Board Efficiency and Internal Corporate Control Mechanism∗ Clara Graziano† and Annalisa Luporini‡ November 22, 2001

Abstract We analyze the interactions between internal and external control mechanisms in a framework in which the board selects the CEO and then decides whether to retain or dismiss him after observing a signal on his ability. The novel aspect of our paper is that we consider both the hiring and the firing of the CEO by the board. The type of the board is defined by its ability to select a good CEO so that the quality of the CEO depends on the type of board. Then, the dismissal/retention decision provides information not only on the quality of the CEO but also on the board’s type. We show that board’s behavior depends on the pressure from the takeover market and on whether its type is publicly known. When the pressure from the takeover market is high and the type of the board is private information, the board prefers not to dismiss the manager even if it has received a very low signal on his quality. Hence, our model endogenously derives a collusive behavior between board and CEO in which the board does not fire a bad CEO. This behavior emerges as an attempt to hide the board’s inability to accomplish the first task, CEO selection, by distorting the second task, the CEO retention/dismissal decision. Keywords: Board efficiency, Board monitoring, Corporate governance. JEL codes: G30, L20, D82. ∗ Acknowledgment: We would like to thank audiences at the EARIE meeting in Lausanne, the third Graz-Udine Workshop in Economic Theory, the Econometric Society in Lausanne, the German Finance Association in Vienna for useful comments. The usual disclaimers apply. † Address: Department of Economics, University of Udine, via Tomadini 30/a, 33100 Udine, Italy. Ph: +39 0432 249216; fax: +39 0432 249229; email: [email protected] ‡ Corresponding author. Address: Department of Economics, University of Trieste, piazzale Europa 1, 34100, Trieste, Italy. Ph:39 040 6767027, fax: 39 040 567543 email: [email protected]

1

1

Introduction

The relative effectiveness of the various governance mechanisms has been a topic of considerable controversy in the academic and business communities. On the one side, the main internal control mechanism, the monitoring by the board of the CEO, has been regarded as ineffective and boards of directors have been criticized for being ”hostages” of the CEO that they are supposed to monitor. On the other side, it has been pointed out that takeovers are costly and that they can correct only the most extreme cases of mismanagement. Furthermore, there is little evidence of the long-term gains for the shareholders of the acquiring firm. Despite the relevance of the issue, only a few studies have provided formal models of the way boards function and of the way (if at all) the market for corporate control affects their behavior. The few notable exceptions are Hermalin and Weisbach (1998), Hirshleifer and Thakor (1994 and 1998), and Warther (1998). Hermalin and Weisbach analyze a model where the level of independence of the board is endogenous. CEO and the board of directors bargain over CEO wage and the identity of new directors. Their main results are consistent with the findings of empirical literature: CEO turnover is negatively related to firm’s performance (and this relationship is stronger when the board is more independent), independent directors are more likely to be added to the board when performance is poor, and finally board independence declines with CEO tenure. Warther, instead, analyzes the voting procedure by which boards decide whether to retain or fire the manager. His model predicts that boards take this decision unanimously and that they are an important source of discipline, despite the lack of debate and the apparent passivity. Hirshleifer and Thakor (1994 and 1998) study the trade-off between internal and external control in a setting in which the board and a potential acquirer observe different signals about the CEO’s quality. After observing the signal, the board updates its prior on the CEO quality and decides whether to retain or to fire him. In the 1994 paper they focus mainly on the information conveyed by the bid price and on the acceptance of the bid by the board. In the 1998 paper they concentrate on the effect of the takeover threat on the board’s retention/dismissal decision and they point out two effects: a ”substitution effect” and a ”kick-in-the-pants-effect”. The first refers to the fact that an active takeover market leads to better information since the information of the board is aggregated to that of the acquirer and this enables the latter to replace inefficient managers if directors do not do so. The second effect refers to the fact that the board may dismiss the manager more often because of the threat of being replaced by the external acquirer if perceived as inefficient. A common element of all these models is that they analyze the functioning of the board of directors with respect to its monitoring task and its incentive to fire a bad CEO. No attention has been paid to another important task of the board of directors: the selection of the CEO. The object of the present paper is to analyze the interactions between internal and external control mechanisms in a framework in which the board has two different tasks: to select the CEO and to decide whether to retain or dismiss him after observing a signal on his quality. Hence, contrary to previous literature that focuses only on the retention/dismissal decision, our model explicitly consider both the hiring and the firing of the CEO by the board. By relating these two tasks we are able to investigate why some boards are stricter in their dismissal/retention decision than other boards. We assume that boards differ in their ability of selecting the ”good” CEO: the efficient board has a higher probability of selecting the good CEO relative to the inefficient board. Therefore the quality of the selected CEO depends on the type of board of directors. This in turn implies that the dismissal/retention decision conveys information about both

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the quality of the CEO and the type of board. We show that the board’s behavior depends on the pressure from the takeover market and on whether the type of the board is public information. When the type of the board is publicly known, the takeover threat makes the efficient board stricter in its retention decision while the inefficient board becomes more lenient and never dismisses the manager. When the type of board is instead private information, the equilibrium depends on the efficiency of the (potential) acquirer relative to the efficiency of the average board. The higher the efficiency of the potential acquirer, the more likely is its bidding for the firm. Then, our model shows that when the efficiency of the acquirer is high (i.e. the pressure from the takeover market is high) both boards prefer to ignore the signal on the manager’s quality and they always retain him. When instead the efficiency of the acquirer is low in addition to the equilibrium in which the manager is always retained, there is another equilibrium in which both boards decide whether to retain the manager according to the signal observed. In other words, in this equilibrium both types of boards dismiss the manager with positive probability. The novel aspect of our paper is that the board has two closely related but different tasks. The board may try to hide its inability in accomplishing the first task, CEO selection, by distorting the second one, retention/dismissal decision. This behavior leads to the main result of the paper: pressure from the takeover market induces the board, irrespective of its type, not to use the information on the CEO and to retain him. Manager retention is a sort of defensive strategy for the board that minimizes the probability of takeover. Hence, our model endogenously derives situations where the board has an incentive to retain a bad CEO. Our paper is closely related to Hirshleifer and Thakor (H-T hereafter) 1998. As in H-T the board and the acquirer observe different signals on the manager’s quality and the manager has to undertake an investment whose return depends on his own type. However, in H-T the board has only a monitoring role and the selection of the new manager is not explicitly considered. Then, the only case in which the acquirer can do better than the incumbent board is when a ”bad” manager is retained by the board. This explains why in the H-T model takeover can take place only when the acquirer observes manager retention. On the contrary, in our model, takeover can occur also after a dismissal decision if the acquirer believes he is more efficient than the incumbent board in the selection of the new manager. As a consequence, despite the fact that in both models the threat of a takeover can make the board either stricter or more lenient, we get opposite predictions with respect to their model. H-T show that when the board is most concerned about the possibility of being displaced, and the probability of being displaced is high, the threat of a takeover makes the board stricter. In our model, instead, when the probability of being displaced is high, the board becomes ”manager friendly” and ignores the signal received. Empirical studies have tried to set the controversies on whether control mechanisms are effective by providing evidence on the functioning of both the internal and external control systems. A large empirical literature has studied whether board of directors are effective in monitoring and disciplining the CEO on behalf of the shareholders (for example Coughlan and Schmidt, 1985; Kaplan, 1994, Hermalin and Weisbach, 1988, Denis et Al., 1997). Other studies have tested whether takeovers can reduce managerial discretion (Jensen, 1988; Scharfstein, 1988) and remove inefficient managerial teams (Martin and McConnell, 1991; Franks and Mayer, 1996). Finally, some recent works have addressed the issue of whether internal and external monitoring mechanisms are complements or substitutes. Mikkelson and Partch (1997) and Huson et al. (1998) accomplish this by analyzing the behavior of boards of directors during periods of ”active” and ”inactive” takeover markets. Mikkelson and Partch find that disciplinary CEO departures have declined over 3

time and they consider this a result of the reduced takeover activity in recent years. On the contrary, Huson et Al. find that CEO forced departures have increased over time and they conclude that ”internal monitoring mechanisms are not less effective during period of inactive takeover markets than during periods of active takeover markets” (p.2). Thus, empirical evidence on the interplay between internal monitoring by the board and the takeover market is inconclusive. Our model offers a possible explanation of this by showing that takeover threat has an ambiguous effect on boards’ behavior that depends on the type of the board and on whether the board’s type is publicly known. Our model may also contribute to the debate on whether different corporate governance mechanisms are substitutes or complements (see, for example, Rediker and Seth, 1995). Indeed, it suggests that when the board is in charge of both the hiring and the firing of the CEO and the type of the board is private information, internal and external monitoring are substitutes. Under a takeover threat both types of board prefer to retain the CEO irrespective of his quality and the external acquirer substitutes the board in the retention/dismissal decision. When instead the type of the board is publicly known, internal and external control mechanisms are complements if the board is efficient (i.e., the efficient board becomes stricter in its retention decision) and are substitutes if the board is inefficient. The rest of the paper is organized as follows. Section 2 presents the model. Section 3 discusses the benchmark case in which we assume no market for corporate control. Board behavior under takeover threat is analyzed in section 4 that presents the basic model. Section 5 and 6 analyze the equilibria of the game in the two cases in which the acquirer does and does not know the type of board respectively. The two following sections present two extensions of the model. Section 7 discusses how our result change if we allow the acquirer to dismiss the CEO but retain the board. In Section 8 instead, we assume that the acquirer observes the signal also when the manager is dismissed by the board. Finally, Section 9 concludes.

2

The Model

Consider a firm that is represented by a three-tier hierarchy: shareholders/board of directors/manager. The firm has to undertake an investment whose return depends on the quality of the manager (the CEO). The manager has private information on his type that can be good or bad. If the manager is good profits are positive, π = π > 0, and they are zero π = π = 0 if the manager is bad. The probability of π is strictly positive, 1 > Pr(π) > 0, and represents the proportion of good managers in the economy. Since profits are uniquely determined by the manager’s quality, in the following we will use the notation π and π rather than good and bad. The board hires the CEO who in turn selects and supervises the investment. There are two types of board: efficient (EB) and inefficient (IB). The ex-ante probability of the efficient board is 0<λ <1. The efficient board selects the good CEO with probability 0 < ξ E 6 1, and the inefficient with probability 0 < ξ I < ξ E . We take the ability of selecting the good type of CEO as exogenously given and we rule out any moral hazard problem. For example, the inefficient board may be one that approves any proposal made by the incumbent CEO without questioning, while the efficient board may be one in which directors really look for the best candidate. Empirical evidence shows, for instance, that boards with a larger proportion of outside directors are more likely to choose outside CEO and that shareholders benefit from outside appointments (Borokhovich, Parrino and Trapani, 1996). Hence, the different behavior of the board may be motivated by differences in the proportion of independent directors on the board: the efficient

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board would have a higher proportion of independent directors than the inefficient one. Besides choosing the manager, the board also performs a monitoring task. After selecting the CEO the board privately observes a signal y on the CEO’s quality, updates its prior and decides whether to retain or dismiss him. We assume that different types of board are equally efficient in performing this task, i.e. the signal y only depends on the level of profits. If the efficient board were also a more effective monitor (i.e. if it received a more precise signal than the inefficient board) our results would not change. We consider two different cases according to whether the type of board is publicly known or not. First, we examine the case in which there is symmetric information between the acquirer and the board: the acquirer knows the type of board and neither knows the quality of the manager. Then, we introduce asymmetric information between the acquirer and the board by assuming that the acquirer knows neither the board’s type nor the CEO’s quality. The acquirer’s type (i.e., the probability of his choosing a good manager) is instead, common knowledge and is denoted by ξ A . To make the case interesting, we assume that the acquirer has higher probability of choosing a good CEO than the inefficient board but lower than the efficient one: ξ E > ξ A > ξ I . The acquirer observes the board’s retention/dismissal decision and, if the manager has been retained, also a private signal z representing all the information that he can gather on the firm’s expected profits. Then, he updates his prior on the CEO quality and on the type of the board and, finally, he decides whether to make a takeover bid. In section 8 we extend our analysis to the case where the board observes the signal z also when the CEO has been dismissed. In this case, the signal refers to the effects of the decisions of the old CEO. Although the manager has already been fired, it may still be useful for the acquirer, because it indirectly conveys information on the type of the board. To simplify notation, we assume that the two signals are identically distributed with density function f (x) and cumulative density function F (x). Assuming different distribution function would not affect our results. For simplicity we assume that both the board and the acquirer can obtain the signal y and z respectively, at no cost. Again, results would not be affected by considering a positive cost of obtaining such information. We make the following assumptions on the signals. Assumption 1: Both signals depend on the manager’s quality in the sense of first order stochastic dominance (FOSD) of the conditional distribution functions: e|π) F (x 6 x e|π) 6 F (x 6 x

x = y, z.

