3.2.1 Basic Setup
Consider a firm that hires a new CEO to run the business in the following two periods. After the second period, the CEO leaves. The firm and the CEO are risk-neutral. The CEO can be a good or a bad match for the job, denoted H and L, respectively. The match quality determines the expected payoff a CEO produces in a particular firm; a good match gives the firm a higher payoff than a bad match. As in Eisfeldt and Kuhnen (2013) the match quality of a CEO is different for different firms. In the first period the match quality is unknown, but the CEO and the firm assign probabilityq to a good match and probability 1−q to a bad match. For an incumbent CEO the firm updates this probability in the second period. If the firm decides to discontinue employment, then it hires a new CEO for the second period with probabilityq for a good match.
Firm and CEO
Figure 3.1: Structure of the Contracting Problem.
The sequence of events is identical for both periods. Figure 3.1 depicts the time structure of the contracting problem. At t = 0 the firm offers a compensation
contract to the manager. It consists of a base salary a and a participation rate b of the total firm profit, which is equivalent to a cash bonus. The firm also decides whether it commits to the payment of the base salary and/or bonus.7 When the firm does not commit, it only promises to pay, but the CEO is unable to enforce this in court. When the firm commits to compensation, both parties can enforce the respective payments in court.
The CEO decides whether she accepts the offer of the firm. She only accepts the contract, if her expected utility is at least as high as her reservation utility U. The reservation utility is independent of the match quality. If the CEO rejects the contract, then the firm’s profit in this period is zero.
If the CEO accepts the contract, she decides at t = 0 + how much effort she exerts in the first period. The firm profit is eix, where ei is managerial effort and x is a random productivity factor, which is higher for a good than a bad match.
Effort is unobservable for the firm, whereas firm profit is observable at the end of the period. fi(x) is the density of the productivity factor, defined on x∈[x, x] and for i∈ {H, L}.8 Expected firm profit is higher for a manager who is a good match than for a manager who is a bad match. Let µi be the mean of the productivity factor x for match quality i, then µH > µL. The distributions fi(x) are common knowledge. A higher effort level linearly increases expected firm profit. The cost of effort is convex, c(ei) = e22i. This function is the same for both types of match quality. When choosing the effort level the CEO knows the match quality and the compensation contract.
At the end of the first period, t = 1, the firm observes the profit and decides whether to continue employment of the manager. If the firm fires the CEO, it pays her only the parts of compensation to which it is committed. If the firm wants to retain the CEO, it has to pay the promised base salary and bonus, regardless of commitment. Otherwise, the CEO leaves. For an incumbent CEO, the match quality may differ between periods one and two, but the first period gives both parties an indication about the compatibility of the firm and the CEO in the second period. Garrett and Pavan (2012) explain that the match quality may change from period one to period two because of external shocks like changes in technology or
7The case where the firm neither commits to the base salary nor to the variable compensation is not part of the analysis. It seems unlikely that a CEO would agree to a contract that allows the firm to withhold compensation completely.
8The domain of the distribution function does not necessarily have to be bounded. The model also allows for distribution functions that are defined on the whole set of real numbers.
the opening of new markets. The firm’s probability of an incumbent CEO being a good match in the second period is p(eix), because it only observes firm profit and not managerial effort. For the firm, the higher the firm profit, observed at the end of the first period, the higher is the probability that a CEO has a high match quality in the second period. If the firm decides to keep the CEO, it updates the belief about the match quality and adjusts the compensation contract in the second period accordingly.9 If the firm decides to hire a new CEO, the probability of a good match is q as in the first period. The simple setup of the firing decision implies that the contracting problem with an incumbent CEO only differs in the probability distribution of the two match types. If the firm would not learn about the match quality, then it would have no incentive to retain the CEO in the second period. Hence, it would never pay uncommitted compensation. This would imply a full commitment contract in the first period.
The CEO decides about how much effort she exerts in the second period at t = 1 +. The firm’s profit function, the densities of the productivity factor, and the cost of effort function remain the same in period two. The CEO also knows the match quality and the compensation contract when she decides about effort.
