following objective function10 : When " b " and b 0 8 > E( > > " ) w w0 # > > 1 2 1 > ( ) (p ") F] B [ > 1 > if b (1 ) > > ( p+2") > +(1 + > 2 )(p + ") > > > > E( ) w w0 < " # 1 WCB ( ) = 1 ( ) B F [ ] > 1 > )( 1 )(p ") if b > (1 ( p+2") > +(1 + 2 ) pp p > > > > > > E( ) w w0 > > > > [B 1 1 F ] > > + (1 ) pp p if (1 )( 1 )(p ") : ( p+2")

When "

b "; or b

WCB ( ) =

0

0

0

8 > > > > > > > < > > > > > > > :

(1

[B

)

(

E( " ) w w0 # 1 2 ( ) (p ") F ] 1 if p+2") +(1 + 2 )(p + ") 1

E( ) (1

)

1

F 1 ] ( p+2")

[B

(

1

)(p

w

0

w0 ") + (1

)(p + ") if

h Recall that shareholders set the penalty F as high as possible, i.e. such that B The following Proposition summarizes our results:

0 1

i F = K: 1

Proposition 8 When " b "; and 0 b; it is optimal for the shareholders to select a Board of Directors with a low intensity of monitoring, i.e. = b and to o¤ er contracts avoiding collusion between the Board and the CEO. In all other cases, it is optimal for the shareholders to select a Board of Directors with a high intensity of monitoring, i.e. = 0 . In this case, the shareholders should not care about collusion because collusion is not pro…table for such Boards. 10

As b

0

8"

18

Contrary to the usual idea that the optimal Board should strongly monitor the CEO, we …nd that shareholders may prefer to select a Board of Directors with a low intensity of monitoring. However, the result is not due, as in Adams and Ferreira (2007), to the fact that the CEO is more prone to reveal information to a "friendly" Board. Here, there is a trade-o¤ between the information that shareholders may extract from the Board and the costs from both extracting it and avoiding collusion. Higher is , more di¢ cult it is for the coalition Board-CEO to engage in collusion, but less they have information about the projects. The intuition for this result is the following. Shareholders should not care about hiring a Board with a high intensity of monitoring when it is too costly to do so and when potential collusion between the CEO and the Board has not a big impact on the …rm’s decision which is the case when the projects are similar in terms of risk and the intensity of monitoring necessary to have a perfectly honest Board is too high. Indeed, collusion allows the CEO to undertake projects with a level of risk that is higher than what would be optimal for shareholders. This means that closer are the risk of projects, lower are the costs of collusion. As choosing a higher intensity of monitoring leads to extract less information and as it would be too costly to choose a perfectly honest board (because 0 is high), choosing a board with a low intensity of monitoring is therefore optimal. In theses cases, deterring collusion is less important than gathering information about the projects. However, in all other cases, i.e. when project 2 is much more risky than project 1 or when the intensity of monitoring necessary to have a perfectly honest Board is low enough, it is optimal for shareholders to choose a Board with a high intensity of monitoring. The optimal structure is therefore a perfectly honest Board and the shareholders should not care about collusion because collusion is not pro…table for such Boards. In other words, the optimal structure is a Board with a low intensity of monitoring when: the risk of both projects are close, i.e. the projects among which the …rm has to choose have similar level of risks, and the intensity of monitoring necessary to have a perfectly honest Board is too high, i.e. the loss of information about the projects that would be associated to the choice of a perfectly honest Board would be too important.

6.1

Policy and Empirical predictions

It is therefore optimal for shareholders to select a Board with a low intensity of monitoring in …rms having a stable economic environment (for instance in industries and sectors having achieved a high degree of maturity or in low risk industries, i.e. building, transport, chemistry) and in which it is di¢ cult to …nd e¢ cient and absolutely independent Directors (…rms for which only executives are able to gather information about the projects for strategic reasons, i.e. Investment Banking, Petroleum Industry, Aeronautics, Military sectors. . . ). This is consistent with empirical results that link the …rms’risk and the intensity of monitoring. Indeed, Demsetz and Lehn (1985) show that riskier environments should be associated with more 19

