Mixed Models of agency theory

The pure models of chapter 2 for adverse selection, chapter 4 for moral hazard and chapter 6 for nonverifiability were highly stylized contracting settings. Each of those models aimed at capturing a single dimension of the incentive problems that may be faced by a principal at the time of designing the contract for his agent. In those chapters, the analysis of each of these respective paradigms has already provided a number of important insights that concern, on the one hand, the conflict (if any) between allocative efficiency and the distribution of the gains from trade and, on the other hand, the form of the optimal compensation schedule. Moreover, our investigation of more complex models than those of chapters 2 and 4 has also shown how the insights gleaned from these simple models carry over in more complex economic environments.

In real world settings, contracts are rarely designed with the sole objective of solving one incentive problem. Most often, the principal’s control of the agent requires that they deal simultaneously with both adverse selection and moral haz- ard, or with both the nonverifiability of the state of nature and moral hazard. In those complex environments, the most important question is, how do the agency costs due to the different paradigms interact? More precisely, we would like to assess whether the lessons from the pure models continue to hold in those more complex environments and, if they do not hold anymore, we would like to under- stand in which directions those lessons should be modified.

The aim of this chapter is not to give a complete overview of the huge and extremely heterogeneous literature that analyzes settings where several paradigms are useful to understand the economic problem at hand. Instead, we have tried to isolate three important lessons from those models. More specifically, we assess whether blending together more incentive problems increases or decreases alloca- tive distortions. This simple criterion allows us indeed to clarify somewhat the rather noisy messages of these mixed models.

Lesson 1: Adding the agency costs of the different paradigms may decrease allocative efficiency. First consider a model where the agent knows his type per- fectly before contracting with the principal and performing a task on his behalf. For instance, as in chapter 2, an agent who is privately informed of his marginal cost of production may be supplying a good for the principal but may also exert some costly and nonobservable effort affecting the probability that an efficient trade takes place. Thus adverse selection occurs before moral hazard. With a risk-neutral agent protected by limited liability, we know from chapter 4 that the principal cannot costlessly structure the payments given to the agent for providing the moral hazard incentive. A limited liability rent must be given to the agent to induce effort provision. This rent plays the role of an added fixed cost from the principal’s point of view. Inducing participation by the agent now becomes more difficult. The conflict between the participation and the adverse selection incentive con- straints is thus exacerbated by moral hazard. This leads to possibly more shutdowns of types and to greater allocative distortions than in the absence of any moral hazard.

Insurance contracts are archetypical examples of contracts designed to solve simultaneously an adverse selection problem and a moral hazard problem. A risk- averse driver often has private information on how good a driver he is and also how safely he drives. To induce the high-risk agent to reveal his probability of accident, we saw in chapter 3 that the low-risk agent must receive less than full insurance. Under pure moral hazard, both types of agents should instead receive incomplete insurance in order to induce them to exert safety care. When adverse selection takes place before moral hazard, the mere fact that the high-risk agent should now bear some risk to solve the moral hazard problem makes that agent’s adverse selection rent more costly for the principal. This leads to more distortion for the low-risk agent, who now bears an even greater amount of risk than under pure adverse selection.

The general insight gleaned from these latter two models is that solving the moral hazard problem ex post leads the principal to introduce distortions in the agent’s payoff that increase the cost of his adverse selection information rent. This leads to further allocative distortions and to a reduction in the expected gains from trade with respect to the case of pure adverse selection.

Lesson 2: Adding the agency costs of the different paradigms may improve allocative efficiency. Let us now consider the case where moral hazard takes place before adverse selection. For instance, an agent may carry out, on behalf of the principal, an effort that is privately known by the agent and stochastically affects the value of trade. The simplest way to do so is to merge the basic models of chapters 2 and 4. By choosing a nonobservable and costly effort, the agent increases the probability that a low marginal cost is realized. Contrary to chapter 4, we now assume that the random state of nature, i.e., how large the gains are from trade, is a piece of information that is privately learned by the agent. In such a context, the principal must offer a contract with a double objective in mind. On the one hand, the contract must provide the agent with enough incentives to exert effort at the ex ante stage. On the other hand, the contract must also induce the agent to reveal his private information ex post.

Of course, ex ante contracting has no cost for the principal if he deals with a risk-neutral agent. Both adverse selection and moral hazard can be solved cost- lessly by making the agent residual claimant for the value of trading with the principal, as we have seen in chapters 2 and 4. Hence, a second-best analysis arises only with risk aversion or limited liability. To fix ideas, we consider the case of a risk-neutral agent who is protected by limited liability. One of the main lessons of chapter 2 is that the agent should receive a higher rent when he is efficient in order to satisfy his adverse selection incentive compatibility constraint. It is precisely this rent differential that also helps the principal to incentivize the agent to exert effort. The rent necessary to solve the adverse selection prob- lem may be either below or above the limited liability rent necessary to solve the moral hazard problem. Different regimes of optimal contracts can be found, depending on the parameters of the model. To solve the moral hazard problem, the principal might have to raise the agent’s rent, and the principal does so by increasing the volume of trade. Then, the interplay between adverse selection and moral hazard improves allocative efficiency with respect to the case of pure adverse selection.

Lesson 3: Adding the agency costs of the different paradigms may have no new impact on allocative efficiency. We already know from the analysis in chapter 6 that the nonverifiability of the state of nature does not put any real constraint on the ability of the contractual partners to achieve the first-best by agreeing to contract, before the state of nature is realized, on a game form to be played ex post, i.e., once they both know which state of nature has been realized. In addition, we suppose that the agent can perform a nonobservable effort affecting the probability that an efficient trade takes place. If the state of nature were verifiable, this setting would be akin to a pure moral hazard model similar to chapter 4, and the principal and the agent would sign the pure moral hazard contract, which leads to an allocative distortion that is now well known. Once the nonverifiability of the state of nature is taken into account, the principal and the agent can agree, on top of this moral hazard contract, on a game form solving the nonverifiability constraint ex post, just as was done in chapter 6. We are then back to a standard pure moral hazard problem. The main point to stress here is that not all of the solutions to the nonverifiability problem perform equally well now. Indeed, we will show that Nash implementation strictly dominates both incentive contracts and ex post negotiations.

In section 7.1, we first analyze the case of adverse selection taking place before moral hazard. By means of an example, we show that solving the moral hazard problem exacerbates the allocative distortions due to adverse selection. This section also provides a version of the revelation principle, generalizing its applica- bility to models with both adverse selection and moral hazard. Lastly, we analyze false moral hazard problems, where the moral hazard and the adverse selection unknowns are blended together, in a deterministic way, into a single observa- tion available for contracting. These models, which have been used extensively in the regulation and optimal taxation literatures, end up being pure adverse selec- tion models. However, the interplay between moral hazard and adverse selection enriches considerably the interpretation of the models. In section 7.2, we change the timing above and focus on models where moral hazard takes place before adverse selection. We show that these models tend to reduce allocative ineffi- ciency with respect to the case of pure adverse selection. Finally, in section 7.3 we analyze the case of moral hazard followed by the nonverifiabilty of the state of nature. Here we show that nonverifiability does not put a real constraint on contracting.

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

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