Second-Best Contract in Period One

Before turning to the contracting problem in the first period, it is necessary to describe how the decision of the firm to continue employment with the CEO or not influences the payments at the end of the first period. As described above, the firm hires a new CEO for the second period, if paying non-committed compensation and keeping the old CEO delivers a lower expected payoff for the firm than hiring a new CEO. This implies that the firm discontinues employment with the old CEO, when the realization of firm profit is below some threshold, which indicates that the expected payoff from an incumbent CEO is lower than from a new CEO. If on the other hand the realization of firm profit is high and the present CEO gives the firm a higher expected profit in the subsequent period than a new CEO, the firm continues employment.

When the firm continues employment, it has a higher expected profit from an incumbent CEO (minus the cost of non-committed compensation) than for a new CEO in the second period. The CEO knows about this rent the firm receives, if employment continues. This raises the question how this rent is distributed between the firm and the CEO. Assume that realizations of firm profit that suggest a good match quality of the CEO in period two also improve the outside options of the CEO. This implies that the firm has to pay a retention premium to keep an incum-bent CEO. Assume further the CEO stays at the firm in the second period, if the firm pays the CEO the compensation it promises at the beginning of the first pe-riod. This characterization of the firing decision and the payment of unenforceable compensation components, makes discretionary compensation feasible in the first period.

16This is the condition assuming a discount rate of zero. With a positive discount rate the firm invests, if the non-committed compensation is smaller than the discounted difference between the incumbent and the new CEO.

Full Commitment

When the firm offers a full commitment contract in period one, the optimization problem for the firm in the first period is the same as in the second period. The firm hires a new CEO in the first period, so the probability that the CEO is a good match is q for the firm and the CEO. The firm maximizes equation (3.9) subject to the constraints (3.10) to (3.12), where p(eix) and pi are replaced by q. The optimal contract with full commitment in the first period is identical to the full commitment contract of a new CEO in period two excluding the learning option.

Since compensation is completely enforceable under the full commitment contract, the firm pays out all parts of compensation and the CEO stays at the firm, if the firm offers the incumbent CEO a contract for period two.

Commitment to Variable Compensation

Consider the case where the firm does not commit to the base salary, but commits to variable compensation in the contract. The contract with enforceable variable compensation is similar to paying the CEO a provision. The CEO (and the firm) can enforce the performance related pay, but not the base salary.

As described above, the non-enforceable base salary is only credible as long as the firm has an interest in continuing the employment relationship. This means that in the first period the firm only pays the base salary, if it decides to retain the CEO in the second period. The base salary in this setting is similar to a digital call option for the CEO. As in the previous sections the decision whether to continue employment depends on the probability that the incumbent CEO is a good match in the second period and on the size of the non-committed compensation in the first

period. The optimization problem of the firm in the first period is where Fi is the probability that employment stops after period one given the re-spective match types,i∈ {H, L}.

This optimization problem is very similar to the full commitment case and the interpretation of equations (3.13) to (3.16) follows from the interpretation of equa-tions (3.9) to (3.12). The only difference is the factor 1−Fi, which indicates that the firm only pays the base salary when employment continues. Optimal effort of the CEO, (3.16), balances marginal costs and the marginal benefit of effort. The marginal benefit of effort consists of the increase in firm profit and the CEO’s in-fluence on the probability of continuing employment. When the CEO exerts higher effort, this increases the probability that firm profit is above the critical threshold and that the incumbent CEO stays at the firm. The second part of equation (3.16) represents the impact of CEO effort on the probability of remaining at the firm with ^δ(1−F_δe ⁱ⁾

i > 0. The following proposition characterizes the optimal solution to this optimization problem.

Proposition 3 The optimal second-best contract in the first period, when the firm only commits to variable compensation gives the CEO a participation rate ofb^{V C} =

E[µ^{δeV C}_δb ]−a(E[(µ+1)^δ(1−F)

In the first period the contract with commitment to variable compensation trades off the rent of a good match against providing incentives to the CEO as in the full commitment case. It is not straightforward to compare the optimal effort levels

under full commitment and under the contract with commitment only to variable compensation.¹⁷ For a given participation rate, b, and assuming a positive base salary, the optimal effort under commitment only to the base salary is higher than under full commitment. The optimal base salaries under these two forms of com-mitment are different. When the firm leaves the base salary to its discretion, it is larger by a factor of _1−F¹

L compared to the contract with commitment to the base salary for a given effort level and variable compensation. Under the contract with-out commitment to the base salary the CEO receives no base salary, if employment stops after the first period. To satisfy the utility constraint of the CEO the firm has to account for this and increase the base salary accordingly.