Assumption 2: The monotone likelihood ratio property (MLRP) holds so that as the signal increases, the likelihood of getting the signal x if the level of profits induced by the manager is π relative to the likelihood if the level of profits is π must increase: f(x|π) is decreasing in x f(x|π) with x = y, z. The MLRP also implies that a higher value of either signal indicates a greater ∂ Pr(π|x) > 0 with x = y, z. probability that the manager is good: ∂x Assumption 3: lim_ Pr(π|x) = 1

and

x→ x

5

lim Pr(π|x) = 0 with x = y, z.

x→x

Assumption 4: The two signals are positively correlated but conditionally independent: with π = π, π.

f (y, z|π) = f(y|π)f(z|π)

Assumption 5: The level of profits π is a sufficient statistic for the type of board with respect to x : f (x|iB, π) = f(x|π)

(1)

with x = y, z and i = E, I. >From Assumption 5 it follows1 that the signal and the type of board are conditionally independent: f(x, iB|π) = f (x|π)f (iB|π) with i = E, I. Assumption 6: i.e. :

∂

∂

µ

µ

1 − F (x|π) F (x|π) and are decreasing in x with x = y, z, F (x|π) 1 − F (x|π)

F (x|π) F (x|π)

1 − F (x|π) 1 − F (x|π)

¶

¶

/∂x =

/∂x =

f (x|π)F (x|π) − f (x|π)F (x|π) <0 [F (x|π)]2

−f (x|π) [1 − F (x|π)] + f (x|π) [1 − F (x|π)] <0 [1 − F (x|π)]2

Assumptions 1 and 2 are standard. Assumption 3 states that for very small or very large values the signal becomes perfectly informative. Assumption 4 says that the two signals are positively correlated but they are independent when we look at the conditional density functions. Assumption 5 states that y and z are signals on the level of profits: information on the board’s type adds nothing to the conditional probability on π. Assumption 6 means that the cumulative distributions conditional on π and π get continuously closer and closer as y increases. It points out a sort of monotone likelihood ratio property on the cumulative distribution function. It says that the likelihood that a signal is lower/higher than a given level of x when it comes from the distribution conditional on π decreases as x increases relative to the likelihood that the signal is lower/higher than the level of x when it comes from the distribution conditional on π. The objective of the board is to maximize its expected compensation. We assume that the compensation is designed to align the board’s and the shareholders’ objectives and is given by a fraction of the profits απ (with α < 1). This could be the case if directors own some shares of the firm or if their compensation is related to the firm’s profits. This assumption is meant to capture the fact that incentive compensation, widely used for executives (inside directors), has become a common practice also for outside directors. Moreover, stock ownership by directors has substantially increased in the last two decades. We rule out private benefits so that the acquirer makes a bid only if the expected profits with a takeover are larger than the expected profits without takeover: 1 f (x, iB|π)

=

f (x,iB,π) Pr(,π)

=

f (x|iB,π) Pr(iB,π) Pr(π)

= f (x|π) Pr(iB|π)

6

E(π|N T ) < E(π|T ) where N T and T stand for non takeover and takeover, respectively. We assume no active role for the shareholders except for the acceptance of a takeover bid whenever there is an expected surplus but we do not model how the surplus is divided between the bidder and shareholders. Shareholders’ information set is restricted to public information. This implies that, according to the different hypothesis made in the following sections they may or may not know the efficiency of the board while they always know the efficiency of the acquirer and as a consequence, they know E(π|T ). We assume that the price offered is consistent with their expectation on profits so that they tender their shares and the bid is successful. We restrict our attention to hostile takeovers and in the first part we assume that if there is a takeover both the manager and the board are replaced. Thus, we analyze the behavior of the board under the highest possible takeover pressure. Such assumption is motivated by two considerations. First, in our model the CEO’s quality and the board’s quality are correlated: an efficient board selects a good CEO with higher probability than the inefficient board. Second, empirical evidence suggests that post-takeover turnover rates are very high both for CEOs and other board members (see, for example, Martin and Mc Connell 1991). In Section 7 we relax this assumption and we allow the acquirer to fire the CEO but to retain the board. Observe that in our model, firm’s profits are affected by the board only through the initial choice of the manager and the subsequent retention/dismissal decision. Once the manager has been selected and the board has decided to retain him, the type of the board becomes irrelevant: it is the manager who makes the difference between high and low profits. This leads to different motivations for the takeover when the acquirer observes manager retention and when it observes manager dismissal. In the first case the takeover bid is justified by the acquirer’s belief that the incumbent manager is bad despite the retention decision of the board. In the second case, instead, the takeover is justified by the acquirer’s belief of being more efficient than the incumbent board in selecting a new manager. Also the type of information useful to the acquirer in order to decide whether to make the takeover bid is different in the manager dismissal and manager retention cases. In the first case, it is crucial to know the type of board to anticipate whether the new manager selected by the board will be good or bad (i.e., whether profits will be low or high). When instead the acquirer observes manager retention, he is interested in knowing the type of the manager, and the information on the type of the board can be useful only when boards have different retention/dismissal strategies. Summarizing, the timing of the game is the following: 0. Nature selects the type of both the board and the CEO. 1. At the start of the game the board selects a new CEO. The CEO undertakes an investment. Investment returns are determined by the quality of the CEO that is unknown. 2. The board privately observes a signal of the manager’s quality, y and decides whether to retain the CEO or to dismiss him. If the incumbent CEO is dismissed a new CEO is selected from the population. 3. If the manager has been retained, a private signal, z, is made available to the external acquirer. After having observed the board’s dismissal/retention decision and possibly the realization of z, the acquirer updates his estimate of the manager’s quality and decides whether to make a takeover bid. 4. Profits π are realized.

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3

Internal control with no takeover threat

As a benchmark let us analyze the behavior of the board under the assumption that there are no takeovers. This may be the case either because they are forbidden by law or simply because concentrated ownership and the limited contestability of firms make hostile takeovers virtually impossible. This was, for instance, the situation in Continental Europe until few years ago. After observing the realization of y, the board decides whether to retain or to dismiss the manager by comparing the expected compensation (απ) in the two cases, conditional on the realization of y. The point is that the probability of receiving a positive level of profit depends on the board’s choice between manager retention and manager dismissal. Let MD and MR denote the case in which the manager is dismissed and the case in which the manager is retained respectively. The board’s objective is to maximize its compensation. Thus, it retains the manager when: απ Pr(π|MR) > απ Pr (π|MD) and it dismisses him otherwise. The dismissal/retention decision is based on the signal y observed by the board. Then, a threshold value yeiNT , with i = E, I (where E and I stand for efficient and inefficient respectively) is determined as the level of the signal that makes the board of type i indifferent between retaining or dismissing the manager. The decision rule of the board is to retain the manager when the signal is above the threshold level ( y > yeiNT ) and to dismiss him whenever the signal is below such level (y < yeiNT ). Without loss of generality we assume that in case of indifference ( y = yeiNT ) the board dismisses the manager. Note that in case of manager dismissal a new manager is selected from the population. Therefore Pr(π|MD) = ξ i . This allows us to establish the following proposition. Proposition 1. Under the assumption that there does not exist a market for corporate control, each type of board retains the manager when ye > yeiNT and dismisses him otherwise. The threshold level yeiNT is defined by: with i = I, E.

¢ ¡ ¯ Pr π ¯y = yeiNT = ξ i

(2)

¡ ¯ ¢ Note that from ξ i > 0 together with Pr π ¯y = 0 and Pr (π |y ) strictly increasing in y, it follows that the threshold level is unique and strictly higher than the lower bound of the support of y: yeiNT > y. This means that each board dismisses the CEO with positive probability. Observe also that eq. (2) together with ξ E > ξ I implies that the efficient board selects a threshold level higher than the NT > yeINT . Being more efficient in the choice of a new manager, inefficient board: yeE the efficient board dismisses the manager under higher values of the signal y. This, however, does not imply that the efficient board dismisses the manager more often than the inefficient one since higher values of the signal are more likely when the manager is good and a good manager is more likely to be chosen by the efficient board than by the inefficient one2 . 2 The efficient board dismisses the manager more frequently than the inefficient one when the yE |π)(1 − ξ E ) ≥ F (e yI |π)ξI + F (e yI |π)(1 − ξ I ). following inequality is satisfied: F (e yE |π)ξ E + F (e Whether this condition is satisfied or not depends on the parameter of the model.

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4

Internal versus external control: the basic model

Let us now assume that there is an active market for takeovers. A potential acquirer observes the retention/dismissal decision taken by the board and in case of retention, a private signal z on the manager’s quality. Then, he decides whether to make a takeover bid. We consider two different situations according to the amount of information available to the acquirer. First, in Section 5 we assume that the type of board is common knowledge. Then in Section 6 we consider the case in which it is private information. As we pointed out before, the proportion of outside directors on the board determines the intensity of the monitoring activity of the board and its attitude toward hiring outside CEOs. Thus, the proportion of outside directors can be considered a good proxy for the type of board: an outsider-dominated board would be efficient, while an insider-dominated board would be inefficient. If we accept this interpretation, knowledge of the type of the board can be a realistic assumption for several companies, and in particular for listed companies that have stricter information requirements. However, although most boards can be classified as insider- or outsider-dominated, there are relevant cases in which the number of ”grey” directors (i.e. directors that fall in neither category) makes it quite difficult to identify the ”type” of board. We capture these situations by considering the case in which the type of board is private information. When the type of board is common knowledge a sequential game of complete information takes place between the board and the potential acquirer, when instead there is private information a signalling game is played where the manager retention/dismissal decision acts as a signal of the board’s type. In the following two subsections we examine the decision problem of both the board and the acquirer with reference to the signaling game. The case in which the type of the board is common knowledge can be considered as a particular case where beliefs always take value zero and one. After observing whether the incumbent manager has been dismissed or retained, the potential acquirer forms a belief on the board’s type that is reflected in his expectation on the ability of the manager. If the incumbent manager is dismissed, the acquirer attaches to the event ”the new manager selected by the board is good” a different probability according to his belief on the type of the board. If the incumbent manager is retained, the acquirer forms his expectation on the manager’s ability on the ground of the signal z and of his beliefs on the type of board. In the latter case the acquirer defines a threshold level zeR such that a takeover will occur only when z < zeR . The board however anticipates such behavior when taking its decision.