At the end of the second period,t= 2, the firm profit realizes and the firm pays the CEO. Employment of the CEO at this firm cannot continue and the CEO leaves the firm. Therefore the firm only pays the committed compensation components.
As a consequence, non-commitment makes no sense in period two. The second period-contract is a full commitment contract.
3.2.2 First-Best Solution for Both Periods
The starting point of the analysis is the case where there is no uncertainty about the match quality of the CEO. Therefore the firm only hires a CEO who is a good match for the firm. As the firm would replace the CEO at the end of the first period without cost, the CEO only accepts a full commitment contract in the first period.
First consider the expected payoffs of the CEO and the firm. A CEO receives the base salary,a, and her profit sharebmultiplied with firm profit,eix, which is the product of the effort level, ei, and the productivity factor,x. A CEO chooses effort to maximize her expected utility. Under a full commitment contract with fixed a
9The firm cannot offer a screening contract for the second period, because the focus of this paper is the commitment decision.
and b, the expected utility of a risk-neutral CEO of quality i, EUi, is her expected income minus the effort cost
EUi =
x
Z
x
[bxfi(x)ei+a]dx−e2i
2 =bµiei+a− e2i
2, (3.1)
whereµi is the expected firm profit before compensation given the match qualityi with i∈ {H, L}. The first order condition of the CEO, when she knows the match quality is
δEUi
δei
=bµi−ei = 0. (3.2)
This is the incentive compatibility constraint of the CEO. It gives the standard condition that the CEO balances marginal expected income and marginal costs.
For a given compensation contract, a CEO with higherµi provides a higher level of effort. This means that with µH > µL the good match exerts higher effort than the bad match.
The CEO only agrees to the contract when her expected utility is at least as high as her reservation utility U, which is assumed to be independent of the match quality.
The individual rationality constraint when the CEO knows the match quality is EUi =bµiei+a− e2i
2 ≥U. (3.3)
The payoff to the owners of the firm is the realized firm profit minus the payments to the CEO. The expected payoff of the firm is
EPi =
x
Z
x
[(1−bi)xfi(x)ei−ai]dx= (1−bi)µiei−ai. (3.4)
When the firm knows the quality of the CEO, it can offer different compensation contracts for the two match types.
The first-best optimization problem of the firm is identical for both periods and
looks as follows:
maxai,bi
EPF B = (1−bi)µiei−ai (3.5) s.t. EUiF B =biµiei+ai−e2i
2 ≥U, (3.6)
and eF Bi =biµi. (3.7)
Equations (3.6) and (3.7) are the conditions that the CEO at least wants to earn the reservation utility (individual rationality) and that she chooses effort to maximize her expected payoff (incentive compatibility), respectively. The firm choosesai and bito maximize the expected payoff (3.5) given conditions (3.6) and (3.7). Proposition 1 gives the first-best contract for both periods.
Proposition 1 The first-best compensation contract for each period offers the CEO a participation rate of bF B = 1 and a base salary of aF Bi =U − µ22i <0.
Proof: See appendix.
This is the standard ”sell to the agent” result. In this two-period setting instead of selling the firm to the CEO, the owners make the CEO the residual claimant and collect a fixed rent in return. bF B = 1 implies that the firm gives all the firm profit to the CEO. In turn the CEO pays the amount aF Bi = U − µ22i to the firm, which implies a negative base salary for the first-best contract.10 As the manager is risk-neutral, the firm transfers all the risk to the agent and takes a fixed payment instead of a share of the risky firm profits. Only the fixed payment, aF Bi , is match-specific and depends on the productivity of the CEO, µi. The owners of the firm receive a higher rent for the company from the good match than from the bad match as the reservation utilityU is independent of the match quality. This implies that the firm hires a CEO only, if she is a good match for the firm.
As there is no hiring and firing cost, the firm is indifferent between retaining the good CEO in the second period or replacing her by another good CEO.