monitoring. Ferreira, Ferreira and Raposo (2011) also …nd that more complex …rms require more monitoring. As …rms relying on incentive based compensations schemes usually need a high intensity of monitoring, our result, stating that the intensity with which Boards monitor CEOs should be higher in innovative or riskier industries, is therefore also consistent with Murphy (1999) who show that incentive compensation are lower in regulated utilities than in other industries and with Ittner, Lambert and Larcker (2003) or Murphy (2003) who …nd that stock-based compensation is more frequently used by new economy …rms than by old economy …rms. Using the number of non independent directors, of interlocked directors, of mandates held by each director, the power of the main committees, or the quality of the internal audit process as proxies of the intensity of monitoring, could be a way to test empirically this result both in terms of the optimal intensity of monitoring and the CEO’s incentive compensation. In particular, we could test if industries that di¤er in the level of risk they face and in which it is di¢ cult to hire informed Directors who are not connected with the …rm’s top executives do not choose the same intensity of monitoring and the same executive compensation schemes. Moreover, notice that the intensity of monitoring of the Board, ; can also be interpreted as the shareholders’ willingness to increase the degree of toughness and enforceability of the Corporate Governance regulations and the laws against collusion. A proxy for would be the toughness of laws and regulations, the ownership concentration or the ownership structure. It would therefore be interesting to test if the Boards’structures of …rms having the previous characteristics have changed in countries that have modi…ed the Corporate Governance regulations (see Cornelli, Kominek and Ljungqvist, 2012), or for …rms in which we have observed a modi…cation of the ownership structure (see Ferreira, Ferreira and Raposo, 2011).

7

Conclusion

In this paper, we analyze the e¤ect of collusion between a Board of Directors and a CEO on the optimal intensity of monitoring. We also characterize the optimal compensation contracts. We show that when there is no CEO’s monitoring by the directors the variable part of the wage is higher for a high ability CEO than for a low ability CEO. When we introduce Board monitoring, still without collusion, the Board behaves as a perfectly honest Board and the optimal compensation contract takes the same form as without monitoring. Allowing for the possibility of collusion between the board and the CEO, we show that the optimal contract is collusion proof: it is always optimal for the shareholders to o¤er a contract preventing collusion to emerge. We also prove that there exists an intensity with which the Board monitors the CEO above which it is not pro…table for the coalition Board-CEO to engage in collusion. Such Boards therefore behave as perfectly honest Boards. We also derive the optimal intensity with which the Board of Directors monitors the CEO from

20

the shareholders point of view. Contrary to the usual idea that an optimal Board should strongly monitor, we …nd that shareholders may prefer to choose a low intensity of monitoring of the CEO by the Board of Directors. More precisely,the optimal structure is a Board with a low intensity of monitoring when the projects among which the …rm has to choose have similar level of risks, and the intensity of monitoring necessary to have a perfectly honest Board is high enough. Finally, we provide practical and empirical implications of our model.

8

Appendix

Proof of Proposition 1. When there isn’t any CEO’s monitoring from the Board, shareholders maximize their expected pro…ts under the usual Participation and Incentive constraints. P Cij is the Participation constraint of a CEO with ability i 2 fH; Lg when the project is of type j 2 fH; Lg. The Participation constraints ensure that the CEO will earn at least her reservation wage w. ICij!kl is the Incentive constraint of a CEO who reveals that her ability is k 2 fH; Lg and the project is of type l 2 fH; Lg while her true ability is i and the true type of the project is j. The Incentives constraints ensure that the CEO earns a higher wage revealing the truth than lying to the shareholders. Through this process, shareholders induce the CEO to reveal his real type. As usual in this kind of problem, the binding constraints are : +

LL LH HL HH

+

HH

+

p R

HL

(p + ") R

+

LH

p R

(p + ") R

I =w+

I =w+

LL

LL R

LL R

I =w

I =w+ p+

p+

LH R

LH R

p

(P CLL ) LL R

p

p

p p

" "

In order to minimize the CEO’s informational rents, shareholders set

+ +

LL ;

+B +

LH

HL R

and

HL

p+B as low as

possible while satisfying the other Incentive constraints. We now check what are the conditions due to the other Incentive constraints (and will check later that Participation constraints are satis…ed). There is no constraint on LL ; we can therefore set:

LL

+

LL

LH

+

p R LH

I

LH

+

(p + ") R ,

LL

=0

LH

p

I LH

and then LH

=

LH R

"

R

(p + ")

B R [ p + 2"] B R [ p + 2"] 21

I +B = p

"

(ICLL!LH ) +B

HH

+

,w+

(p + ") R

HH

p+

LL R

LH R

,

+

p p R

HL

,w+

LL

p

LH R

which is satis…ed, as p HL

I

p

"

+

p+

p

"

+

LH

+

+

"