4.1

The decision problem of the board

The board observes the signal y and then decides whether to dismiss or to retain the manager on the basis of the expected compensation it obtains in either case. Recall that in case of a takeover (T ) the board is displaced and receives no compensation. However, if directors hold shares of the firm they can have monetary gain from a takeover. In the following analysis we abstract from such a gain and we concentrate only on the directorship income. This is consistent with empirical evidence found by Harford (2000) who documents that the gain on the equity is too small to compensate directors from the loss of directorship income. The board chooses manager retention (M R) when α [π Pr (π, N T |M R )] > α [π Pr (π, NT |M D )] and manager dismissal (MD) when the inequality holds in the opposite direction. Again, we assume that in case of indifference the CEO is dismissed. If there is a 9

positive probability of no takeover (N T ) both when MD and when MR are chosen, there may exist a threshold level of the signal yei that equates the probabilities on the two sides of the inequality: Pr (π, N T |MR ) = Pr (π, N T |MD )

(3)

The above expression can be written as: Pr (π |N T, MR ) (Pr N T |M R) = Pr (π |NT, MD ) (Pr N T |M D ) When the manager is dismissed and there is no takeover, the incumbent board selects a new manager from the population. Then, we have that Pr (π |N T, M D ) = ξ i . Since in case of manager retention the probability of no takeover is represented by Pr (z > ze), we can substitute these two terms in the above equation and we obtain that the threshold level yei is given by: Pr (π |z > zeR , y = yei ) Pr (z > zeR |y = yei ) = ξ i Pr (NT |y = yei )

(4)

Pr (z > zeR |π ) Pr (π |y = yei ) = ξ i Pr (N T |y = yei )

(5)

with i = E, I. After some manipulation, by using Assumption 4, eq. (4) can be conveniently rewritten as:

There may also be cases in which the RHS (LHS) of the above equations is always greater than the LHS (RHS). This means that it is profitable for the board to always dismiss (retain) the manager and we have a corner solution with threshold yi = y). level yei = y (e

4.2

The decision problem of the acquirer

A takeover takes place only if the acquirer, after observing the dismissal/retention decision of the board and possibly the realization of z, believes that the probability of high profits under incumbent management is lower than ξ A , that represents the probability of high profits with a takeover (which is always successful by assumption). The acquirer’s expectation on profits depends on his beliefs on both the board’s and the CEO’s type. In particular, when the manager is dismissed and no takeover takes place, the probability of high profits depends entirely on the type of the new CEO, which in turn depends on the board’s type. The dismissal/retention decision acts as a signal from the board to the acquirer that makes the latter revise his prior on the type of the incumbent board. Then, the acquirer makes a takeover only if he believes he is more efficient than the board. When instead, the manager is retained, the probability of high profits depends only on the manager’s type. Given his beliefs on the type of the board, the acquirer determines a threshold level of the signal, zeR such that it equates the expected profits from not acquiring the firm to ξ A π. Then, when the signal observed is more favorable than zeR the acquirer believes that the expected profits under incumbent management are higher than ξ A π and no takeover takes place. On the contrary, when the signal is below zeR a takeover takes place. 10

Manager dismissal Suppose the acquirer observes manager dismissal (M D). Denoting with µ (π |Mj ) , j = D, R the beliefs of the acquirer and assuming that in case of indifference he does not acquire the firm, a takeover bid occurs if : _

_

_

_

πµ(π|N T, M D) < πP r(π|T, M D) After a takeover a new manager is chosen by the acquirer. This implies that _ P r(π|T, M D) = ξ A . Substituting this value in the above expression we have that a takeover takes place only when the acquirer believes that under incumbent board _ π occurs with probability lower than ξ A : _

µ(π|N T, M D) < ξ A

(6)

Since the beliefs concern the type of board, the LHS of eq.(6) can be written in the following way: _

_

Pr(π|NT, MD, EB)µ(EB|N T, M D) + Pr(π|N T, M D, IB)µ(IB|NT, MD)

(7)

_

Finally, consider that P r(π|N T, M D, iB) = ξ i , i = E, I. By substituting these two terms in the above equation we have that the acquirer makes a takeover when: ξ E µ(EB|N T, M D) + ξ I µ(IB|NT, MD) < ξ A When the firm is not taken over and manager dismissal is observed the probability of high profits depends on the efficiency of the board in replacing the manager (ξ i ) as well as on the belief that the dismissal comes from an efficient/inefficient board. Hence, the acquirer decides to make a takeover only if his belief on the board being inefficient is sufficiently high. Since in equilibrium it must be the case that _ _ µ(π|N T, M D) = Pr(π|N T, M D), this means that we must have a sufficiently high probability that the board is efficient in order to have no takeover after manager dismissal.

Manager retention When the manager is retained (MR), the acquirer observes, in addition to the board’s decision also the signal z. He chooses a threshold level zeR by equating the probability of high profits with a takeover to the probability of high profits without a takeover: _

_

µ(π|N T, M R) = Pr(π|T, M R) _

where as before µ(π|N T, MR) can be written as: _

_

Pr(π|N T, M R, EB)µ(EB|NT, MR) + Pr(π|N T, M R, IB)µ(IB|N T, M R)

(8)

_

Considering that Pr(π|T, M R) = ξ A , the acquirer’s problem takes the following form: _

Pr(π|z _ Pr(π|z

= zeR , y > yeE , EB)µ(EB|z = zeR , y > yeE ) + = zeR , y > yeI , IB)µ(IB|z = zeR , y > yeI ) = ξ A 11

(9)

To evaluate the LHS of (9) a few observations are in order. First, the board’s decision to retain the manager is a signal on the latter’s ability. Second, such a signal also depends on the type of board since the two boards have different threshold levels for their dismissal/retention decision. Then, knowledge of the board’s type is necessary to infer from the retention decision the signal observed by the board. As to zeR , we might have in principle both an interior and a corner solution. The following Lemma simplifies the problem by ruling out the possibility that the acquirer never zR = z) after he observes zR = z) or always makes a takeover (e makes a takeover (e manager retention. Lemma 1. When manager retention is observed, the acquirer chooses an interior value for the threshold level zeR : Proof. See Appendix 1.

zeR ∈ (z, z).

The reason why corner solutions can be excluded is quite intuitive. A threshold zR = z) would imply to always (never) make a takeover. However, value zeR = z (e a signal z = z (z = z) perfectly reveals that profits are high (low) thus makes a takeover unprofitable (profitable).

5

The equilibrium of the game when the acquirer knows the board’s type

In the present section we assume symmetric information between the board and the acquirer: the acquirer knows the type of the board and none of them knows the manager’s quality. Knowledge of the type of the board greatly simplifies the acquirer’s behavior. Indeed the game between board and acquirer becomes a sequential game of complete information that can be solved by backward induction.

Inefficient Board In case of manager dismissal, the acquirer makes a takeover bid with probability one if the board is inefficient since ξ I < ξ A . Given the acquirer’s strategy, the inefficient board always chooses manager retention (M R) if Pr(N T |M R ) > 0 since: Pr (π |NT, MR ) Pr(N T |M R ) > 0

(10)

where the LHS is the expected payoff from manager retention and the RHS is the expected payoff from manager dismissal. Hence the threshold level chosen by the board is yeI = y. The threshold level selected by the acquirer in case of manager retention zeRI then solves: Pr (π |z = zeRI ) = ξ A

(11)

and, by the same reasoning followed in section 3 when establishing yeiNT , it is an interior solution and is unique which effectively implies Pr(N T |M R ) > 0.

In other words, since the board never dismisses the CEO, the acquirer has to rely only on his signal z when taking his decision .

12

Efficient Board Suppose now the board is efficient. If the acquirer observes manager dismissal it never makes a takeover since ξ A 6 ξ E . Then the efficient board chooses the threshold level yeE to satisfy: _

Pr(z ≥ zeRE |π) Pr(π|y = yeE ) = ξ E

(12)

where the RHS represents the expected payoff in the case of manager dismissal (given that the probability of no takeover after manager dismissal is equal to one) and the LHS is the expected payoff from manager retention. The acquirer chooses zeRE so as to satisfy: _

Pr(π|z = zeRE , y > yeE ) = ξ A

(13)

_

where the LHS is the probability of _obtaining π in the case of no takeover and the RHS is the probability of obtaining π in the case of takeover. The solution to the system of equations (11)-(13) gives the equilibrium values of yeE , zeRI and zeRE . The next Proposition shows that these values exist and are NT is the threshold level of y chosen by the efficient board unique. Recall that yeE when there does not exist a market for corporate control. Then:

Proposition 2.When the type of board is publicly observable there is a unique subgame perfect equilibrium in which the inefficient board always retains the CEO, ∗ NT yeI∗ = y, and the efficient board selects yeE ∈ (e yE , y). The acquirer chooses zeRI and zeRE ∈ (z, z) with zeRI >e zRE and never makes a takeover when the efficient board dismisses the CEO. Proof. See Appendix 1.

Proposition 2 shows that the introduction of a market for corporate control modifies the behavior of both types of boards, but changes go in opposite directions. Because of the takeover threat the efficient board becomes stricter in its retention decision ∗ NT > yeE ) while the inefficient board yE and dismisses the manager more often (e yI∗ = y). The acquirer makes becomes more lenient and never dismisses him (e zRI >e zRE ) . takeover bid more often when the board is inefficient (e The inefficient board chooses to always retain the manager because there is no takeover if the acquirer receives a sufficiently high signal on the manager’s quality. The takeover would instead take place with probability one if the manager were dismissed by the inefficient board since by assumption the acquirer is more capable of selecting a good manager. Using Hirshleifer and Thakor’s terminology, when the board is inefficient there is a ”substitution effect” and the task of replacing the manager is shifted from the board to the acquirer. This has a twofold effect. On the one side, it brings a gain in efficiency because of the higher ability of the acquirer in replacing the CEO. On the other side, we must consider that a takeover is made following the realization of z, i.e. the information of the acquirer is substituted to that of the board, and this leads to a gain or a loss in efficiency depending on the relative precision of the two signals. In summary, when the board is inefficient the introduction of the financial market leads to a gain to the shareholders unless z is much less precise than y. When instead the board is efficient there is the ”kick-in-the-pants effect” and the board becomes stricter in its retention/dismissal decision than it would be in the absence of a takeover threat. This happens because the board is more efficient than the acquirer in selecting the manager and it is never replaced after manager dismissal. 13

Observe that the more efficient the acquirer the higher is the probability of takeover after manager retention. Indeed, equation (11) and equation (13) imply that both zeRI and zeRE , increase with ξ A .3 An increase in zeRE in turn leads to an ∗ to satisfy the board’s problem. To see this, consider equation (12). increase in yeE It is easy to see that the LHS of the equation that defines the board’s problem ∗ . Thus, keeping ξ E constant, an increase is decreasing in zeRE and increasing in yeE ∗ . Summing up, an increase in in zeRE must be accompanied by an increase in yeE the efficiency of the acquirer leads to higher probability of takeover which in turn leads the efficient board to become stricter in its dismissal/retention decision. Thus an increased takeover pressure makes the efficient board tougher on the manager. Again the effect in terms of shareholders’ welfare is twofold. A stricter behavior implies a loss in efficiency4 . However this loss is counterbalanced by the fact that the decision on manager dismissal is taken following both the realization of y and z 5 , i.e. the information of the acquirer is aggregated to that of the board. The final result cannot be established a priori: whether the takeover threat brings a gain or a loss in efficiency depends on which effect prevails. If we want to evaluate the overall effect of the financial market on shareholders’ welfare we must first of all take into account the proportion of efficient board λ: unless z is much less precise than y, the lower is λ the better it is to have disciplinary takeovers. Note that because of the substitution effect, when the board is inefficient it is also better to have a relatively efficient acquirer, i.e. a high value of ξ A . When instead the board is efficient, a high value of ξ A implies a strong “kick-in-the-pants” effect which might offset the positive effect of information aggregation. Again, the overall consequences of the introduction of a financial market depends on the parameters of the problem, in particular on the proportion of efficient boards λ and on the relative efficiency of the acquirer with respect to the board (ξ A v. ξ E , ξ I ). The information structure is crucial in the derivation of this result. In the next section we show that when the acquirer does not know the type of the board, the takeover threat also induces the efficient board to always retain the manager. In other words, the acquirer’s uncertainty about the board leads to a greater distortion relative to the case in which the board’s type is publicly known.

