Multistage Contracting with Applications to R&D and Insurance Policies

An agent undertakes a nonobservable first‐stage effort. The principal observes whether the effort results in a successful project or not. If the project succeeds, only the firm observes its interim quality, and can further improve it with a nonobservable second‐stage effort. If the agent accepts penalties when the first‐stage fails, moral hazard and asymmetric information do not prevent the principal from implementing her first‐best outcome. However, if the agent is bounded by the maximum loss he can bear when the first‐stage fails (limited liability), the principal induces the agent to exert a first‐stage effort below the first‐best level and a second‐stage effort above the first‐best level when the interim quality of his project is low. This distortion in efforts implies that the ex post rent left to the agent with a project of high interim quality is above the first‐best level. This provides a rationale for the optimality of expanding the use of the “carrot” (second‐stage rent) when the use of the “stick” (first‐stage penalty) is restricted. Implications of the theory for R&D, bank, job, and insurance contracts are discussed.     

When vagueness induces indirect competition: strategic incompleteness of contracts

Summary. A class of employment contracts entailing production targets and consequent rewards is studied. In a nondiscriminatory environment, a principal hiring many agents faces the problem of writing a common contract which induces the highest possible effort from each one of his agents. While a very high target may get the best out of highly skilled agents, low skilled ones tend to shirk. On the other hand, although low targets make every agent put positive effort, there are efficiency losses from the high skilled agents. Also, in such environments the principal often has better information regarding the skills of all his agents than what each agent has regarding the rest of the agents at work. We show that if skills of agents are sufficiently close, the informed principal earns strictly higher profits by offering incomplete contracts as against being specific, as incomplete contracts reduce flow of information and induce indirect competition amongst agents. Received: May 19, 2000; revised version: August 28, 2001     

Collusion, Delegation and Supervision with Soft Information

This paper shows that supervision with soft information is valuable whenever supervisors and supervisees collude under asymmetric information and proceeds then to derive an Equivalence Principle between organizational forms of supervisory and productive activities. We consider an organization with an agent privately informed on his productivity and a risk averse supervisor getting signals on the agent's type. In a centralized organization, the principal can communicate and contract with both the supervisor and the agent. However, these two agents can collude against the principal. In a decentralized organization, the principal only communicates and contracts with the supervisor who in turn sub-contracts with the agent. We show that the two organizations achieve the same outcome. We discuss this equivalence and provide various comparative statics results to assess the efficiency of supervisory structures.     

Group insurance and lending with endogenous social collateral

We construct a dynamic model of self-enforcing insurance provision and lending to a community of borrowers who are connected by risk-sharing arrangements that are themselves subject to enforcement problems, as in Kocherlakota (1996). We show that an outside lender offering constant-consumption contracts can earn a higher profit if he conditions his repeated interactions with each borrower on the history of his interactions with all the group members (a joint liability contract), rather than on his history with that borrower only (individual liability contracts). This result holds even in the absence of informational asymmetries. The observation driving it is that with individual liability contracts, a joint welfare-maximizing group may prefer to have one or more group members default on their contracts, so that the group can consume a mix of outside funds and the defaulters' stochastic income. One contribution of our work is to give precise economic content to the concept of “social collateral” as the per-agent surplus from group risk-sharing over autarky. The group can deter its members from defaulting on their contracts with the principal by threatening to reduce that surplus.     

Fairness and Incentives in a Multi‐task Principal–Agent Model

This paper reports on a two‐task principal–agent experiment in which only one task is contractible. The principal can either offer a piece‐rate contract or a (voluntary) bonus to the agent. Bonus contracts strongly outperform piece‐rate contracts. Many principals reward high effort on both tasks with substantial bonuses. Agents anticipate this and provide high effort on both tasks. In contrast, almost all agents with a piece‐rate contract focus on the first task and disregard the second. Principals understand this and predominantly offer bonus contracts. This behavior contradicts the self‐interest theory but is consistent with theories of fairness.     

Collusion and Renegotiation in a Principal–Supervisor–Agent Relationship

We describe a principal–supervisor–agent relationship in which agent and supervisor may collude. To prevent collusion, the principal may contract on a noisy signal which is correlated with the occurrence of collusion. When the signal is informative enough, the principal uses it and no collusion occurs in equilibrium. These contracts, however, are ex post inefficient and are only optimal if the principal can commit not to renegotiate. With renegotiation it is never optimal for the principal to prevent collusion and, at the same time, condition contracts on the signal. In fact, when the signal is informative enough collusion occurs in equilibrium.     