I =w+ +

+

HL R

+

LL R

p

p+B

HL R

p w+

p+B

(ICHH!LL ) LL R

p

p

0

0:

LL

+

LH R

p

LH R

p R

LL

"

p

, As p

p

I

LL R

+

p R

LL

p

"

p

p

I =w+

"

+

LL Rp

+B

+

(ICHL!LL )

w+

+B

LL Rp

0

0; (ICHL!LL ) is not binding. (p + ") R

LH

= ,w+

+

HH

I

+

w+

LL R

HL R

,

+

(p + ") R

HH

(p + ") R

HH

p

LL R

HH

I p+

p+B

HH R (p LH R

HH R (p

p

(ICLH!HH )

+ ") p

"

+

+ ")

B = R [ p + 2"]

HH

I

LH :

This is satis…ed from the Spence Mirrlees condition. LH

+

(p + ") R

LH

,w+

p

LL R

I

HL

w+

LL R

,

HH

+

HH

(p + ") R

+

I

HL

p R LH R

p+

HL

p

"

p

B p HL

I =

"

R [ p + 2"] p

LH

+

HL

p R

HL R

p p (ICLH!HL )

I HL R

+ =

p

(p + ") R

LH

+

p

p

+B

1 HL

I =w+

LL R

p+

LH R (p

+ ")

(ICHH!LH ) ,w+

LL R

p+

LH R

p

p

" ,

LL

+

LL

p R

I

HL

+

+

HL R

B R p

HL

HL

+

p R

p+B

LL R

p+

LH R (p

+ ")

2 HL

=

I =

w+

HL

+

HL

p R

I

HL Rp

(ICLL!HL ) ,w

w+

LL R

p+

LH R

p

p

HL

B p " Rp [ p + 2"] 22

"

+

HL Rp

+B

This is always veri…ed as +

LL

p R

LL

LH

B (p ") R [ p+2"]p

+

and due to the Spence Mirrlees condition.

LH

I

LH

+

(p + ") R

LH

,w

w+

p

LH

I

"

p

I +B =

(p + ")

LH R

LL R

R

LH R

p

"

(ICLL!LH ) +B

[ p + 2"] + B

(ICLL!LH ) is thus not binding. HL

=w+

+

LL R

p+

+

I

LH R

HH

p

p

HH

R [ p + 2"]

p R

+

HH

I

HH

+

p

+

(p + ") R

+

p

HL [(p

+R

[(p

I +B

HL R

p

(ICHL!HH )

HH R

B = R [ p + 2"]

"

R

HH R p

R

p+

p

HH

I

+

HH

"

p

[p LH [(p ,

p

HH

" 2

LL

HH

+ "

B p

,

LL

p R

HL

[ p + 2"] + 2B 1 HH

I +B =

(p + ")

p

(ICLL!HH )

"

+B

"( + )] )+"( + )]

p p )+"( + )] 2B p )+"( + )]

=

2 HH

We therefore have:

We now have to show that

HL

We only have six cases: 1 2 1. LH HL HL () LH

1 HL

LL

= 0

LH

=

HL

= max

LH ;

1 HL ;

2 HL

HH

max

HL ;

1 HH ;

2 HH

=

8 > < > :

HL

2 HL

=

B R [ p + 2"]

1 HL

if "

2 HL

if "

2 HL

() () ()

p p +p

(

p

= "nb

p

+p

if "

(

= "nb

p

p

1 p + 2" "

23

p p

" p

h

+

"

i

p p

"

( p + 2") p p

p

"

p

p " ( p + 2") p p +

p p

: Indeed, we have :

p p

For the following cases (2, 3 and 4), we use the same inequalities to obtain. 2 2 " 2. 1HL LH HL () HL = HL if hp i p 2 1 1 3. LH p 2" () = if " + HL HL HL HL p 2 1 1 2" 4. HL p LH HL () HL = HL if 1 5. 2HL LH () impossible. Indeed, we would eventually obtain HL "

"

p

p p

+

which is not possible because the last term is strictly superior to the …rst one. 2 6. 1HL LH () impossible HL We therefore have the result of the lemma. And then : ULL = LL + LL p R I = w ULH = UHL =

LH

HL

+

+

LH

(p + ") R

HL

p R

I =w+

p

UHH =

HH

HH

(p + ") R

I =w+

UHH =

p " + [ p + 2"]

p

B p " + [ p + 2"] " p(

)2

[ p + 2"] p

p

B p

() UHH = w + Moreover, when "

p=w +B

= "nb

p +p

+

B p

LL R

B p " [ p + 2"]