6

The equilibria of the game when the acquirer does not know the board’s type

As we discussed before, there are cases in which it may be difficult to know the type of board either because the number of ”grey” directors sitting on the board is large relative to the number of inside and outside directors, or because it may be difficult to get reliable information on boards of non listed companies. We address these cases in the present section where we discuss the solution of the signalling game played between the board and the acquirer when the latter does not know the type of the former. We adopt perfect Bayesian equilibrium as the solution concept of the game. First of all, note that Lemma 1 excludes the existence of equilibria in which zeR takes extreme values z and z. This means that there cannot exist equilibria in which there is a takeover with probability one or zero after manager retention: a 3 This is immediate for eq. (11). In the proof of Proposition 2 it is shown that (13) is increasing in z. 4 Since EB is more efficient than the acquirer in replacing the manager, we know that the first best would be established if only the CEO and not the board were dismissed after a takeover. In ∗ is equal to y NT . More on this in Section 8. this case yeE eE 5 Again with respect to the case in which EB were not displaced following a takeover, z eRE is too low. See Section 8:

14

takeover is always conditional on the level of the signal z. Consider then the event ”manager dismissal”. Since the acquirer has no opportunity to observe any signal he only has a binary unconditional choice: to make or not make the takeover6 . As a consequence we need to consider two possible types of equilibria: those in which there is a takeover after manager dismissal and those in which the takeover does not take place. We can then establish the following proposition. Proposition 3 There always exists a perfect Bayesian pooling equilibrium in which both types of board always retain the manager, i.e. they choose yei = y i = E, I, and the acquirer chooses zeR ∈ (z, z) . Out-of-equilibrium-path beliefs are such that if the board were to dismiss the manager, the acquirer would always make ξ A can be determined with λξ E + (1 − λ)ξ I > b ξ A >ξ I such a takeover. A value b ξ A . For ξ A < b ξ A there also that the above equilibrium is unique for ξ E > ξ A ≥ b exists another equilibrium in which both types of board dismiss the manager with positive probability, i.e. they choose yei ∈ (y, y) i = E, I, and the acquirer chooses zeR ∈ (z, z) while he never makes a takeover if the manager is dismissed. Proof

See Appendix 1.

Asymmetric information induces the efficient board to change its strategy radically. The only equilibrium that always exists is the one in which both types of board never dismiss the manager. This is so because the acquirer believes that manager dismissal is a signal of board inefficiency and this in turn induces him to bid for the firm. When the acquirer is relatively efficient with respect to the average board (high ξ A , low ξ E or λ ) the equilibrium in which the manager is always retained is unique. If the acquirer were to observe manager dismissal he would always prefer to replace the board in the task of choosing a new CEO and this prevents the existence of the equilibrium in which the dismissal of the manager is not followed by a takeover. When instead the acquirer is relatively inefficient, the equilibrium in which the manager is always retained still exists because it can be sustained by beliefs that the board that dismissed the manager is sufficiently inefficient. However, there also exists the other equilibrium in which both boards dismiss the manager with positive probability. In our model, manager retention is a sort of ”defensive strategy” for the board. When the manager is retained, the type of board becomes irrelevant and the decision of the acquirer is based on the expected ability of the manager given the signal observed. Hence, if the realization of z is sufficiently high, the takeover is not profitable. When the manager is dismissed, the acquirer’s decision is based only on its efficiency relative to the board’s expected efficiency. This explains why manager dismissal always leads to a takeover and the board’s optimal strategy is manager retention if the acquirer is more efficient than the expected board in selecting the manager. As in all signaling models, the bad type (the inefficient board) imposes a cost on the good type (the efficient board) that cannot credibly signal its type. Hence, asymmetric information about the board’s type leads to a distortion with respect to both the case of symmetric information and the benchmark case with no market for corporate control. In the first equilibrium in which the manager is always retained, the acquirer substitutes the board in the firing decision and this, besides resulting in an ex post inefficiency when the board is efficient, is also ex ante inefficient whenever λξ E + (1 − λ)ξ I ≥ ξ A . Moreover, in such equilibrium the information of the acquirer is substituted for that of the board and this, if the latter is efficient, imposes a loss 6 In other words, in this section we only consider pure strategies for the acquirer. Note that considering mixed strategies would be formally equivalent to analyzing the case where the acquirer is allowed to observe z even after manager dismissal that is studied in section 8.

15

with respect to the case in which both signals are used. In addition, it may also impose a loss with respect to the benchmark if z is less precise than y. As to the second equilibrium, after manager dismissal there is no takeover bid and this means no ex ante inefficiency since such equilibrium exists only when the average board is more efficient than the acquirer. However, if the board is inefficient there is an ex post inefficiency since the latter is not replaced (recall that ξ I < ξ A ). After manager retention there is information aggregation, i.e. both y and z are used. From the shareholders’ viewpoint the second equilibrium is better than the first when the board is efficient, and viceversa, the first is better than the second when the board is inefficient7 . In order to compare social desirability of the two equilibria we must then take into account the proportion of efficient boards λ and the difference in the efficiency of the average board and of the acquirer (which depends both on λ and on ξ A v. ξ E and ξ I ): the higher λ and/or such difference, the more the second equilibrium is preferred to the first. The results presented in Propositions 3 have been derived under the implicit assumption that there is no cost in dismissing the board. This assumption is stronger than necessary and it may be relaxed. For example we can assume that there is an exogenous cost in displacing the board, c. The introduction of an exogenous cost is equivalent in our model to a decrease in the acquirer efficiency, ξ A and it does not affect our findings. To see this, consider the problem of the acquirer if manager dismissal has been observed. The acquirer now makes a takeover if _

_

_

_

πµ(π|NT, MD) < πP r(π|T, M D) − c

which can be written as: _

_

µ(π|N T, M D) < ξ A − c/π where the LHS represents the expected profits in the case of no takeover and the RHS represents the expected profits in the case of a takeover. The cost of dismissing the board reduces the expected profits in the case of a takeover. The same applies when the acquirer observes manager retention. The acquirer now chooses the threshold level zeR to satisfy the following equation _

_

µ(π|N T, M R) = ξ A − c/π

The introduction of a cost of dismissing the board clearly does not modify the equilibrium behavior of the acquirer after manager dismissal but it makes the acquirer less aggressive after manager retention by inducing him to set a higher threshold level zeR . Furthermore, such a cost would make the equilibrium in which each type of board always retains the manager less likely in the sense that the range of the parameter values such that manager retention is the unique equilibrium would be smaller. This confirms that in our model a takeover threat is the source of the distortion in board behavior: the more likely board’s displacement, the more distorted is board’s dismissal/retention decision with respect to the case with no market for corporate control. It might look as if our results depend on the dismissal of the board after a takeover. In the next section we extend the analysis by allowing the acquirer who has taken the firm over to retain the board while dismissing the manager and we show that the main results carry on also in this framework. 7 Unless

z is much less precise than y. See the comment to Proposition 2.

16

7

Extension 1: The board may be retained after a takeover

In the previous sections we assumed that the acquirer always dismisses the board after a takeover. We believe this captures a possible feature of hostile takeovers where the dismissal decision may be driven by reasons other than board capabilities. For example the acquirer may consider it difficult to cooperate with the incumbent board. Moreover such an assumption allows us to analyze the behavior of the board under the highest possible takeover pressure. However, the assumption is undoubtedly restrictive, especially in the case in which the acquirer knows the type of the board. Indeed, it is irrational to dismiss a board that is known or is believed to be efficient. In this section we address this issue and we allow the acquirer to fire the manager but to retain the board after a takeover. This modifies the decision problem of the acquirer and, as a consequence, also that of the board as the analysis of the two following subsections shows.

7.1

The decision problem of the board

The decision problem of the board must be modified so as to take into account the event of not been displaced after a takeover. Denoting board retention and board dismissal with BR and BD respectively, (3) can be written as Pr (π, N T |M R ) + Pr (π, T, BR |MR ) = Pr (π, N T |M D ) + Pr (π, T, BR |MD ) (14) Observe that Pr (π, N T |MR ) = Pr (π, N T, BR |M R ) 8 which implies that the LHS of (14) can be written as Pr (π, BR |MR ) . Hence (14) can be rearranged into Pr (π |M R ) = Pr (π |N T, M D ) Pr (N T |MD ) +

Pr (π |T, BR, M D ) Pr (BR |T, M D ) Pr (T |M D )

(15)

where Pr (π |T, BR, M D ) = Pr (π |N T, M D ) = ξ i since the manager is always dismissed after a takeover.

7.2

The decision problem of the acquirer

When making a takeover, the acquirer must now decide also whether to retain the board or not. Since the manager is always fired, the decision whether to retain the board is made on the ground of the latter’s relative ability to select a new manager. The acquirer retains the board if he believes the latter to be more efficient than himself in accomplishing this task. 8 This

follows from the fact that it is Pr (π, NT, BD |MR ) = 0.

17

Manager dismissal

The acquirer now makes a takeover if: _

_

µ(π|NT, MD) < µ(π|T, MD) where the LHS can be decomposed as in (7) above, while the RHS can be written as _

Pr(π|T, MD, EB, BR)µ(EB|T, M D, BR) Pr(BR|T, M D) +

_

Pr(π|T, MD, EB, BD)µ(EB|T, MD, BD) Pr(BD|T, MD) +

_

Pr(π|T, MD, IB, BR)µ(IB|T, M D, BR) Pr(BR|T, M D) +

_

Pr(π|T, MD, IB, BD)µ(IB|T, M D, BD) Pr(BD|T, M D) _

_

which, considering that Pr(π|T, MD, iB, BR) = ξ i while Pr(π|T, M D, iB, BD) = ξ A , i = E, I, can be simplified into [ξ E µ(EB|T, M D, BR) + ξ I µ(IB|T, M D, BR)] Pr(BR|T, M D) + ξ A Pr(BD|T, MD) (16) where Pr(Bj|T, MD), j = R, D depends on the decision of the acquirer himself. Since we do not allow for mixed strategies such probabilities can only take value zero or one. In particular Pr(BR|T, M D) = 1 if [ξ E µ(EB|T, M D, BR) + ξ I µ(IB|T, M D, BR)] ≥ ξ A while Pr(BR|T, M D) = 0 otherwise. In other words, the acquirer retains the board if he believes the latter to be more efficient than himself. Note that µ(iB|T, M D, BR) = µ(iB|NT, MD, BR) = µ(iB|N T, M D). Manager retention When the acquirer observes manager retention he also observes the signal z. He then chooses the threshold level zeR by equating _

_

µ(π|N T, M R) = µ(π|T, MR)

(17)

where the LHS can be decomposed as in (8) while the RHS can be written analogously to (16), i.e.: [ξ E µ(EB|T, M R, BR) + ξ I µ(IB|T, M R, BR)] Pr(BR|T, MR) + ξ A Pr(BD|T, MR) (18) Recall that after a takeover the manager is always fired. Then, the board is retained only if it is believed to be more efficient than the acquirer. As a consequence Pr(BR|T, MR) = 1(0) if [ξ E µ(EB|T, M D, BR) + ξ I µ(IB|T, MD, BR)] ≥ (<)ξ A . Again we have µ(iB|T, MR, BR) = µ(iB|NT, MR, BR) = µ(iB|N T, M R)

18

7.3

The equilibrium of the game when the acquirer knows the board’s type

Recall that when the acquirer knows the board’s type, a sequential game of complete information is played that is solved by backward induction. If the board is inefficient nothing changes with respect to the case where the acquirer does never retain the board after a takeover. The acquirer knows that the board is inefficient and therefore is willing to replace it in the task of manager selection. Then in equilibrium the board always chooses to retain the manager in the hope that a high realization of signal z induces the acquirer not to make a bid while the acquirer establishes the threshold level zeRI as in (11) and always replaces the board when making a takeover. On the other hand, the acquirer is always willing to assign the task of selecting a new manager to an efficient board. As a consequence, if the board is efficient and the manager is dismissed, there is no takeover, i.e. Pr (N T |M D ) = 1. Observe that given that the acquirer knows that the board is efficient, Pr (π, BR |MR ) = Pr (π |M R ) .9 Therefore the decision problem (15) of the board becomes: Pr (π |M R ) = Pr (π |N T, M D ) or Pr (π |y = yeE ) = ξ E

(19)

Pr (π |z = zeRE , y > yeE ) = ξ E

(20)

which is identical to the problem facing the board in the absence of a takeover NT . Since threat. We know from Proposition 1 that (19) has solution yeE = yeE the board is not displaced, it has no fear of a takeover, or, the existence of an active financial market does not induce a stricter behavior of the board. The acquirer, knowing for sure the type of board (which implies µ(EB|.., M R) = 1 and Pr (BD |T, MR ) = 0 in 18), determines zeRE from

which gives zeRE ∈ (z, z)10 . Considering that the LHS of (20) is increasing in both zeRE and yeE , this implies that the system (19)-(20) has a solution with a lower yeE and a higher zeRE than the system (12)-(13) that gives the solution values with an active takeover market in the case in which the board is always dismissed. Note that the solution to the system (19)-(20) represents the first best for the shareholders: there is information aggregation because both signals y and z are used and there is no substitution of the relatively inefficient acquirer for the efficient board in the task of selecting the manager. In other words, both the “kick in the pants” and the substitution effect are neutralized while use is made of all information that can be generated.

