Incentive and Participation Constraints with Adverse Selection

The main theme of chapter 2 was to determine how the fundamental conflict between rent extraction and efficiency could be solved in a principal-agent rela- tionship with adverse selection. In the models presented in chapter 2, this conflict was relatively easy to understand because it resulted from the simple interaction of a single incentive constraint with a single participation constraint. A major diffi- culty of incentive theory in general, and adverse selection models in particular, lies in the numerous constraints imposed by incentive compatibility when one moves away from the simple models of chapter 2.

In this chapter, we consider more complex contractual environments that have in common the fact that they raise further difficulties for the determination of the binding incentive and participation constraints. Those difficulties are not only purely technical ones due to the increased mathematical complexity of the models, but they are also deeply rooted in the economics of the problems under scrutiny. They often lead to a quite novel analysis of the rent extraction-efficiency trade-off, sometimes challenging its main insights, but always offering sharp and interesting economic conclusions.

We can roughly classify the features of the new contractual settings analyzed in this chapter into three broad categories. Each of these categories yields a partic- ular perturbation of the standard rent extraction-efficiency trade-off. Let us briefly describe these three categories.

  • Conflict between several of the agent’s incentive constraints: In envi- ronments that are more complex than the bare-bones model of chapter 2, the agent may have more than two possible types. These models include the relatively straightforward three-type extensions of the basic set up of chapter 2, the case of a continuum of types often found in the literature, and also the less easy-to-handle multidimensional modelling of adverse selection. In the case of multidimensional modelling, new conflicts arise between several of the agent’s incentive constraints of the agent.

In a unidimensional model with three types, the Spence-Mirrlees property enables us to simplify the analysis considerably, because it suggests that only local incentive constraints need to be taken into account. However, the sole consider- ation of upward incentive compatibility constraints may be misleading, and the optimal contract may call for some downward incentive compatibility constraints to be binding as well. Bunching of different types on the same contract arises quite naturally when the distribution of types does not satisfy the monotone hazard rate property. Three-type models alone are enough to highlight this bunching phe- nomenon. However, for the sake of completeness, appendices 3.1 and 3.2 at the end of this chapter are entirely devoted to the case of a continuum of types. We solve there for the optimal contract with a continuum of types. Also, we present the techniques needed to replace the infinite number of incentive constraints with a local incentive constraint, and we show the validity of this approach when the Spence-Mirrless property holds. Then, we move on to solve for the optimal con- tract with a continuum of types in the presence of bunching.

In practice, the agent’s private information is often multidimensional. A reg- ulator is ignorant of both the marginal cost and the fixed cost of a regulated firm. A bank is ignorant of both the quality of an investment and the risk aversion of the investor. A monopolistic seller knows neither the willingness to pay nor the marginal utility of income of the buyer. By the mere multidimensionality of the type space, different types of agents cannot be unambiguously ordered, and multidimensional models are still characterized by some conflicts between various incentive constraints. Nothing like the monotone hazard rate property guarantees the full separation of types on different allocations in the multidimensional model. However, at least in two by two discrete models, some analogies with the unidi- mensional model of chapter 2 can still be drawn.

  • Conflict between the agent’s incentive and type-dependent participation constraints: Another significant simplification made in chapter 2 was to assume that the status quo utility level of the agent was independent of his type (and normalized to zero). Quite often, outside his relationship with the principal an efficient agent has better opportunities than an inefficient agent. To model those valuable opportunities, we assume that the agent gets an exogenous type-dependent utility level when he is not trading with the principal. When the efficient type’s status quo utility level becomes high enough, the principal finds that it is no longer useful to reduce allocative efficiency to decrease the agent’s information rent, which is bounded below by this outside opportunity. Keeping the efficient agent within the relationship may even lead the principal to give him such a great deal that the inefficient agent is also willing to take this offer, i.e., to mimic the efficient The inefficient agent’s incentive constraint is then binding, a case of so called countervailing incentives.

Instead of being deterministic, the agent’s outside opportunities may also be random. This leads to random participation constraints and thus to a probabilistic participation of some types. In a two-type model where only the inefficient type’s participation is random, the contract must not only induce information revelation by the efficient type but must also arbitrate between the benefit of trading more often with an inefficient type and the cost of providing that inefficient type with enough incentives to participate.

  • Constraints on transfers: So far we have assumed that the monetary trans- fers between the principal and the agent were unlimited. Several kinds of con- straints can be imposed on these Under ex ante contracting and with a risk-neutral agent, we showed in section 2.11.1 that the first-best allocation was implementable provided that the agent receives a negative payoff in the bad state of nature. However, agents are often financially constrained and have limited liability. When such penalties are restricted by different kinds of limited liability constraints, it becomes harder to induce information revelation. The conflict between incentive compatibility and ex ante participation constraints is no longer costless to solve. Second-best volumes of trade are then distorted away from their first-best values. Nevertheless, the direction of the distortion depends on the nature of the limited liability constraints.

In section 2.14.1 we have already seen how informative signals on the agent’s type enabled the principal to improve the terms of the rent extraction-efficiency trade-off. Auditing is an endogenous way to obtain such signals. Audit allows a costly enlargement of the principal’s tools that are available to screen the agent’s types.2 At some cost, the principal may be able to verify with some probability the agent’s message on his type. In cases where a lie is detected, the agent is punished and has to pay a penalty, which again can be limited in different ways either by the agent’s assets or his gains from trade with the principal. Of course, this threat of an audit relaxes the incentive compatibility constraint. But the trade-off between incentive compatibility and participation constraints is again dependent on the particular constraints imposed on punishments.

Most of this book is concerned with principal-agent relationships where the conflict between the principal and the agent is quite obvious and leads to binding participation constraints. However, when the principal is a benevolent government willing to redistribute income between heterogeneous agents, the agency conflict comes from the interaction between the principal’s budget balance constraint and the agent’s incentive constraint. Solving such problems requires slightly different methods than those we have used so far. Indeed, for such models one cannot deter- mine, sequentially, the distribution of information rents that implement a given output profile at a minimal cost and then the second-best outputs. Instead, the technical difficulties of such models come from the simultaneous characterization of the second-best outputs and the profile of information rents. Those taxation models highlight a new trade-off between allocative efficiency and redistribution. Section 3.1 presents the straightforward three-type extension of the standard model of chapter 2. In this section we discuss the Spence-Mirrlees property and the monotone hazard rate property, which together ensure monotonicity of the optimal schedule of outputs and the absence of any bunching of types. Section 3.2 deals with a bidimensional adverse selection model—solving it for the optimal out- puts and comparing it with a standard unidimensional model. Section 3.3 offers a careful analysis of a two-type model with type-dependent reservation utilities, discussing all possible regimes of the solution. We also discuss several instances where this modelling has turned out to be useful for understanding various eco- nomic phenomena. Section 3.4 introduces random participation constraints. In section 3.5, we look at the impacts that different limited liability constraints, on either transfers or rents, may have on the allocation of resources under ex ante contracting. The first constraints increase the volume of trade whereas the second ones reduce it. In section 3.6, we analyze audit models and derive optimal audit policies for punishments satisfying various constraints. Audit models are then com- pared to models where incentives for truthful revelation are based on the threat of terminating, with some probability, the relationship between the principal and the agent. Finally, section 3.7 analyzes the trade-off between efficiency and redistribu- tion. It shows how to optimize such an efficiency-equity trade-off. Appendices 3.1 and 3.2 deal with the case of a continuum of types for the basic model of section 2, which exhibits a simple rent-efficiency trade-off.

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

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