() UHL = w + Moreover, when "

I =w+

B p

"

[ p + 2"] p

= "nb

p

+p

HH

+

HH

(p + ") R

I =w+

() UHH = w +

B

B p " B + [ p + 2"]

(p + ") [ p + 2"]

To sum up, here are the CEO’informational rents when there is no monitoring: ULL = w ULH

= w

UHL = w +

UHH

=

B p " [ p + 2"]

8 < w+ :

w

B (p ")p(

)2

if "

[ p+2"][p p ] (p+") + B [ p+2"] if "

24

"nb "nb

p p

We can verify now that we have ULL

ULH

UHL

UHH

When " "nb , we need to see if pp p 1, which is true since p p =p p. Subsequently, we have UHL UHH . When " "nb , since p " p + ", we also have UHL UHH . Rewriting the shareholders’expected pro…ts depending on those informational rents, when there is no monitoring, we have: WN M = E( )

ULL p

This gives, for "

(1

p p

+p

(1

) UHL

(1

) (1

) UHH

= "nb

p

+p

WN M = E( ) And for "

) ULH

(1

)B p " ( p + 2")

(1

) (p + "

w

"

#

p+p p p

= "nb

WN M = E( )

w

p

B ( p + 2")

2 ")

Proof of Proposition 2. The binding constraints are: LL LH HL + HL

HH

+

p R

HH

I = (1

(p + ") R

+

LH

(1

LL

p R

I =w

(p + ") R

I =w+

LL R

LH R

( )) w + I =

+

p+

( )) w +

(P CLL ) LL R

p

p

"

p

LL R

+

p + LH R p " p + ( ) (w F ) + HL R p

+ B + ( ) (w +

+B

Again, in order to minimize the informational rents, shareholders will set LL ; LH and HL as low as possible while satisfying the other incentive constraints. We now check what are the conditions due to the other Incentive constraints (and will check later that Participation constraints are satis…ed). LL = 0 HH

+

HH

(p + ") R =w+

I LL R

LL

p

25

+ p

LL

p R

=w

I

(ICHH!LL )

F)

LL

+

p R

LL

I

(1

(1

( ))

( ))

(

LH

+

, (1

( ) ( )) F

B

LH

R

(1

+

HL

, (1

p R (

( ))

+

I

=

HH

( ) ( )) F

+

8 > < (1 , > :

HH

B

(

F)

( ) ( )) F

p

"

LH R

p

(p + ")

p

p R

LL

p

"

"

I =w+ )

p +

R p

LL Rp

p

(ICHL!LL )

( )F

+B

( ) ( )) F

(1 LH

( ) ( )) F

(1

LL R

I

LH

+

LH

w + LL R + LH R p p "

+ ( ) (w

F) +

(p + ")

LL Rp

B

"

(1

(p + ") R

p +

HL R

+B

p ( )) p

HL

+

LH

+

(p + ") HL

LH

=

"

LL R

p

(1

w+

> ;

I

R

( )) p

HL

HL

p R (

+

I

HL

h

( )) p p

p 26

LH R (p

(p + ")

"

p R

HL R

p

" LH

=

p+

LH R (p

i

1

( ) (1 ( )) F

B

p

=

1 HL

"

+ ")

(ICLH!HL )

p

2 HL

+ ")

A

I

w + LL R ( )) + LH R p p " + ( ) (w F ) HL R p (1

p+

LL R

p

(p + ") R

HL

LL R

(ICHH!LH )

) 9 > = @

LH

HL + 8 > < (1 > :

I =w+

0

p ,

,w+

+ ( ) (w

F) = (ICLL!LH )

0; this is satis…ed

(p + ") R

( ))

R +

LL

, (1

)

I + B + ( ) (w

0; we have

LH

As

R

+B

(p + ")

B

HL

"

w + LL R p (p + ") p " LH R B

As

p

LH

p + p

+B

) 9 > = > ;

We can verify that

if "

2 HL

if "

p + 2" + ( ) p

"

=

Indeed, we have : 1 HL

=

1 HL

() () () "

p

and when "

LL

(1

+

LL

,

(2 ( )) p + (1 ( )) p (1

( )) p

= "ib

p

= "ib

(1

( ))

+p

(1

( )p p

( ))

+p

p

#

p p

( )) p

(1

"

p

( )) p

p

p + ( )p

p

p

( )p

( ))

+

p p

; one can easily check that : HL

=

1 HL

LH

HL

=

2 HL

LH

p

+p

p R

I

HL

HL Rp

(1 (1 HL

, Since (1

p

( )) +p p ( )p

( )p

( ))