7.4

The equilibria of the game when the acquirer does not know the board’s type

Suppose now that the acquirer can retain the board but does not know its type. Also in this case the introduction of asymmetric information between the board and 9 This

follows from Pr (π, BD |MR ) = Pr (π, NT, BD |MR ) + Pr (π, T, BD |MR ) = 0. LHS of (20) is equivalent to the LHS of (13) whose characteristics have been analyzed in Proposition 2. In particular it guarantees the existence of a feasible solution. 10 The

19

the acquirer radically changes the behavior of the efficient board. This is reflected in the next proposition that presents the equilibria for this new case. Proposition 4 There always exists a perfect Bayesian pooling equilibrium in which both types of board always retain the manager, i.e. they choose yei = y i = E, I, and the acquirer chooses zeR ∈ (z, z) . Out-of-equilibrium-path beliefs are such that if the board were to dismiss the manager, the acquirer would always make ξ A can be determined with λξ E + (1 − a takeover and dismiss the board. A value b λ)ξ I > b ξ A . For ξ A >ξ I such that the above equilibrium is unique for ξ E > ξ A ≥ b b ξ A < ξ A there also exists another equilibrium in which both types of board dismiss the manager with positive probability choosing yei = yeiNT i = E, I, the acquirer chooses zeR ∈ (z, z) and retains the board after a takeover while he never makes a takeover if the manager is dismissed. Proof. See Appendix 2.

The equilibria given in the above proposition are similar to those illustrated in Proposition 3 where the acquirer always replaces the board after a takeover. This follows from the fact that when the acquirer does not know the type of the board, he (the acquirer) is willing to retain the board only when his own efficiency is low relative to the one of the expected board. When instead the acquirer is efficient, he prefers to replace the board. This is also the reason why in the second equilibrium, which exists only for relatively low values of ξ A , the board is retained after a takeover. Since the board is never displaced there is no ”kick in the pants” effect and we have that yei = yeiNT . If the board is efficient this brings a gain in efficiency with respect both to the pooling equilibrium and to the case in which the board is dismissed after a takeover. When instead the board is inefficient, it would be better to dismiss it after a takeover. Hence the pooling equilibrium dominates the other one. Note however that the latter equilibrium exists for relatively low values of ξ A which implies that the loss for not substituting the inefficient board is not too high. Again to compare social desirability of the two equilibria we must then take into account the proportion of efficient boards λ and the difference in the efficiency of the average board and of the acquirer: the higher λ and/or such difference, the more the pooling equilibrium is dominated by the other one.

8

Extension 2: Additional Information after manager dismissal

Consider now the case in which the acquirer observes the realization of the signal z even when the CEO has been dismissed. The signal concerns a manager that is no longer with the firm. Hence it is to be interpreted not as a signal on future profits but as a signal of the efficiency of the board. Actually, z conveys information on the level of profits that would have occurred if the CEO had not been dismissed. This in turn tells something of the efficiency of the board that selected (and then dismissed) such a manager. Formally this implies that even after M D the acquirer selects a threshold value zeD of the signal.

8.1

The decision problem of the board

Consider the decision problem of the board as it is represented in (3). The event ”no takeover” after manager dismissal can now be represented as the realization of z being no lower than the threshold value zeD . As a consequence (5) becomes: 20

8.2

Pr (z > zeR |π ) Pr (π |y = yei ) = ξ i Pr (z > zeD |y = yei )

i = E, I

(21)

The decision problem of the acquirer after MD

The decision problem of the acquirer in case of manager retention is clearly the same as before. When instead the manager is dismissed, the acquirer must determine the threshold value zeD . To do this, he compares the probabilities of high profits with no takeover to the probabilities of high profits if he acquires the firm. In other terms the threshold zeD is the value that satisfies: _

_

µ(π|N T, M D) = P r(π|T, M D)

(22)

_

where again P r(π|T, MD) = ξ A since it represents _the probability of the acquirer _ selecting a good manager while µ(π|N T, M D) = µ(π|z = zeD , M D). Recall that the belief in LHS of the above equation can be written as: _

_

Pr(π|N T, M D, EB)µ(EB|NT, MD) + Pr(π|N T, M D, IB)µ(IB|N T, M D) _

where P r(π|N T, MD, iB) = ξ i , with i = E, I. Then, the acquirer’s problem is to find a value zeD such that:

8.3

ξ E µ(EB|z = zeD , y 6 yeE ) + ξ I µ(IB|z = zeD , y 6 yeI ) = ξ A

(23)

The equilibria

Since in equilibrium beliefs must be confirmed, (23) can be written as: ξ E Pr(EB|z = zeD , y 6 yeE ) + ξ I Pr(IB|z = zeD , y 6 yeI ) = ξ A

(24)

Note also that the decision problem of the board given in (21) can be rearranged as: Pr (z > zeR |π ) Pr (π |y = yei ) = ξi Pr (z > zeD |y = yei )

i = E, I

(25)

We can now establish the following lemma that will prove useful in Proposition 5.

Lemma 2 The LHS of equation (24) is increasing in both zeD and yeE and decreasing in yeI . The LHS of equation (25) is increasing in both zeD and yei i = I, E, and decreasing in zeR . Proof. See Appendix 2. The next proposition characterizes the equilibria of the game and shows that manager retention is still a valid defence if the board is faced with a takeover threat and the acquirer has a larger information set.

21

Proposition 5 There always exists a perfect Bayesian pooling equilibrium in which both types of board retain the manager with probability one, i.e. they choose yei = y i = E, I, and the acquirer chooses zeR ∈ (z, z) . Out-of-equilibrium-path beliefs are such that if the board were to dismiss the manager, the acquirer would always make λξ E2 + (1 − λ)ξ 2I the above a takeover, i.e. he would choose zeD = z. If ξ A ≥ λξ E + (1 − λ)ξ I equilibrium is unique. (1 − ξ E )λξ E + (1 − ξ I )(1 − λ)ξ I another equilibrium exists in which the If ξ A < 1 − (λξ E + (1 − λ)ξ I ) board chooses yei ∈ (y, y) i = E, I, and the acquirer chooses zeR ∈ (z, z) and zeD = z, i.e. he never makes a takeover if the manager is dismissed. Proof. See Appendix 3.

Proposition 5 basically confirms the results of Proposition 3 also for the case in which the acquirer observes z after MD. In particular it shows that when the acquirer’s ability in selecting the manager is high with respect to the ability of the average board11 the unique equilibrium is the one in which the manager is always retained by both types of board. When instead the acquirer’s efficiency is low, there also exists an equilibrium in which the manager is fired with positive probability. As in the previous case, manager retention is a defensive strategy and therefore is always chosen when the takeover threat is ”severe”. When instead the threat is not ”severe”, i.e. relatively low values of ξ A , the board can risk to dismiss the manager and in addition to the equilibrium with manager retention there exists another equilibrium in which the manager is dismissed with positive probability and there is no takeover after M D. In other words, we find exactly the same kind of equilibria as in the absence of additional information after manager dismissal. Note, however, that if we allow the acquirer to observe z even after MD, there λξ E2 + (1 − λ)ξ I2 (1 − ξ E )λξ E + (1 − ξ I )(1 − λ)ξ I > ξA ≥ , in exists a range of ξ A , λξ E + (1 − λ)ξ I 1 − (λξ E + (1 − λ)ξ I ) which there does not exist the equilibrium with no takeover after M D but there may exist an equilibrium such that the manager is dismissed with positive probability and a takeover takes place with positive probability after M D (i.e. zeD ∈ (z, z)). The existence of this equilibrium will however depend on the specific form of the problem (form of the F () and f () besides the values of the parameters ξ i , ξ A and λ)12 . Again, when it exists it might be preferred to the equilibrium in which there always is M R and zeD = z depending on the values of the parameters. Still there is an ex post inefficiency13 in the case of an inefficient board but there may also be an inefficiency when the board is efficient since the latter is sometimes replaced after M D even if ξ E > ξ A . After manager retention there is information aggregation, i.e. both y and z are used. Summing up, to compare the two equilibria we must again take into account the specific parameters of the problem, especially the proportion of efficient boards λ and the difference in the efficiency of the acquirer and of the average board. Note that this equilibrium exists when the efficiency of the acquirer is intermediate which implies that the inefficiencies connected with the equilibrium that exhibits only manager retention are not so strong. However there still is a tendency to prefer the other equilibrium the higher is λ and the higher is the difference between ξ A and the average ability of the board. 11 Note

that

2 λξ E + (1 − λ)ξ 2I

>λξ E + (1 − λ)ξI . λξ E + (1 − λ)ξ I such equilibrium to exist we need to find values of yei i = E, I, zeD ∈ (z, z) and zeR ∈ (z, z) that satisfy (24), ( 9) and (25). 12 For

13 Note, however, that it is less severe than in the equilibrium with z eD = z since the board is now replaced after MD if z is sufficiently low.

22

9

Concluding remarks

We have analyzed how the takeover threat affects the board’s retention/dismissal decision in a setting where the board of directors has two different tasks: first, it selects a CEO of unknown quality from the population, then it observes a private signal on the quality of the CEO and decides whether to retain or dismiss him. After the board’s decision, a potential acquirer privately observes a different signal and decides whether to make a takeover bid. The novel aspect of our paper is that the board has two closely related but different tasks: CEO selection and CEO retention/dismissal decision. The board’s ability to choose a good CEO defines its type (efficient or inefficient). We consider two cases. First, we assume that the acquirer knows the type of board. Then, we assume that the type of board is private information. The main result of the paper is that the takeover threat makes the board more lenient: the board is less likely to dismiss the manager under takeover threat than with no market for corporate control. This is so because the board is afraid that the firing of the CEO may signal its inability to select a good CEO and this in turn may trigger a takeover. We show that the result depends on whether the type of board is publicly known and on the pressure from the takeover market. When the acquirer knows the type of board, the inefficient board always retains the CEO while the efficient board is stricter in its retention/dismissal decision. If instead the acquirer does not know the board’s type, the result depends on the relative efficiency of the acquirer versus the expected efficiency of the incumbent board. If the acquirer is more efficient than the expected board, the unique equilibrium has both boards retaining the manager irrespective of the signal received. Otherwise, there also exists an equilibrium in which both boards dismiss the CEO with positive probability. Our model rationalizes the collusive behavior of the board and the CEO, and shows that such a behavior may be the result of the optimizing behavior of the board to the threat of being displaced by a takeover. Indeed, manager retention is the unique equilibrium strategy when takeover threat is more credible. This result is in contrast with the finding of Hirshleifer and Thakor (1998) who show that the board becomes stricter when it is most concerned with the possibility of being displaced. The opposite predictions of the two models are due to the fact that in the H-T model the board has only a monitoring task while in our model the board has two tasks: the hiring and monitoring of the CEO. Then the board may try to hide its inability to accomplish the first task by distorting the second one. Observe that none of our results depend on the size of the incentive component α in the board’s compensation. The distortion in board’s behavior cannot be eliminated or reduced by increasing the incentive component of the pay. Indeed, we would have the same result under the assumption that the board receives the entire profit, i.e. α = 1. Furthermore, there would be no major change in our results under the assumption of a more general form of the board compensation that includes also a fixed component F . It is immediately clear that there would be no change at all in the case with no market for corporate control. With a takeover market, if, the acquirer does know the type of the board the behavior of the inefficient board would

