Incentive and Participation Constraints with Moral Hazard

In chapter 4, we stressed the various conflicts that may appear in a moral hazard environment. The analysis of these conflicts, under both limited liability and risk aversion, was made easy because of our focus on a simple 2 × 2 environment with a binary effort and two levels of performance. The simple interaction between a single incentive constraint with either a limited liability constraint or a participation constraint was quite straightforward.

However, moral hazard models also inherit the major difficulties of Incen- tive Theory, which we have already encountered in our investigation of complex adverse selection models carried out in chapter 3. Indeed, when one moves away from the 2 × 2 (by far too simplistic) model of chapter 4, numerous incentive con- straints have to be taken into account in complex moral hazard environments. The analysis becomes much harder, and characterizing the optimal incentive contract is a difficult task. Examples of such complex contracting environments abound.

Effort may no longer be binary but, instead, may be better characterized as a continuous variable. A manager may no longer choose between working or not working on a project but may be able to fine-tune the exact effort spent on this project. Even worse, the agent’s actions may no longer be summarized by a one- dimensional parameter but may be better described by a whole array of control variables that are technologically linked. For instance, the manager of a firm may have to choose how to allocate his effort between productive activities and mon- itoring his peers and other workers. The manager’s performances, i.e., his profit, may also be better approximated as a continuous variable, a less crude assumption than the one made in chapter 4.1 Real-world incentive schemes for the manager of the firm are not based on a discrete number of performances but instead on the more continuous level of profit of the firm. Lastly, the agent’s preferences over effort and consumption may no longer be separable as we have assumed in chapter 4.

Mirroring the analysis performed in chapter 3 for the case of adverse selec- tion as much as possible, we argue here that complex contractual environments with moral hazard also raise many new difficulties for the characterization of the binding incentive and participation constraints. Again mimicking what was done in chapter 3, we propose a classification of the new contractual settings analyzed in the present chapter. Each of those categories corresponds to a particular pertur- bation of the standard moral hazard trade-offs analyzed in chapter 2.

  • Conflict between several of the agent’s incentive constraints: Let us con- sider a first class of models where the agent can exert more than two possible levels of effort. The agent may choose his one-dimensional action within a finite set, or he may be able to fine-tune his effort supply continuously. In both cases, the agent’s performance remains a single dimensional vector. Alternatively, the agent may be performing several tasks on the principal’s behalf, thus controlling various dimensions of effort and with each of those efforts affecting a particular aspect of the agent’s performance. In those complex contracting environments, a major difficulty is to ensure that local incentive constraints, which are the easiest ones to handle, still drive the design of When the agent’s performance has a single dimension, we first derive the second-best cost of implementing any given level of effort. This cost is obtained by minimizing the agent’s expected payment subject to his incentive and participation constraints. As in chapter 4, it is true that the second-best cost is greater than the first-best cost as soon as one incentive constraint is binding. Second, we generalize the second-best analysis of chapter 4 to find the optimal effort level that the prin-cipal wants to induce under moral hazard. This analysis already shows that there is no general lesson on the nature of the distortion entailed by moral hazard. The second-best level of effort may be either higher or lower than its first-best value, contrary to our findings in the binary effort model of chapter 4. We then develop the so-called first-order approach to moral hazard problems where effort is a con- tinuous variable. This approach replaces the set of possible incentive constraints by a local incentive constraint, a legitimate step provided that the agent’s problem is concave. This concavity is in turn obtained under rather stringent assumptions, namely that the cumulative distribution function of the performance level should be a convex function of the agent’s effort (CDFC) and MLRP should also be sat- isfied. As we have already seen in chapter 4, this latter property also implies that the agent’s compensation schedule is nondecreasing with his performance.