Instead of committing to variable compensation and not committing to the base salary, the firm can refrain from committing to the base salary and variable compen-sation (no commitment). This would give the firm a very strong incentive to fire the CEO after the first period to avoid the payment of compensation and potentially leaves the CEO without any income. Hence, the contract with no commitment is not part of the analysis.

Commitment to Base Salary

Now consider the other case where the firm partially commits to the compensation contract. It only commits to the base salary, but not to variable compensation.

The firm only pays the bonus at the end of period one, if employment with the CEO continues. The manager anticipates that there are no payments beyond contracted compensation, when the firm discontinues employment. This means that for some realizations of the firm profit the CEO only receives the base salary. As in the previous section, if the CEO is likely to be a good match in the following period, the firm pays the promised variable compensation to motivate the manager to stay at the company. The optimization problem of the firm for the optimal compensation

17See section 3.4 for a detailed discussion of optimal choice of commitment.

contract in the first period is where µ^F_i is the mean of the truncated distribution of productivity of a CEO with match quality i. It is the mean of CEO productivity for all realizations that imply that employment of the CEO continues. It reflects that the CEO only receives variable compensation, if employment continues and depends on the effort of the CEO.

The optimization problem of the principal has the same structure as in the the previous sections. The interpretation of equations (3.17) to (3.20) is the same as the interpretation of equations (3.9) to (3.12). The lack of commitment to variable compensation is reflected in the expected payoffs of the firm and the CEO through the presence of the mean of the truncated distribution ofx,µ^F_i , instead of the mean of the full distribution, µi, as the determinant of the CEOs variable compensation.

The incentive compatibility constraint of the CEO (3.20) again states that the CEO equals marginal costs and benefits of effort to obtain the optimal effort. As for the discretionary base salary the marginal benefit is twofold. A higher effort increases firm profit and the probability that the realization of firm profit is high enough to continue employment of the CEO. The second part of the marginal benefit of effort in equation (3.20) reflects the impact of CEO effort on the truncated firm profit, µi. Higher effort increases the probability that employment continues and, consequently, the mean of the truncated productivity distribution, ^δµ_δe^Fi

i >0.

This implies that the µ^F_i ’s can be higher or lower than the µi’s, depending on the underlying distribution of CEO productivity. Ifx only has positive realizations, then µ^F_i < µi. When CEO productivity, x, can be negative, however, it is also possible thatµ^F_i > µi. The only restriction is that the possibility of firing the CEO leaves the order of good and bad matches unaffected; the mean of the truncated distribution of the good match is larger than the mean of the truncated distribution of the bad match,µ^F_H > µ^F_L.

Effort costs and reservation utilities are again identical for the good and the bad match. The following proposition characterizes the optimal second-best contract with discretionary variable compensation for the first period.

Proposition 4 The optimal second-best contract when the firm chooses commit-ment only to the base salary in the first period gives the CEO a base salary of a^{P C} = (U −b^{P C}µ^F_Le^{P C}_L + ^{(eP CL}₂ ⁾²) and b^{P C} = ^{E[µδeP Cδb ]−E[µFeP C]+µFLeP CL}

E[µ^{F δe}_δb^{P C}]+E[e^{P C δµ}_δb^F] is the optimal participation rate.

Proof: See appendix.

The utility constraint (3.19) together with the identical base salary for both match types implies that in expectation the CEO receives the reservation utility plus a rent, when she turns out to be a good match for the firm. In case the CEO is a bad match the expected utility equals the reservation utility. The firm trades off the benefits from providing incentives and the costs for the rent paid to a good match.

The base salary under the discretionary bonus contract is identical to the base salary under the full commitment contract for a given effort and variable compen-sation. Consequently, keeping effort and variable compensation the same it is lower than under the contract with discretionary base salary. As explained in the last section, the firm pays a lower base salary, if the CEO receives it independent of the realization of firm profit; a discretionary base salary forces the firm to increase the base salary to satisfy the individual rationality constraint of the CEO.

Comparing the second-best contracts with full commitment and commitment only to the base salary is not straightforward. Whether the CEO provides higher effort under the contract with full commitment or the contract with commitment only to the base salary, depends on the conditional distributions,µ^F_i . Which contract delivers the higher expected payoff for the firm also depends on the µi and the probability that the CEO is a good match,q. A discussion of optimal commitment choice follows in the next section.