23

be the same while the efficient board would choose a higher threshold level14 . The rationale for this is quite simple: the higher is its compensation, the safer the board plays. If instead we assume that the acquirer does not know the type of board it is easy to verify that the equilibrium in which both boards always retain the manager is not affected by the change in the board’s compensation. This is so because the distortion in the behavior of the board is due to the fear of being displaced and therefore of losing its compensation and not on the size of the compensation. This is not surprising since we do not have any moral hazard problem in our model. Our model has some interesting policy implications. First, it points out the importance of the information on the type of board by showing that the better the information on the board the smaller the distortion in its behavior. Second, it underlines the positive effects of an increase in the average quality of the boards: when the fraction of the efficient boards λ increases the range of parameters values such that the pooling equilibrium is the unique equilibrium decreases. Thus, the model suggests that recommendations on board composition aimed at improving board’s effectiveness, such as fraction of outside directors and separation between CEO and Chairman, are very useful. Finally, it provides a new setting in which antitakeover provisions may be optimal. Usually, antitakeover provisions are thought to increase agency costs and to benefit management at the expenses of shareholders. There are two cases however where antitakeovers defences may have more advantages than costs. De Angelo and Rice (1983) have shown that antitakeover provisions may facilitate the bargaining by the management with the acquirer and this in turn may allow shareholders to get a larger premium if the acquisition takes place. In addition, Stein (1988) has proved that antitakeover provisions may reduce managerial myopia. Our model shows that, when the type of board is private information, antitakeover provisions may be optimal because they reduce the distortion in board’s retention/dismissal decision. 14 To

verify this, consider the decision problem of the efficient board. Now it can be written as: F F yE απ Pr(z ≥ zeRE |π) Pr(π|y = yeE ) − F Pr(z < zeRE |e ) = απξE

F indicates the threshold level chosen by the board when its compensation includes F > 0. where yeE By comparing this equation with equation (12) it is easy to see that the LHS of the above equation F ) with a negative yE is smaller than the LHS of equation(12) because of the term F Pr(z < zeRE |e F the smaller is this sign. If we assume that z and y are affiliated random variables, the higher yeE F the higher is the first (positive) term. Then, negative term and, at the same time, the higher yeE F it must be yeE > yeE .

24

10

References

Coughlan, A.T. and R.M. Schmidt (1985) ”Executive Compensation, Managerial Turnover, and Firm Performance: an Empirical Investigation” Journal of Accounting and Economics, 7, 43-66. Borokhovich, K.A., R. Parrino and T. Trapani (1996) ”Outside Directors and CEO Selection” Journal of Financial and Quantitative Analysis, 31, 337-355. De Angelo, H. and E.M. Rice (1983) ”Antitakeover Charter Amendments and Shareholder Wealth”, Journal of Financial Economics, 11, 329-360. Denis et Al. (1997) ”Ownership Structure and Top Executive Turnover” Journal of Financial Economics, 45, 93-221. Franks, J. and C. Mayer (1996) ”Hostile takeovers and the corrections of Managerial Failure”,Journal of Financial Economics, 40,163-181. Harford, J. (2000) ”Takeovers Bids and Target Directors’ Incentives:retention, Expertise, and Settling-Up” Working Paper, University of Oregon. Hermalin, B.E. and M.S. Weisbach (1988) ”Determinants of Board Composition” Rand Journal of Economics, 19, 95-112. Hermalin, B.E. and M.S. Weisbach (1998) ”Endogenously Chosen Boards of Directors and Their Monitoring of the CEO” American Economics Review, 88, 96118. Hirshleifer, D. and A. Thakor (1994) ”Managerial Performance, Board of Directors and Takeover Bidding” Journal of Corporate Finance, 1, 63-90. Hirshleifer, D. and A. Thakor (1998) ”Corporate Control Through Dismissals and Takeovers” Journal of Economics and Management Strategies, 7, 489-520. Huson, M.,R. Parrino and L. Starks (1998) ”The Effectiveness of Internal Monitoring Mechanisms: evidence from CEO turnover between 1971 and 1994”, University of Texas Jensen, M. (1988) ”Takeovers: Their Causes and Consequences” Journal of Economic Perspectives, 2, 21-48. Martin, K. and J. McConnell (1991) ”Corporate Performance, Corporate Takeovers and Management Turnover” Journal of Finance, 46, 671-88. Mikkelson, W. and M. Partch (1997)” The Decline of Takeovers and Disciplinary Turnover” Journal of Financial Economics, 44, 205-228. Scharfstein, D. (1988) ”The Disciplinary Role of Takeovers” Review of Economics Studies, 55, 185-99. Stein, J. C. (1988) ”Takeover Threat and managerial Myopia”, Journal of Political Economy, 96, 61-80. Warther, V. A. (1998) ”Board Effectiveness and Board Dissent: a model of the board’s relationship to management and shareholders” Journal of Corporate Finance, 4, 53-70.

25

11

Appendix 1

Proof of Lemma 1. Consider equation (9). Note that for zeR = z the LHS must be smaller than be greater than or equal to ξ A while for zeR = z the LHS must _ ξ A . Note also that, using equation (1) and Assumption 4, Pr(π|z = zeR , y > yei , iB), i = E, I, can be written as 1 Pr(z = zeR |π) Pr(y ≥ yei |π) Pr(iB, π) 1+ Pr(z = zeR |π) Pr(y ≥ yei |π) Pr(iB, π)

Therefore the acquirer’s problem given by equation (9) can be written as: 1 µ(EB|NT, MR) + Pr(π|z = zeR ) Pr(e zR ) Pr(π) Pr(y > yei |π) Pr(EB, π) 1+ Pr(π|z = zeR ) Pr(e zR ) Pr(π) Pr(y > yei |π) Pr(EB, π)

1 µ(IB|N T, M R) = ξ A Pr(π|z = zeR ) Pr(e zR ) Pr(π) Pr(y > yei |π) Pr(IB, π) 1+ Pr(π|z = zeR ) Pr(e zR ) Pr(π) Pr(y > yei |π) Pr(IB, π)

From Assumption 3 we know that Pr(π|z) = 0 and Pr(π|z) = 0. Then the LHS of the above equation is zero when zeR = z irrespective of the values taken by the beliefs while it should have been greater than or equal to ξ A , and it is equal to 1 when zeR = z while it should have been smaller than ξ A . Therefore it must be the case that zeR ∈ (z, z).¥

Proof of Proposition 2. From Lemma 1 we know that zeRE , zeRI ∈ (z, z). The part on the inefficient board follows immediately from equations (10) and (11). That the acquirer never makes a takeover when the efficient board dismisses the CEO follows from the assumption that ξ A ≤ ξ E together with the assumption that the acquirer makes a takeover bid only when there are expected gains from a change in management. Then, we need to prove that there exist interior values of yeE and zeRE that satisfy equation (12) and equation (13). Note that, given ξ E , (12) defines yeE as an increasing function of zeRE . It is imNT mediately clear that the minimum value of such a _function is yeE (z) = yeE since zeRE = z implies that the LHS of (12) becomes Pr(π|y = yeE ) making (12) = (2). That its maximum is yeE (z) = y follows from the fact that zeRE = z implies that the LHS of (12) tends to 0 i.e. that always dismissing the CEO is optimal for the board. Next we show that the LHS of equation (13) is strictly increasing in yeE . Rewrite such expression as: f(z = zeRE |π) Pr(y > yeE |π) Pr(π) f (z = zeRE |π) Pr(y > yeE |π) Pr(π) + f (z = zeRE |π) Pr(y > yeE |π) Pr(π)

(26)

Taking the derivative of (26) with respect to y we obtain:

f(z = zeRE |π) Pr(π)f (z = zeRE |π) Pr(π)[−f(e yE |π)(1 − F (e yE |π)) + D2 f (e yE |π) (1 − F (e yE |π))] . 2 D where D ≡ f(z = zeRE |π) Pr(y > yeE |π) Pr(π) + f (z = zeRE |π) Pr(y > yeE |π) Pr(π)

∂(26)/∂y =

26

Since yE |π)) − f (e yE |π) (1 − F (e yE |π))]} sign∂(26)/∂y = sign {[f (e yE |π)(1 − F (e it follows from Assumption 6 that ∂(26)/∂y > 0. The LHS of equation (13) is also increasing in zeRE . Taking the derivative with respect to zeRE : ∂f (z = zeRE |π) Pr(y > yeE |π) Pr(π) Pr(y > yeE |π) Pr(π)[ f(z = zeRE |π) ∂zRE ∂(26)/∂zRE = D2 ∂f (z = zeRE |π) f(z = zeRE |π)] ∂zRE . D2 Since sign(∂(26)/∂z RE ) = µ ¶ ∂f (z = zeRE |π) ∂f (z = zeRE |π) f(z = zeRE |π) − f(z = zeRE |π) sign ∂z ∂z −

it follows from Assumption 2 on MLRP that sign(∂eq(26)/∂z) > 0. Hence the LHS of (13) is strictly increasing in both yeE and zeRE . Moreover rewriting (26) as

zRE ) Pr(y > yeE |π) Pr(π|z = zeRE )f (e Pr(π|z = zeRE )f (e zRE ) Pr(y > yeE |π) + Pr(π|z = zeRE )f(e zRE ) Pr(y > yeE |π)

and considering that Pr(π|z) = 0 and Pr(π|z) = 1 from Assumption 3, it is immediately evident that it takes the following extreme values independently of the values of yeE : _ Pr(π|z, y > yeE ) = 0 _ Pr(π|z, y > yeE ) = 1 While rewriting (26) as:

Pr(π|y > yeE ) Pr(y > yeE )f(z = zeRE |π) Pr(π|y > yeE ) Pr(y > yeE )f(z = zeRE |π) + Pr(π|y > yeE ) Pr(y > yeE )f (z = zeRE |π)

and considering that it is also Pr(π|y) = 0 and Pr(π|y) = 1, it follows that : _

_

Pr(π|z = zeRE , y > y) = Pr(π|z = zeRE ).