,

( )p

(1

2 HL

p (1

> :

p

"

() " Moreover, when "

p

1 HL

HL

HL

8 > <

p

+

LH R

( )) ( )) p p

I = p

(1

HH

= max 1HL ; 8 > < 1HL if " = > : 2HL if "

@

h

R

( )) p p LH ,

HL

p 0

"

HL

and since HL

p R

HL

"

+

"

HL

p R

HL Rp

+

+B ( )F i 1 B (1 ( () )) F A (p + ") p " LH

ICLL!HL is also satis…ed. Finally, we get

2 HL p

( )p p

= "ib

p

= "ib

(1

( )) +p p ( )p

(1

( ))

27

I

+p

LL

(1 ,

HH

+

( )) (

HL

= (1 ,

p R

LL

+

( ))

HH

(1

(1

+

(1

p R

( ))

HH

(p + ") R

HH

+

I

p

HH

HH R

+B

LH R

( ))

(1

HL R

p

( ))

( )

HH

LH R

HH

+

R

I + B + ( ) (w p

F) = (ICLL!HH )

" h B

+ B + ( ) (w F ) i 1 ( ) F (1 ( )) @ A = 1HH R (p + ") p "

)0

I + B + ( ) (w F ) (ICHL!HH ) ) ( )) w + LL R p + LH R p p " + +B + ( ) (w F ) + ( ) (w F ) + HL R p HH R [ p + 2"] + B

(1

I

"

(p + ")

p " + p ( )F + HL R p

( ))

HL

(

I

p

HH

p

"

p

"

+

R

+ (1

( )) B

( )F

R [ p + 2"]

LH

+

LH

(p + ") R

= (1 ,

HH

( ))

+

I

HH

LH R

+

HH

+

HH

(p + ") R

p

p

HL R

(p + ") R

I

"

HH R (p

+

+ (1

p

HH

I

=

2 HH

(ICLH!HH )

+ ") ( )) B

( )F =

R (p + ")

3 HH

We thus have: = 0

LL

B =

LH

=

HL

R 8 > < > :

max

HH

ULL = ULH =

UHL =

HL

+

= w + (1

HL

p R

( )) p

LH

+

LH

I = (1

"

0 @

(1

( ) ( )) F

(p + ") 1 HL

if "

2 HL

if " HL ;

LL

+

p

" p

( )p p

= "ib

p

= "ib

(1

( )) +p p ( )p

(1

( ))

+p

2 HH ;

3 HH

1 HH ; LL

(p + ") R (

p R

I =w

I =w+

LL R

w + LL R ( )) + LH R p p " h i 1 B (1 ( () )) F A (p + ") p " 28

p=w p +

+B

)

+ ( ) (w

F)

UHH

=

=

HH

+

HH

(p + ") R

+ ( ) (w F ) + HL R 8 (p ")p( )2 [(1 ( > > < w+ [ p+2"][p > > :

w+

h B

(p+")

(1

I = (1

(

( ))

w + LL R p " + LH R p

p +

+B

)

p ))B

( )F ]

]

p

( ) F ( ))

[(p+") (p ")]

i

p

if "

(1 p

if "

(1

( )p

= "ib

p

( ))

+p

( )p

= "ib

p

( ))

+p

To sum up, here are the CEO utilities when there is a monitoring Board: ULL = w ULH

= w

UHL = w + (1

UHH

=

( )) p

8 (p ")p( > < w+ [ > :

w+

h

0 @

"

)2 [(1

(p + ")

( ))B

p+2"] h [p B (1 (p+")

p

( )F ]

]

( ) F ( ))

[(p+") (p ")]

( ) (1 ( )) F

B

i

if "

if "

p "ib

i

"

1 A

"ib

We can verify now that we have ULL When "

"ib , we need to see if

p p

ULH

UHL

UHH

1, which is true since p

p

p =p

p. Subsequently,

p + ", we also have UHL UHH . we have UHL UHH . When " "ib , since (1 ( )) p " One can remark that types (HL) and (HH) informational rents are lower with monitoring than without. i 1 0 h B (1 ( () )) F B p " A @ UHLib UHLnb () (1 ( )) p " [ p + 2"] (p + ") p " () (1

( )) B

Moreover, we can prove that "ib

p (1

)

p

"nb

0

p +

() 2 which is true since we have p

B , which is true

"nb . Indeed, "ib

()

( ) F ( ))