Informed principal with correlation

In this paper we analyze an adverse selection model with one principal and one agent, who are both risk neutral and have private information. We assume that the private information of the principal is correlated with that of the agent. The main result of the paper is that the principal can extract a larger share of the surplus from the agent than in the case where her information is public. The principal can design such a contract because she exploits the fact that her type is an informative signal on the agent's one. We fully characterize the equilibrium of the game in which different types of principal offer the same menu of contracts that leaves the agent uninformed about the principal's type. This gives more freedom to the principal when setting the transfers because the agent's constraints need to hold only at an interim stage.     

Contracts with endogenous information

I study covert information acquisition and reporting in a principal agent problem allowing for general technologies of information acquisition. When posteriors satisfy two dimensional versions of the standard First Order Stochastic Dominance and Concavity/Convexity of the Distribution Function conditions, a first-order approach is justified. Under the same conditions, informativeness and riskiness of reports are equivalent. High powered contracts, that make the agent's informational rents more risky, are used to increase incentives for information acquisition, insensitive contracts are used to reduce incentives for information gathering. The value of information to the agent is always positive. The value of information to the principal is ambiguous.     

FIXED‐WAGES,WAGE DIFFERENTIALS AND WORKER HETEROGENEITIES

We study incentive‐compatible labour contracts in the case where individual productivity, preference for leisure and time preference rate are unobservable by the principal in a two‐period model. We first reduce this three‐dimensional problem to a standard one‐dimensional screening problem. Features of second‐best labour contracts provide a rationale for both fixed‐wages and wage differentials.     

Optimal Contracting with Private Knowledge of Wealth and Ability

We examine the optimal design of contracts when an agent is privately informed about his wealth, his ability, and his effort supply. We find that the agent's wealth and ability act as perfect complements in determining the power of the incentive scheme under which he operates. Only if his ability and his wealth both increase can an agent be assured of operating under a more powerful scheme. Consequently, severe under-utilization of wealth and ability arise in equilibrium.     

Contracts and Productive Information Gathering

We modify a standard Baron–Myerson model by assuming that, instead of knowing the state of nature, the agent has to incur a cost γ to learn it. Under these conditions, the principal will offer contracts that, depending on the value of γ, try to induce the agent to gather or not to gather information. We study the tradeoffs that are involved.Journal of Economic LiteratureClassification Numbers: D82, D83.     

Regulation and Coordination of International Environmental Externalities with Incomplete Information and Costly Public Funds

In this article, we study cross-border externalities in a game played by two principal-agent pairs with adverse selection. Each firm/agent is located in one country and generates pollution by producing complementary or substitute goods, sold on a common market. A fraction of pollution is transferred from one country to another. Each regulator/principal is imperfectly informed about the marginal cost of his domestic firm and accordingly uses secret incentive contracts with costly public funds. We show the necessity of cooperation between competing regulators to effectively internalize all the damages caused to the environment, while reaching the first best. If the level of uncertainty is sufficiently low, we obtain an infinity of noncooperative Bayesian differentiable equilibria, which may necessitate competing regulators to coordinate on an equilibrium. Such coordination constitutes an incentive for competing regulators to cooperate. Our major result states that under some circumstances asymmetric information relaxes the transborder externality problem. Indeed, we show that, when there is a major transfer of pollution and firms' marginal costs are sufficiently high, competing regulators are better off under uncertainty. Therefore, asymmetry of information can have the very consequence of generating regulation that is too strict from the domestic viewpoint but that improves social efficiency when the benefits to both countries are taken into account.     

Adverse selection and bilateral asymmetric information

A simple principal-agent model with bilateral asymmetric information and common values is developed. The agent(s) has private information about his characteristics but does not knowhow these affect outcomes. The principal knows how the characteristics translate into outcomes, but does not observe the characteristics. It is shown that equilibrium contracts aresimple in being designednot to reveal the agent's characteristics. When the agent knows howsome of his characteristics affect the outcome, contracts will be differentiated with respect to precisely those characteristics. An application to the use of genetic information is considered.     