_

Moreover applying L’Hospital rule to (26) it follows Pr(π|z = zeRE , y > y) = 1. It is in fact: limy→y (26) = −f(e yE |π) Pr(π)f(z = zeRE |π) =1 = limy→y −f (e yE |π) Pr(π)f (z = zeRE |π) − f (e yE |π) Pr(π)f (z = zeRE |π)

∗ > z,there will exist a (unique) pair of equilibrium As a consequence, given that zeRE ∗ NT yE values yeE and zeRE with yeE >e that satisfy equations (12) and equation (13). Suppose in fact that it were zeRE = z + ² with ² arbitrarily _small. For (12) to be ∗ NT NT yE + δ. But we know that Pr(π|z + ², y > yeE + δ) satisfied it should be yeE =e tends to 0. Therefore (13) cannot be satisfied. Then raise zeRE above z + ² and NT + δ so as to satisfy (12). Since the LHS of both correspondingly raise yeE above yeE (12) and (13). are continuous in y and z, at some point we will find a couple of zeRE

27

and yeE that satisfies both equations at the same time. The upper bounds of the relevant probabilities guarantee that such values are in the range of y and z. The fact that the LHS of both (12) and (13) are continuous and strictly increasing in y and z guarantee uniqueness. To see why y < y observe that if y = y, the LHS of equation (13) is equal to 1. ∗ ∗ < zeRI Finally, that zeRE follows from (11), (12) and (13) and the fact that _ _ _ ∂ Pr(π|z) > 0 and Pr(π|z, y > yeE ) 6 Pr(π|z).¥ ∂z Proof of Proposition 3. The proof is divided into three steps. In the first step the existence of the pooling equilibrium is proved. In the second step we show that such equilibrium is unique for ξ A ≥ λξ E + (1 − λ)ξ I . In Step 3 we show that an ξA. equilibrium in which the there is no takeover after M D exists for ξ A < b Step 1. There always exists a perfect Bayesian pooling equilibrium of the signaling game in which both types of board choose yei = y i = E, I, and the acquirer chooses zeR ∈ (z, z) and to always make a takeover after MD. Consider out-of-equilibrium-path beliefs µ(iB|N T, M D), i = E, I, such that: ξ E µ(EB|N T, M D) + ξ I µ(IB|N T, M D) < ξ A . If the acquirer observes manager dismissal when holding such beliefs, he will make a takeover. Consider then the decision problem of the board. Given such behavior on the part of the acquirer, manager dismissal gives a payoff equal to zero (the RHS of 4 is equal to zero), while manager retention gives a non negative expected payoff (the expected payoff is equal to zero only when the realization of y is y), no matter the value of zeR (since zeR = z has been excluded by Lemma 1). Hence the choice of yei = y i = E, I. To determine the behavior of the acquirer after manager retention note that, given that both types of board choose the same threshold level ye = y, observing manager retention does not provide any information. Hence, the acquirer’s equilibrium beliefs after MR are: µ(EB|z = zeR , y > y) = λ and µ(IB|z = zeR , y > y) = (1 − λ). The value zeR is determined at such a level that _

_

_

Pr(π|z = zeR , y > y, EB)λ + Pr(π|z = zeR , y > y, IB)(1 − λ) ≡ Pr(π|z = zeR ) = ξ A

Step 2. When ξ A ≥ λξ E +(1−λ)ξ I the equilibrium in which the manager is always retained is unique. Recall that we are taking into account only pure strategies of the acquirer. Hence an equilibrium different from the one considered should never have a takeover after M D, or it should be the case that: ξ E Pr(EB|y 6 yeE ) + ξ I Pr(IB|y ≤ yeI ) ≥ ξ A

(27)

where we have substituted the actual probabilities for the acquirer’s beliefs since in equilibrium they must coincide. Note that the LHS of the above expression can be written as: AE λξ E + AI (1 − λ)ξ I where Ai ≡

Pr(y 6 yei |π)ξ i + Pr(y 6 yei |π)(1 − ξ i ) Pr(y 6 yei |π) Pr(π) + Pr(y 6 yei |π) Pr(π) 28

i = E, I.

Note that AE < 1 < AI . Considering that Pr(y 6 yei |π) 6 Pr(y 6 yei |π) i = E, I from Assumption 2, we have:

Pr(y 6 yeE |π) (ξ E − Pr(π)) < Pr(y 6 yeE |π)(Pr(π) − 1 + ξ E ) = Pr(y 6 yeE |π)(ξ E − Pr(π)) and Pr(y 6 yeI |π)(ξ I −Pr(π)) > Pr(y 6 yeI |π)(Pr(π)−1+ξ I ) = Pr(y 6 yeI |π)(ξ I −Pr(π)). ) ) = 1. As a + Pr(IB|MD,NT Observe also that AE λ + AI (1 − λ) = Pr(EB|MD,NT Pr(MD,NT ) Pr(MD,NT ) consequence the LHS of (27) is smaller than λξ E + (1 − λ)ξ I 6 ξ A contradicting the existence of such equilibrium. ξ A < λξ E + (1 − λ)ξ I can be determined such that an equilibrium Step 3. A value b ξA. in which the acquirer never chooses T after MD for ξ A 6 b For the acquirer not to make a takeover after manager dismissal (27) must be satisfied. If there is never a takeover after M D, the probability of high profits after manager dismissal is equal to ξ i . Since Pr (N T |y = yei ) = 1, the decision problem of the board (4) then takes the following form: Pr (z > zeR |π ) Pr (π |y = yei ) = ξ i

i = E, I.

(28)

When the acquirer observes M R he chooses zeR according to (9). Considering again that in equilibrium beliefs must be confirmed, (9) takes the form: _

Pr(π|z _ Pr(π|z

= zeR , y > yeE , EB) Pr(EB|z = zeR , y > yeE ) + = zeR , y > yeI , IB) Pr(IB|z = zeR , y > yeI ) = ξ A

which can in turn be simplified into: _

_

Pr(π, EB|z = zeR , y > yeE ) + Pr(π, IB|z = zeR , y > yeI ) = ξ A

(29)

For the in which there is never a takeover after M D to exist, values £ equilibrium ¤ of yei ∈ y, y i = E, I, and zeR ∈ (z, z) must exist that solve the system (28)(29) and such that (27) is satisfied. Following the same line of reasoning as used in Proposition 2 we can show that this is so for a value of ξ A = ξ I +ε with ε arbitrarily zR ) i = E, I that small. First of all note that from (28) we can define functions yei (e satisfies such a condition. These are increasing in zeR and have extreme values: NT yeE (z) = yeE and yeE (z) = y. We can then rewrite the LHS of (29) as: f (z = zeR |π) Pr(y > yeE |π) Pr(π|EB) Pr(EB) + f (z = zeR |π) Pr(y > yeE |π) Pr(π) + f (z = zeR |π) Pr(y > yeE |π) Pr(π) f (z = zeR |π) Pr(y > yeI |π) Pr(π|IB) Pr(IB) f (z = zeR |π) Pr(y > yeI |π) Pr(π) + f (z = zeR |π) Pr(y > yeI |π) Pr(π)

Paralleling the proof given for (26) it can be shown that the above expression is increasing in both zeR and yei i = E, I. Then rearranging the LHS of (29) as:

Pr(π|z = zeR )f (e zR ) Pr(y > yeE |π) Pr(EB|π) +(30) Pr(π|z = zeR )f (e zR ) Pr(y > yeE |π) + Pr(π|z = zeR )f (e zR ) Pr(y > yeE |π) Pr(π|z = zeR )f(e zR ) Pr(y > yeI |π) Pr(IB|π) Pr(π|z = zeR )f (e zR ) Pr(y > yeI |π) + Pr(π|z = zeR )f (e zR ) Pr(y > yeI |π) 29

and considering that it is Pr(π|z) = 0 and Pr(π|z) = 1 from Assumption 3, it is immediately evident that it takes the following extreme values: _

_

Pr(_ π, EB|z, y > yeE ) + Pr(π, IB|z, y > yeI ) = 0 _ Pr(π, EB|z, y > yeE ) + Pr(π, IB|z, y > yeI ) = Pr(EB|π) + Pr(IB|π) = 1 while, considering that it is Pr(π|y) = 0 and Pr(π|y) = 1, and rearranging the LHS of ( 29) as: Pr(π|y > yeE ) Pr(y > yeE )f(z = zeR |π) Pr(EB|π) + Pr(π|y > yeE ) Pr(y > yeE )f(z = zeR |π) + Pr(π|y > yeE ) Pr(y > yeE )f (z = zeR |π) Pr(π|y > yeI ) Pr(y > yeI )f (z = zeR |π) Pr(IB|π) Pr(π|y > yeI ) Pr(y > yeI )f(z = zeR |π) + Pr(π|y > yeI ) Pr(y > yeI )f (z = zeR |π)

it follows that it takes value: _ Pr(π|z = zeR ) when y =y and 1 when y = y since, applying L’Hospital rule: µ ¶ −f(y|π) Pr(π|z = zeR )f(e zR ) Pr(EB|π) limy→y (30) = limy→y + −f (y|π) Pr(π|z = zeR )f (e zR ) − f(y|ππ) Pr(π|z zR ) µ ¶ = zeR )f (e zR ) Pr(IB|π) −f(y|π) Pr(π|z = zeR )f(e = 1. limy→y −f(y|π) Pr(π|z = zeR )f(e zR ) − f (y|ππ) Pr(π|z = zeR )f(e zR )

As a consequence, given that zeR > z, there will exist equilibrium values yei i = I, E yiNT that satisfy the system ( 28)-(29). and zeR ∈ (z, z) with y > yei >e

Considering that ξ E > ξ I and that (28) imply yeE > yeI , (27) is satisfied since: ξ E Pr(EB|y 6 yeE ) + ξ I Pr(IB|y 6 yeI ) > ξ E Pr(EB|y 6 yeI ) + ξ I Pr(IB|y 6 yeI ) = ξ E Pr(EB|y 6 yeI ) + ξ I (1 − Pr(EB|y 6 yeI )) > ξ I Hence for sufficiently small values of ε such equilibrium exists. Let us now continuously increase ξ A above the ξ A +ε. We know from Step 2 ξ A <λξ E + (1 − λ)ξ I such that for ξ A > b ξA that sooner or later we will reach a point b the above equilibrium no longer exists. ¥

12

Appendix 2

Proof of Proposition 4. The proof is divided into two steps. Step 1 deals with the pooling equilibrium. Step 2 proves the existence of the other equilibrium and shows that there cannot exist an equilibrium with N T after MD and BD after T. Step 1. There exists a pooling equilibrium in which the board always chooses MR and the acquirer chooses to always make a takeover and substitute the board after M D. If ξ A ≥ λξ E + (1 − λ)ξ I this equilibrium is unique. The proof exactly parallels Step 1 of Proposition 2. Out of equilibrium path beliefs ξ E µ(EB|N T, MD) + ξ I µ(IB|N T, M D) = ξ E µ(EB|T, MD, BR)+ ξ I µ(IB|T, M D, BR) < ξ A now guarantee that in case of M D, the acquirer would both make a takeover and dismiss the board. To prove uniqueness for ξ A ≥ λξ E + (1 − λ)ξ I consider the problem of the acquirer after MD and note that for an equilibrium with N T after MD it must be the case that ξ E Pr(EB|N T, M D) + ξ I Pr(IB|N T, M D) ≥ [ξ E Pr(EB|T, MD, BR) +

30

(31)

ξ I Pr(IB|T, MD, BR)] Pr(BR|T, MD) + ξ A Pr(BD|T, M D) where we have substituted the actual probabilities for the acquirer’s beliefs since in equilibrium they must coincide. Note that Pr(iB|N T, MD) = Pr(iB|T, MD, BR) i = E, I. The above expression can at best hold as an equality since, either i) ξ E Pr(EB|T, M D, BR) + ξ I Pr(IB|T, M D, BR) < ξ A which implies Pr(BR|T, MD) = 0 and the inequality not being satisfied, or ii) ξ E Pr(EB|T, M D, BR) + ξ I Pr(IB|T, M D, BR) ≥ ξ A which implies Pr(BR|T, MD) = 1 and the expression being satisfied as an equality. Since we know from Step 2 of Proposition 2 that the LHS of (31) is smaller than λξ E + (1 − λ)ξ I , the expression cannot be satisfied for ξ A ≥ λξ E + (1 − λ)ξ I . Step 2 If ξ A 6 b ξ A < λξ E + (1 − λ)ξ I there exists an equilibrium with N T after M D and BR after T. While there cannot exist an equilibrium with N T after M D and BD after T. We know from Step 1 that for an equilibrium with N T after M D and BR after T to exist, (31) must be satisfied as an equality with Pr(BD|T, MD) = 0. Consider the decision problem of the board. The LHS of (15) becomes Pr (π, BR |M R ) = Pr (π |M R ) because BR after T implies Pr (π, BD |MR ) = 0. Moreover it is Pr (N T |M D ) = 1 which implies that the RHS is equal to ξ i . Hence the decision problem of the board is Pr (π |y = yei ) = ξ i which has solution yeiNT . Consider then the decision problem of the acquirer after M R. It must be the case that the following expression holds with Pr(BD|T, M R) = 0 : _