(1

p p p

+ p

0. 29

p

p p

0

0

This implies that we only have three possible cases to consider for UHH 1. When " "ib UHHib

UHHnb =

sign(UHHib

"

"nb

h

UHHnb =

h

( ) (1 ( )) F

B

p

p

"

UHHnb ) = sign (p + ") B

sign(UHHib Since B

(p + ")

" p

i

p

p

p p

"

UHHib h

UHHnb =

p

)2

[ p + 2"] p

p

0

" p(

)2

[ p + 2"] p

p

B p

p

p

B p

(p + ") p

pp + pp

+

" p

p

" p

p+p

p + p

"

0 h

(p + ")

i

" p

= pp = p

Since " "nb , we have 3. When "ib "nb "

) )

( ) F ( ))

(1

we need to prove that p

(p + ") p

2

" (

( ) (1 ( )) F

B

" p(

B p

( )F ]

p

( ) (B + F ) p

(p + ") UHHib

( )) B

[ p + 2"] p

UHHnb ) = sign(

2. When "ib

)2 [(1

" p(

p

( ) (1 ( )) F

B

(p + ")

p

"

i

B

(p + ") [ p + 2"]

i

Since B B (1 ( () )) F we have UHHib UHHnb . We can now calculate the income of the shareholders. There are two cases to consider. When " "ib , h i" # B (1 ( () )) F p + (1 ) WM = E( ) w w0 (1 )(1 ( ))(p ") ( p + 2") p p When "

"ib ,

WM = E( )

w

w0

(1

h

)

( ) (1 ( )) F

B

( p + 2")

i

(1

( ))(p

") + (1

)(p + ")

Proof of Proposition 7. We have to …nd for which values of ; the contract is collusion proof. 1. " WCP

"ib WCF

=

(1

)(1

+(1

"

)

( ))(p

+ (1

)

h

") p p

p 30

( ) (1 ( )) F

B

#

( p + 2") B

i"

(p ") ( p + 2")

+(1

(1 +

0 for all

( )) ( ) ) pp

2[

min ; 0 ]

p

#

with

0

=

p p

p

WCP

for "

WCF =

(1

"ib : Indeed, 0

+ (1

B B B @

)(p ") ( p + 2")

[(1

( ))B

( )F ]

"

) pp

p

+(1

1

B (1 +

( )) ) pp

( )

p

As, we have ( )ED ( ) = 1 ; this gives

WCP

WCF =

0 B B B B B @

)(p ") ( p + 2")

(1

) pp

+ (1

p

2

(B + F ) + B

B + F + B pp + (B + F ) p

p

p p

C # C C A

1 C C C C C A

This polynomial in with a positive second degree term has 2 positive roots. If those roots are both lower than 0 ; then, WCP WCF 0 for all 2 [ min ; 0 ] : The lowest root is v u 2 u 2 B+F +B p u p p u B + F + B pp p u t 4 (B + F ) pp p + (1 ) pp p (B + F ) + B 1

=

2

) pp

+ (1

(B + F ) + B

p

We have 1

0

4

B B B () B B B @ () 4

4

p

p

!2 "

+ (1

p

B + F + B pp

+ (1

)

)p

p p

p

+ (1

p

!

p p

(B + F ) + B

+ (1

p

p

p p

1

2

p

4 (B + F ) pp

p

p

0

2

) pp

(B + F ) + B

) pp p

#"

p

(B + F ) + B

(B + F ) + B + (1

)

p p

p

C C C C C C A

!

0

#

(B + F )

0

which is true. WCP WCF is therefore positive for all 2 [ min ; 0 ] : The optimal contract is the collusion proof contract for " "ib : 2. "ib " "nb h i B (1 ( () )) F ( ) WCP WCF = (1 ) (1 ( ))2 (p ") + (1 + )(p + ") ( p + 2") " # B (p ") p +(1 ) + (1 ) 0 for all 2 [ min ; 0 ] ( p + 2") p p 31

with

0

=

p+" p "

+ 1 if "

WCP

As, we have

WCF

ED

"ib : Indeed, 0

"

B B (1 ) B = ( p + 2") B @

h + B

+(1

( ) (1 ( )) F

i

) p "p

p

B(p

1

")

( ))2 (p ") + ( ) )(p + ")

(1 +(1

( ) = 1 ; this gives

0

WCP

#

1

3

B (1 )p (1 B p B 2 3 B p B + (1 )p B+2 B 7 6 p ") B B 4 5 B (p+") + (1 ) (p ") (B + F ) + 1) B B i h B (p+") + 2 (B + F ) B 1 + B (p ") @ + (B + F ) 1 + (p+") (p ")

