The analysis of our model revealed that self-esteem and the individual’s eagerness to protect it may facilitate principal-agent relationships even if performance sig-nals are subjective and no third-party can enforce truth-telling. However, only if signals are perfectly correlated, a first best can be achieved - even if the princi-pal can costlessly choose the quality of his own signal. For imperfectly correlated signals, positive effort levels will be implemented by the principal if profits and costs of conflict are sufficiently large. As an incentive compatible contract has to compensate the agent for effort costs and expected psychological costs, the implemented effort level will be below the first best effort.
12Example 1 and Lemma 11 show that this holds true for an appropriate choice ofψ.
This qualifies to some extent the results in MacLeod (2003) which claim the existence of implementable effort levels regardless of the details of the relationship.
The positive result of MacLeod (2003) is crucially depending on the credibility and flexibility of the third-party payments. While in his model, every payment to a third-party was a credible promise, the specific nature of conflict in our setting imposes tighter constraints on the set of feasible contracts. Moreover, following the interpretation of third-party payments as endogenous costs of conflict [see MacLeod (2003), p.229], our analysis demonstrates that the feasibility of welfare-optimal solutions in MacLeod (2003) crucially hinges on the fact that conflicts do not impose any costs on the agent. If - as in our model - conflicts entail some costs for the agent, the need to compensate for these costs raises agency costs above the first best level and prevents welfare optimal solutions even if the truth-telling problem is not an obstacle.
In the extended version of the model we assume that the principal has control over the choice of his evaluation procedure. More precisely, we assume that the principal does not only have to choose the optimal compensation scheme, but can also choose among different evaluation procedures that differ in the quality of their subjective performance signal. In particular, the agent’s psychological costs increase in the bias of the information technology. This resembles a case of procedural concerns as conceptualized by Sebald (2007) in a general class of models with belief-dependent utility. Interestingly, our model shows that it may be optimal for the principal to choose a procedure which is not minimizing the agent’s psychological costs - even if it is costless to do so - but rather facilitates the credible implementation of a positive effort level.
Our assumptions on psychological costs are rather ad-hoc. We simply for-malized the results from the literature in social psychology in a straightforward functional form. We opted for this approach as the main purpose of this paper is the discussion of promoting and inhibiting factors for principal-agent relationships in which neither effort nor output can be measured objectively.
Furthermore, we have chosen to model the agent as risk-neutral and with unlimited liability. While this obviously promoted expositional ease, it focuses on the special case of a principal-agent relationship which never leaves a rent to the agent. In case of risk-averse or limitedly liable agents, a non-trivial dependence of the agent’s rents on his sensitivity to ego-threats and the quality of the information technology is to be expected and definitely worth an investigation. Our results with respect to break-downs of the relationship are, however, not expected to depend on these assumptions.
Finally, it is known since long [see Malcomson (1984)] that the problem of non-enforceable contracts in the presence of subjective performance measures is easily solved if the principal has to deal with a team of agents and can pay them according to a ranking with pre-committed payments for each rank. If agents do not suffer from psychological costs in these kind of tournaments, a first best can be achieved and performance pay as characterized in this paper is always in-ferior. However, it is an empirical question whether tournaments actually lead to lower psychological costs. If self-esteem is threatened fiercely by the explicit
announcement that someone-else is better, incentive compatible payments in the tournament have to compensate the corresponding expected psychological costs.
This may well lead to an inferiority of such a scheme and promote performance pay as discussed in our paper, where self-esteem is not threatened by a relative performance measure but by an absolute evaluation. In this respect, new labora-tory experiments could shed some light on the optimal design of payment schemes in the case of subjective performance evaluation.
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Appendix
Proof of Lemma 2: To save on notation, we denoteY (tP =k, sA=l, α)(1 − q∗) +w(q∗)≡ Yklthroughout this proof.
Part (i). Without loss of generality, suppose that Γ is a revelation contract, i.e., the principal and the agent tell the truth under contract Γ. As Γ implements p > 0, the incentive compatibility constraint
Σk∈SP,l∈SA(Ykl+ckl)dP r{sP =k, sA=l}
dp =v(p) is satisfied. Consider a contract ˆΓ which fixes payments of ˆck =
l∈SAcklP r{sP= k, sA=l} if the principal receives signal sP =k, i.e., payments are independent of sA. These payments also satisfy the incentive compatibility constraint (see
above).13 Moreover, the agent always tells the truth due to indifference. Finally, the principal’s truth-telling constraint is also satisfied under ˆΓ. To see this observe that the principal reportsk given that he has received k under contract Γ if
P r{sA=A|sP=k}(coA− ckA) +P r{sA=U|sP =k}(coU− ckU) (8)
≥ P r{sA=A|sP =k}((q∗ψ)kA− (q∗ψ)oA) +P r{sA=U|sP =k}((q∗ψ)kU− (q∗ψ)oU)
for allo ∈ SP(where (q∗ψ)tA,tP denotes the anticipated conflict costs for a reported configuration (tA, tP)). This set of inequalities holds because Γ implements truth-telling by assumption. ˆΓ implements truth-telling if
cˆo− ˆck≥ P r{sA=A|sP=k}((q∗ψ)kA− (q∗ψ)oA) (9) +P r{sA=U|sP =k}((q∗ψ)kU− (q∗ψ)oU).
holds for allo, k ∈ SP. Inserting ˆckand ˆcoyields
P r{sA=A|sP=k}(coA− ckA) +P r{sA=U|sP =k}(coU− ckU)
≥ P r{sA=A|sP =k}((q∗ψ)kA
−(q∗ψ)oA) +P r{sA=U|sP =k}((q∗ψ)kU− (q∗ψ)oU).
which coincides with System 8 and therefore shows that for ˆΓ the principal’s truthtelling constraint is satisfied as well. Hence, any revelation contract Γ can be substituted by a revelation contract ˆΓ with ckl independent ofl which also implementsp > 0 and leaves the principal weakly better off.
Part (ii). Suppose by contradiction that Γ implementsp > 0 with cA=g and cU =g + with ≥ 0. Then, the incentive compatibility constraint of the agent can be written as
= v(p) − γUAYUA
(γUA+γUU− 1). (10)
Observe that the numerator of the rhs is positive for every p > 0 and vanishes forp = 0 while the denominator is negative. Hence, the rhs is negative and the incentive compatibility constraint is not satisfied for anyp > 0 and > 0. For
= 0, the incentive compatibility constraint is solved by p = 0. A contradiction.
13Individual rationality is trivially fulfilled as expected payments for the agent are the same under Γ and ˆΓ.