Dynamic yardstick mechanisms

This paper shows that the inability of principals to commit to long-term contracts is irrelevant when dealing with several agents whose private information is correlated. This sharply contrasts with the dynamics of contracting without such correlation. The paper also explores what limitations on yardstick mechanisms can justify the use of long-term contracts. We found that the inability of a principal to commit not to renegotiate long-term contracts is without consequence even if there is a bound on transfers that an agent can be asked to pay. In contrast, short-term contracting fails to implement the commitment solution with constraints on transfers. Second, absent current yardstick, the possibility of using correlated mechanisms in the future allows the principal to implement the first-best with a renegotiation-proof long-term contract whereas this cannot be achieved with short-term contracting.     

Contracting with Diversely Naive Agents

In standard contract-theoretic models, the underlying assumption is that agent types differ in their preference or cost parameters, and the principal's objective is to design contracts in order to screen this type. We study a contract-theoretic model in which the heterogeneity among agent types is of a "cognitive" nature. In our model, the agent has dynamically inconsistent preferences. Agent types differ only in their degree of "sophistication", that is, their ability to forecast the change in their future tastes. We fully characterize the menu of contracts which the principal offers in order to screen the agent's sophistication. The menu does not exclude any type: it provides a perfect commitment device for relatively sophisticated types, and "exploitative" contracts which involve speculation with relatively naive types. More naive types are more heavily exploited and generate a greater profit for the principal. Our results allow us to interpret real-life contractual arrangements in a variety of industries.     

Performance Standards and Incentive Pay in Agency Contracts

When the presence of limited liability restricts a principal from imposing monetary fines on an agent in case of poor performance, the principal might use other kinds of punishment threats to deter the agent from shirking. We show that under the optimal contract in this case, the principal sets a performance standard and punishes the agent if the standard is not met, but rewards the agent on a profit-sharing basis if the standard is significantly exceeded. The optimal choice of performance standards for such contracts is discussed. It is shown that punishment threats, although inefficient, often help the principal to discipline the agent.
JEL classification : D 82     

Signaling quality with increased incentives

Previous work on informed-principal problems with moral hazard suggested that the principal should signal project quality by retaining a larger share of the project and hence lowering incentives for the agent. We show that this view is incomplete. If project quality and effort are complements and effort is more valuable for high-quality projects, a principal with a high-quality project may separate from a principal with a low-quality project by increasing incentives for the agent. This holds with a risk-neutral agent who is protected by limited liability as well as with a risk-averse agent and unlimited liability. A dynamic version of our model in which the agent learns project quality in later periods provides an explanation for the use of initially reduced royalty rates in business-format franchising contracts.     

Minimum payments and induced effort in moral hazard problems

Consider a moral hazard problem in which there is a constraint to pay the agent no less than some amount m. This paper studies the effect of changes in m on the effort that the principal chooses to induce from the agent. We present sufficient conditions on the informativeness of the signal observed by the principal and on the agentʼs utility under which when m increases, induced effort (and hence productivity) falls. We also study how the cost minimizing contract for any given effort level varies in m. We present an efficient algorithm for numerically calculating optimal contracts for given parameters and show that induced effort falls when m is increased in many cases even when our sufficient conditions fail.     

Psychology at work

We compare three wage–effort psychological games. In the first game, the agent’s motivation hinges on a degree of altruism influenced by the surprise generated by the principal’s wage offer. The agent works harder when the wage is greater than expected and vice versa when the wage is smaller than expected. Consistent equilibrium beliefs oblige the principal to randomize in order to surprise the agent, which results in the principal being worse off than if she were dealing with an unemotional agent. We then consider an intention-based reciprocity model and a model of guilt aversion. We find that guilt aversion may potentially yield the best outcome for the principal.     

INFORMATION GATHERING BY A PRINCIPAL*

In the standard principal–agent model, the information structure is fixed. In this article the principal can choose to acquire additional information about the state of the world before he contracts with an agent. In the event that the principal acquires this information, the agent never learns what the principal knows about the state of the world. I examine cases where the agent can and cannot observe whether the principal has acquired the additional information. The implications for risk sharing, information acquisition, investment, and welfare are examined for both cases.