(1 ) (p ( p + 2")(

WCF =

) (p+") (p ")

p

C C # C C A

2

C C C C C C C C C C C A

We are now able to show that this degree 3 polynomial, denote it P ( ); is negative for all [ min ; 0 ] : Indeed 1 0 (p+") p 2 3 B(1 ) p C B (p ") p C B @P ( ) B C (p+") p = B +2 B+2 B+ + (1 ) (p ") (B + F ) C + (1 )p C B @ p h i A @ B 1 + (p+") + 2 (B + F ) (p ")

2

Moreover, as

" we have 2

=

B(1

B(1

) )

"

p p

2

0

"

0

1

p #

(p + ") (p ")

p !

p p

p(

"ib ()

p(

2

0

"

0

p

p

!

B(1

)

p p

p

!

and thus 0

3 B(1

B B B B +2 @

@P ( ) @

()

+ (1

) pp

p

+ (1

) pp

p

0

0

p

32

p (p+") ) (p ")

+ 2 (B + F )]

+ 2 (B + F )

B+ B+

1

p

B + 2 B + (1

[ B B

)

+ (1

(

0

C C C 1) (B + F ) C A

) (p+") (p ") (B + F )

0

Moreover, B

0

+ 2 (B + F ) 0

) pp

+ (1 Hence,

@P ( ) @

is negative for all

p

2[ 0

B+ B+ min ; 0 ] :

(WCP

Finally, we will show that (WCP

WCF ) ( 0 )

(p+") ) (p ")

p

" p p

p

(p

we have, together with p p p

"nb () p p+ p

")

p p

(p+") (p ")

p

2 0

0

C C C C C C C A

0

0

(p

p

0

1

3 0

p

WCF ) ( 0 )

")

p (p + ") (p ")

p

p p

p

p

(p + ") (p ")

p

p

p

p+ p p

p

0 ()

(1 )p B (1 p B 2 3 B p (1 ) (p ") B B 6 + (1 )p B+2 B 7 p B 5 ( p + 2") 0 B 4 (p+") B + + (1 ) (B + F ) @ (p ") [ B 0 + 2 (B + F )] 0 + (B + F ) 1 0 (p+") p p ( 0 1) p B(1 )p (p ") p 0 p A () @ +(1 ) 0 ( 0 1) F + ( 0 1) (B + F )

However, as

As

) (p+") (p ") (B + F )

+ (1

0; (WCP

p p p (p

p

p

")

(p + ") (p ")

1

@P ( ) @

WCF ) ( 0 ) is thus positive and as

0

is negative for all

2

[ min ; 0 ] ; WCP WCF is therefore positive for all 2 [ min ; 0 ] : The optimal contract is the collusion proof contract for "ib " "nb : 3. "ib "nb " h i" # B (1 ( () )) F (1 ( ))2 (p ") WCP WCF = (1 ) ( p + 2") +(1 + ( ) )(p + ") +(1 with

0

=

WCP

p+" p "

+ 1 if "

WCF =

(1

) [(p + ")

( p + 2")]

B ( p + 2")

0 for all

2[

min ; 0 ]

"ib : Indeed, )(p ") ( p + 2")

0 B @

h

B

(1

33

[ + (1" i ( ) F ( ))

)( +(1

0

1)] B (1 +

(

( ))2 ) )( 0

1)

1 # C A

As, we have

ED

WCP

( ) = 1 ; this gives

WCF

0

[ (2B + F ) + (1 ) ( 0 1) F ] (1 )(p ") B = [B 0 + 2 (B + F )] @ ( p + 2")( 1) + (B + F ) 0

2

1 C A

This polynomial in with a positive second degree term has 2 positive roots. If those roots are both lower than 0 ; then, WCP WCF 0 for all 2 [ min ; 0 ] : The lowest root is v u 2 2 [B u 0 + 2 (B + F )] t [B 0 + 2 (B + F )] 4 (B + F ) 0 [ (2B + F ) + (1 ) ( 0 1) F ] 2 = 2 [ (2B + F ) + (1 ) ( 0 1) F ] We have

() 4

2 0

"

() 4

(2B + F ) +(1 ) ( 0 1) F 0( 0

2

#2

4

0

0 [B 0

1) [ (2B + F ) + (1

)(

+ (B + F )]

0

"