_

Pr(π|N T, M R, EB) Pr(EB|N T, M R) + Pr(π|N T, MR, IB) Pr(IB|N T, M R) =

[ξ E Pr(EB|T, MR, BR) + ξ I Pr(IB|T, M R, BR)] Pr(BR|T, MR) +

ξ A Pr(BD|T, MR) or _

NT NT Pr(π|z = zeR , y > yeE , EB) Pr(EB|z = zeR , y > yeE )+ _

Pr(π|z = zeR , y > yeINT , IB) Pr(IB|z = zeR , y > yeINT ) = NT = [ξ E Pr(EB|z = zeR , y > yeE , BR) + ξ I Pr(IB|z = zeR , y > yeINT , BR)]

(32)

Note that for Pr(BD|T, M R) = 0 it must be the case that ξ E Pr(EB|T, M R, BR) +ξ I Pr(IB|T, M R, BR)] > ξ A where Pr(iB|T, MR, BR) = Pr(iB|N T, M R). (32) is an equation in zeR . We know from Step 3 of Proposition 2 that the LHS of (32) is increasing in zeR , going from 0 when zeR = z to 1 when zeR = z. Moreover following the same line of proof used in Lemma 2, it can be shown that the RHS is increasing in 31

λξ

2

+(1−λ)ξ 2

E )λξ E +(1−ξ I )(1−λ)ξ I zeR , going from (1−ξ1−(λξ > 0 when zeR =z, to λξE +(1−λ)ξ I < 1 when E +(1−λ)ξ I ) E I zeR = z. Hence (32) has solution zeR ∈ (z,z). Moreover, by a symmetric argument as that used in Step 2 of Proposition 3, it can be shown that ξ E Pr(EB|T, M R, BR) + ξ I Pr(IB|T, M R, BR)] > λξ E + (1 − λ)ξ I > ξ A . Consider a value of ξ A = ξ I + ε with ε arbitrarily small. Then taking into NT > yeINT , it is account that ξ E > ξ I and yeE NT ξ E Pr(EB|z = zeR , y 6 yeE ) + ξ I Pr(IB|z = zeR , y 6 yeINT ) > ξ E Pr(EB|z = zeR , y 6 yeINT ) + ξ I Pr(IB|z = zeR , y 6 yeINT ) = ξ E Pr(EB|z = zeR , y 6 yeINT ) + ξ I [1 − Pr(EB|z = zeR , y 6 yeINT )] > ξ I + ε. Hence (31) is satisfied as an equality with Pr(BD|T, MD) = 0. Let then continuously increase ξ A above ξ I +ε. Sooner or later we will reach point b ξ A < λξ E +(1−λ)ξ I such that the solution to (32) and yeiNT no longer satisfy (31) as ξ A = λξ E +(1−λ)ξ I an equality with Pr(BD|T, M D) = 0. It cannot be the case that b because the LHS of (31) is strictly smaller than λξ E + (1 − λ)ξ I . Notice that the fact that ξ E Pr(EB|T, MR, BR) + ξ I Pr(IB|T, MR, BR)] > λξ E + (1 − λ)ξ I > ξ A does not depend on yei = yeiNT , i = E, I. This would be true for any triple zeR , yei , i = E, I satisfying the decision problem of the acquirer after MR and is what prevents the existence of equilibrium with NT after M D and Pr(BR|T, MR) = 0, i.e. board dismissal after a takeover.

13

Appendix 3

Proof of Lemma 2. Observe that the LHS of (24) can be written as: f(z = zeD , y 6 yeE |π)ξ E + f(z = zeD , y 6 yeE |π)(1 − ξ E ) λξ + f (z = zeD , y 6 yeE |π) Pr(π) + f(z = zeD , y 6 yeE |π) Pr(π) E

f(z = zeD , y 6 yeI |π)ξ I + f(z = zeD , y 6 yeI |π)(1 − ξ I ) (1 − λ)ξ I f (z = zeD , y 6 yeI |π) Pr(π) + f(z = zeD , y 6 yeI |π) Pr(π)

which, applying Assumption 4, becomes:

f(z = zeD |π) Pr(y 6 yeE |π)ξ E + f(z = zeD |π) Pr(y 6 yeE |π)(1 − ξ E ) λξ +(33) f (z = zeD |π) Pr(y 6 yeE |π) Pr(π) + f(z = zeD |π) Pr(y 6 yeE |π) Pr(π) E f(z = zeD |π) Pr(y 6 yeI |π)ξ I + f(z = zeD |π) Pr(y 6 yeI |π)(1 − ξ I ) (1 − λ)ξ I f (z = zeD |π) Pr(y 6 yeI |π) Pr(π) + f(z = zeD |π) Pr(y 6 yeI |π) Pr(π)

Pr(π|x)f(x) , that Pr(π|x = x) = 1, Pr(π|x = x) = 0, Pr(π) Pr(π|x = x) = 0, Pr(π|x = x) = 1 x = y, z, it follows immediately that the LHS of (24) takes the following extreme values: Considering that f (x|π) =

(1−ξE )λξ E +(1−ξI )(1−λ)ξ I 1−(λξE +(1−λ)ξI ) (1−ξE )λξE 1−(λξE +(1−λ)ξI

λξ E

h

when zeD =z, h ξI α + (1 − λ)ξ I λξ +(1−λ)ξ + )

ξE α λξE +(1−λ)ξI

E

+

(1−ξ E )(1−α) 1−(λξE +(1−λ)ξI )

I

i

+

2 λξ E +(1−λ)ξ I2 λξE +(1−λ)ξI

(1−ξI )(1−α) 1−(λξ E +(1−λ)ξI )

(1−ξI )(1−λ)ξI 1−(λξE +(1−λ)ξI )

i

when zeD = z;

when yeE =y and yeI = y when yeE = y and yeI =y

f (z=e zD |π) Pr(π) where α = f (z=ezD |π) Pr(π)+f (z=e zD |π) Pr(π) . Taking the derivatives of (33) with respect to zeD and yei we obtain: µ ¶ ∂f(z = zeD |π) ∂f (z = zeD |π) ∂(33) = f (z = zeD |π) − f(z = zeD |π) × ∂e zD ∂e zD ∂e zD

32

[ξ E Pr(π) + (1 − ξ E ) Pr(π)] + Den E2 [ξ Pr(π) + (1 − ξ I ) Pr(π)] } (1 − λ)ξ I Pr(y 6 yeI |π) Pr(y 6 yeI |π) I Den 2I 2 where Den 2i = [f (z = zeD |π) Pr(y 6 yei |π) Pr(π) + f (z = zeD |π) Pr(y 6 yei |π) Pr(π)] i = I, E. µ ¶ ∂(33) = Since sign zD ¶ µ ∂e ∂f(z = zeD |π) ∂f (z = zeD |π) f (z = zeD |π) − f (z = zeD |π) sign ∂e zD ∂e zD ∂(33) > 0. it follows from Assumption 2 on MLRP that ∂e zD ∂(33) = Bi f(z = zeD |π)f(z = zeD |π)× ∂e yi {λξ E Pr(y 6 yeE |π) Pr(y 6 yeE |π)

[ξ i Pr(π) − (1 − ξ i ) Pr(π)][f(e yi |π)F (e yi |π)) − f(e yi |π)F (e yi |π)] Den 2i λξ E and BI = (1 − λ)ξ I whereµ BE = ¶ ∂(33) sign = ∂e yi yi |π)F (e yi |π)) − f(e yi |π)F (e yi |π)]} sign {[ξ i Pr(π) − (1 − ξ i ) Pr(π)][f (e yi |π)) − f (e yi |π)F (e yi |π)] > 0 from Assumption 6 and [ξ E Pr(π) − yi |π)F (e where [f (e ∂(33) (1 − ξ E ) Pr(π)] > 0; [ξ I Pr(π) − (1 − ξ I ) Pr(π)] < 0. As a consequence >0 ∂ yeE ∂(33) < 0. and ∂e yI Consider now the LHS of (25). It takes extreme values: Pr(π|y=e yi ) Pr(z> z eD |y=e yi )

f (z) Pr(π|y=e yi ) eR = z; Pr(z> z eD |y=e yi ) Pr(π) for z Pr(z> z eR |π ) Pr(π|y=e yi ) for zeD = z; f (z|y=e yi )

for zeR = z,

Pr (z > zeR |π ) Pr (π |y = yei ) for zeD =z,

Pr(z> z eR |π ) Pr(z> z eD |y )

0 for yei = y,

for yei = y

i = E, I

It is immediately clear that the LHS of (25) is increasing in zeD and decreasing in zeR . To prove that it is increasing in yei i = I, E, rewrite it as:

Pr (z > zeR |π )

f (π, y = yei ) f (z > zeD , y = yei )

Pr (z > zeR |π )

Pr (z > zeR |π )

=

f (y = yei |π ) Pr (π) f (z > zeD , y = yei |π ) Pr (π) + f (z > zeD , y = yei |π ) Pr (π)

=

1

f (y = yei |π ) Pr (π) f (y = yei |π ) Pr (π) which is clearly increasing in yei because of Assumption 2.¥ Pr (z > zeD |π ) + Pr (z > zeD |π )

Proof of Proposition 5. We know from Lemma 1 that zeR ∈ (z, z). Considering

that zeD = z means that there is always a takeover after M D, the proof of the existence of the pooling equilibrium parallels exactly the proof given in Step 1 of Proposition 3, where the out-of-equilibrium beliefs can now be expressed as. µ(EB | z, M D)ξ E + µ(IB | z, MD)ξ I 6 ξ A 33

∇z

which is equivalent to say that zeD = z. Whatever the value of z, the dismissal of the incumbent manager is interpreted as a signal of inefficiency of the board and leads to a takeover bid. λξ E2 + (1 − λ)ξ 2I parallels Step 2 of Also the proof of uniqueness for ξ A > λξ E + (1 − λ)ξ I Proposition 3. Consider the problem of the acquirer after he has observed MD. To have an equilibrium with zeD ∈ [z, z) it must be the case that: ξ E Pr(EB|z = zeD , y 6 yeE ) + ξ I Pr(IB|z = zeD , y 6 yeI ) ≥ ξ A

But we know from Lemma 2 that the maximum value taken by the LHS of the λξ E2 + (1 − λ)ξ I2 for zeD = z. Hence an equilibrium with zeD ∈ equation above is λξ E + (1 − λ)ξ I 2 λξ E + (1 − λ)ξ 2I [z, z) cannot exist for ξ A > . λξ E + (1 − λ)ξ I To show that there exists an equilibrium with zeD = z when (1 − ξ E )λξ E + (1 − ξ I )(1 − λ)ξ I ξA 6 consider that for an equilibrium with zeD = 1 − (λξ E + (1 − λ)ξ I ) z to exist it must be the case that there are zeR and yei i = E, I, that satisfy (24), (9) and (25) i.e. the following equations: (1 − ξ E )λξ E + (1 − ξ I )(1 − λ)ξ I ≥ ξA 1 − (λξ E + (1 − λ)ξ I ) Pr(π|z Pr(π|z

= zeR , y > yeE , EB) Pr(EB|z = zeR , y > yeE ) + = zeR , y > yeI , IB) Pr(IB|z = zeR , y > yeI ) = ξ A Pr(z ≥ zeR |π) Pr(π|y = yei ) = ξ i ,

i = E, I

where we have substituted z for zeD and applied Lemma 2 to (24) and to (25).

(34)

(35)

(36)

(34) is trivially satisfied. For the equilibrium to exist it must be the case that there exist feasible values for zeR and yei i = E, I, that satisfy the system (35), and (36). Note, however, that such a system exactly coincides with the system (28) - (29) which we know to have a feasible solution from Step 3 of Proposition 3. Another equilibrium would require zeD ∈ (z, z). But if we raise zeD to a value greater than z, the LHS of (34) increases (see Lemma 2) making it impossible to lead to an equilibrium (recall that an interior value of zeD corresponds to (34) being satisfied as an equality).¥

34