In practice, the agent’s effort is often better characterized as a multidimen- sional variable. For instance, a retailer selling goods on the manufacturer’s behalf must reduce retailing costs but also improve after-sales services. A worker is not only involved in productive tasks but also must sometimes monitor his peers. A tenant must simultaneously choose the quality of the crops he seeds and the level of physical investment he makes. A teacher must allocate his time between doing research and supervising students. All of these examples belong to the class of mul- titask incentive problems. In those models, agency costs are significantly affected by the conflicts that may arise when incentivizing the various tasks performed by the agent. The characterization of the optimal contract depends on the complementar- ity or substitutability of the tasks. The technological relationship between tasks thus has strong incentive consequences. Viewing the relationship between the principal and his agent as a cluster of various transactions significantly expands the scope of standard incentive theory. New issues arise in such a framework. For instance, one can study how the distribution of efforts along those different dimensions of the agent’s activity or the degrees of informativeness of the different performances affect the power of incentives, deriving rich lessons for organizational design from such an analysis.

We also present a number of important examples of the multitask principal- agent models. These applications cover a broad range of issues, such as the inter- linking of agrarian contracts, the design of incentive schemes based on aggregate performances, and finally the choice of whether to integrate vertically or not a downstream unit and its consequences for the comparison between the power of incentives in market environments and within firms.

  • Strong conflict between the agent’s incentive and participation con- straints: One peculiarity of the principal-agent models with risk aversion presented so far is that, even though various incentive constraints might be taken into account by the principal, the separability of the agent’s utility function between consump- tion and effort implies that giving up an ex ante rent to the agent is never optimal from the principal’s point of The conflict between incentives and insurance is not strong enough to leave a rent to the agent. Instead, with a nonseparabil- ity between consumption and effort in the agent’s utility function, the conflict between incentive and participation constraints may become stronger, and it may be better solved by leaving a positive ex ante rent to the agent. Leaving such a rent allows the principal to benefit from wealth effects, which may reduce the cost of providing incentives.
  • Constraints on transfers: Finally, we also replace the conflict between incentive and participation constraints by the conflict between incentive and bud- get balance constraints that appear in the optimal taxation literature. Again, in a model with a binary level of effort, under-provision of effort appears with moral Section 5.1 presents the straightforward extensions of the standard model of chapter 4 to the cases where the agent can perform more than two and possibly a continuum of levels of effort. In this section we discuss there the two-step charac- terization of the second-best optimum, first with the derivation of the second-best cost of implementing a level of effort, and second with the analysis of the trade-off between the benefit and the cost of implementing any given effort. We prove, by exhibiting an example, that the second-best level of effort in an insurance-efficiency trade-off can be distorted upwards. Therefore, this shows that complex moral haz- ard models may fail to perpetuate the simple lessons of chapter 4. Nevertheless, we also provide a limited liability rent-efficiency trade-off with a continuum of levels of effort where the basic lessons of section 4.5.1 carry over. There, the trade-off between the extraction of the limited liability rent and allocative efficiency always calls for a reduction in the expected volume of trade. Finally, this section ends with an exposition of the first-order approach. The first-order approach allows the modeler to replace the infinity of incentive constraints, which arise when the agent controls a continuous effort variable, with a simple first-order condition. Section 5.2 deals with a multitask model, solving first for the optimal contracts that induce efforts on both dimensions of the agent’s activity and then deriving the second- best level of effort on each of these dimensions. This analysis is first performed in the simple framework of a risk-neutral agent who is protected by limited liability. Then, we turn to the somewhat more complex case of risk aversion. We show the possibility of diseconomies of scope in agency costs, and we discuss their precise origins. Several examples of multitask agency models are then presented. Sec- tion 5.3 analyzes the case where the agent’s utility function is no longer separable between consumption and effort. In this section we discuss the conditions under which the agent’s participation constraint may not be binding at the optimum. We also provide a simple example of preferences where the disutility of effort can be expressed in monetary terms for which, despite the nonseparability between effort and consumption, the optimal contract keeps almost the same features as in the case of separability.3 Finally, section 5.4 analyzes the trade-off between efficiency and redistribution in a moral hazard context.

Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.

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