(2B + F ) +(1 ) ( 0 1) F

1) F ] [ (B + F ) + (1

) 0F ]

#

0

0

which is true. WCP WCF is therefore positive for all 2 [ min ; 0 ] : The optimal contract is the collusion proof contract for "ib "nb ": Proof of Proposition 8. When " b " and b 0 ; we have 8 " # i h 1 2 > ( ) (p ") > 1 > if b B > 1F > > +((1 ) + > 2 )(p + ") > 2 3 > < h 1 2 i ( ) i 1 WCB ( ) = ; 4 h 5 if b B 0 ( 1) p 1 1F > > + (1 ) ( ) + 3 > p p > > > > > p 1 > [( 1) B F ] + (1 )p if : 0 p When "

b " or b

WCB ( ) =

0;

8 > < > :

we have: ( 1

1 1)

[(

2

[( 1) B

1) B F]

F] (

"

( +((1 1)(p

1)2 (p ") ) 2 + )(p + ") ") + (1

#

if

0

)(p + ") if

0

h

;

i 1 Assume …rst " b " and b : As F has to be set as high as possible, we have B F = K; 0 ( 1) due to the CEO’s limited liability constraint. We thus have, if b " #! ! @WCB ( ) 2 2( 1) 2 ( 1)2 2 K (p ") = (p + ") 4 3 @ ! (p ") ( 1) (p + ") = 2K 3 34

However, ") (

(p as

0

=1+

(p+") (p ") :

And then

1)

@WCB ( ) @

2

0: If b

h + (1

K4

WCB ( ) =

(p + ")

0

0; 1 2 )

( 1

)(

(

)+

1) 3

i

p p

p

The …rst derivative of this objective function is in this case: " (1 ) 3 @WCB ( ) 2( 1) + + = K 3 2 @ K

=

4

K

=

4

=

K

2

(

2

2

2

2 2

4

)

2

+ (1

)

2

0

+

2

2

K

=

1) + (1

3

+

(1

) 2

(2 + (1

)

0)

0

+ (3

0

+3

0

0

2

3

5

2

p

4

p

2 )

0

2

p

#!

0

0

4

+2

3

3

(1 +

0)

3

0

The sign of this expression is equivalent to the sign of a second degree concave polynomial in : This polynomial has two positive roots. We will show below that it is negative in b and 0 and that its derivative in b and 0 is also negative. This implies that it is negative for all in [b; 0 ] and that consequently WCB ( ) is non increasing on this interval. Indeed, we have @WCB ( ) j @

K

=

0

4 0

=

K

(1

)

(1

)

3 0

+

+

0

3 0

0

0

0

and

@WCB ( ) jb = @

=

=

K b2

2

6 6 6 B 62 @1 6 4 2

K6 6 6 b2 4

K b2

"

0

1 0

(p+") (p ")

2 + 2 0

3

+4

0 (p+") (p ")

0 0

(p+") (p ")

!

1

C A + (1

)

0

+ 0

+ (1

)

0

2

0

(p + ") 0 (p ")

2 2

35

3

0

(p+") (p ")

(p + ") (p ")

3 7 7 7 5 3

0 0 (p+") (p ")

2

!2

(p + ") (p ")

0

2

#

0 0 (p+") (p ")

3

7 7 !7 7 7 5

2

(p+") 4 (p+") This is always negative as = 16 2 (p+") 0 because (p ") (p ") 2 + 3 (p ") it is easy to check that the derivative of the second degree concave polynomial in ( ) 1 same sign as @WCB ) is negative in 0 and in b (because @ 2 ): This implies that

@WCB ( ) @

If

2 [b;

Moreover, (having the

0] :

0;

@WCB ( ) @

= =

b "; or b

When "

If

0 for all

1 2:

0

we have, if

(

1)

1

"

2

K

3

(

K

2

0

@WCB ( ) @

=

K

=

K

+ (1

+ (1

)

1) (p

")

)

p p

p p

p

#

p

#

0

0

@WCB ( ) = @

WCB ( ) =

K

"

1)2

(

K

2 (

(p

1)

( 2

(

1)

+1 2

(p

") + (1 1)2

(p

") + (1

(p + ")

1

)

") + (1 )

1 2

0

(p + ")

)

1 2

(p + ")

(p + ") 0

This allows us to conclude that when " b " and 0 b; it is optimal for the shareholders to select a Board of Directors with a low intensity of monitoring, i.e. = b. In all other cases, it is optimal for the shareholders to select a Board of Directors with a high intensity of monitoring, i.e. = 0.

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