Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent?s consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent?s income realized to date. We characterize this function in terms of the agent?s outside option value function and the discounted amount of time in which the agent?s income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez–Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley–Aiyagari incomplete-markets models.     

Production and insurance under regret aversion

This paper examines the behavior of a regret-averse producer facing revenue risk. To insure against the revenue risk, the producer can purchase a coinsurance contract with an endogenously chosen coinsurance rate. Regret-averse preferences are characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that the regret-averse producer never fully insures against the revenue risk even though the coinsurance contract is actuarially fair. When the producer is sufficiently regret averse and the loss probability is high, we further show that the regret-averse producer chooses not to purchase the actuarially fair coinsurance contract. Even when purchasing the actuarially fair coinsurance contract is optimal, we derive sufficient conditions under which the regret-averse producer reduces the optimal output level as compared to that without the coinsurance contract. These results are distinct from those under pure risk aversion, thereby making the consideration of regret aversion crucial.     

Regulating a manager whose empire-building preferences are private information

We obtain the optimal contract for the government (principal) to regulate a manager (agent) who has a taste for empire-building that is his/her private information. This taste for empire-building is modeled as a utility premium that is proportional to the difference between the contracted output and a reference output. We find that output is distorted upward when the manager’s taste for running large firms is weak, downward when it is strong, and equals a reference output when it is intermediate (in this case, the participation constraint is binding). We also obtain an endogenous reference output (equal to the expected output, which depends on the reference output), and find that the response of output to cost is null in the short-run (in which the reference output is fixed), whenever the manager’s type is in the intermediate range, and negative in the long-run (after the adjustment of the reference output to equal expected output).     

Dynamic risk-sharing with two-sided moral hazard

A group of risk-averse agents repeatedly produce a perishable consumption good; individual outputs are observable but efforts are not. The contracting problem admits a recursive formulation, and the optimal value function is the fixed point of a contraction mapping. When the agents can be punished to the full extent in a single period, every continuation contract of an optimal contract is itself optimal; the marginal utility ratio between one agent and another is a submartingale. The results imply that it is in general important to restrict an agent whose moral hazard constraint is binding from saving through another agent within the risk-sharing group. Limited commitment and long-run implications of optimal contracting are also examined.     

Task assignment under agent loss aversion

We analyze a task-assignment model in which a principal assigns a task to one of two agents depending on future states. If the agents have concave utility, the principal assigns the task to them contingent on the state. We show that if the agents are loss averse, a state-independent assignment–assigning the task to a single agent in all states–can be optimal even when the principal can write a contingent contract at no cost.     

On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Compensation Convexity without Utility Restriction

We develop an optimal contract model on the use of stock options for chief executive officer compensation under the Mirrlees–Rogerson moral hazard framework. We find that convexity, as know as, the use of stock options, can arise with a broader range of agent utility functions than allowed by Hemmer et al. ( 2000 ). We characterise the necessary conditions regarding the behaviour of the agent's marginal risk tolerance for both the concavity and convexity cases of the likelihood‐ratio function. We find stock options need to be used more intensively, when the agent displays a higher marginal risk tolerance and when the realised task output is higher.     

The value of information in a principal-agent model with moral hazard: The ex post contracting case

In a principal-agent model with moral hazard, a signal about the principal?s technology — the stochastic mapping from the agent?s action to the outcome — is observed before the contract is offered. The signal is either uninformative (null information), informative and observed only by the principal (private information), or also observed by the agent (public information). We show that, from an ex ante standpoint (before the signal is observed): (i) the agent prefers private to both null and public information; (ii) the principal sometimes prefers null to both private and public information; and (iii) when the principal prefers public to null information, she prefers public to private information, whereas the agent prefers private to public information. In this last situation, we also show that (iv) for any separating equilibrium with private information, there exists a contract with public information that both strictly prefer.     

Unemployment insurance with hidden savings

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini (1997) [1]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.     

Ex post participation constraint in a principal–agent model with adverse selection and moral hazard

This paper analyzes optimal contracting when an agent has private information before contracting and exerts hidden effort that stochastically affects the output. Additionally, the contract is constrained to satisfy the agentʼs ex post participation. We highlight three features of this model. First, the agent faces countervailing incentives. Second, the separation of types is never optimal. Third, the optimal constant bonus rewarding success is distorted downward below its efficient level.     

Dynamic contracting with persistent shocks

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound—immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.     

基于声誉理论的研发外包动态激励机制研究

基于声誉理论,本文建立了企业研发外包的动态激励机制模型,研究了承包方在同一个契约里长期激励与短期激励相结合的激励模式,得出了实现声誉有效激励的条件和提高声誉激励效应的途径。研究结果表明:考虑声誉机制时,承包方在第1期、第2期的努力水平比不考虑声誉机制时提高了,承包方从第1期、第2期产出里分享的剩余份额比不考虑声誉机制时提高了。因此,与没有引入声誉机制的契约模型相比,声誉激励机制和显性激励机制相结合的最优动态契约模型可以实现帕累托改进、提高激励强度,并能起到很好的约束作用。     

Repeated moral hazard with effort persistence

I study a problem of repeated moral hazard where the effect of effort is persistent over time: each period's outcome distribution is a function of a geometrically distributed lag of past efforts. I show that when the utility of the agent is linear in effort, a simple rearrangement of terms in his lifetime utility translates this problem into a related standard repeated moral hazard. The solutions for consumption in the two problems are observationally equivalent, implying that the main properties of the optimal contract remain unchanged with persistence. For illustration, I present the computed solution of an example.     

Optimality and renegotiation in dynamic contracting

We characterize the optimal renegotiation-proof contract in a dynamic principal–agent model in which the type of the agent may change stochastically over time. We show that, under general conditions, the optimal contract with commitment is renegotiation proof even when type realizations are serially correlated. When the renegotiation-proofness constraint is binding, it is always optimal to partially screen the types by offering a menu of choices to the agent; and the distortion induced by the renegotiation-proofness constraint is non-decreasing in the persistence of types.     

What's the damage? Environmental regulation with policy‐motivated bureaucrats

In choosing environmental policy, governments rely on information provided by bureaucrats, who may have a political motivation of their own. We analyze the ensuing principal–agent relationship and derive the government's optimal contract. We find that a regulatory agent who is more environmentalist than the government is rewarded for truthfully stating that the environmental impact of the regulated economic activity is low (and vice versa). The bureaucrat has a stronger influence on policy if there is greater uncertainty about the environmental impact, or if the policy choice has a strong weight in his utility function. For some impact values, the bureaucrat is permitted to set his own preferred policy, which is a form of optimal delegation.     

A dynamic model of unsecured credit

We study the terms of credit in a competitive market in which sellers (lenders) are willing to repeatedly finance the purchases of buyers (borrowers) by engaging in a credit relationship. The key frictions are: (i) the lender cannot observe the borrower?s ability to repay a loan; (ii) the borrower cannot commit to any long-term contract; (iii) it is costly for the lender to contact a borrower and to walk away from a contract; and (iv) transactions within each credit relationship are not publicly observable. The lender?s optimal contract has two key properties: delayed settlement and debt forgiveness. Finally, we study the impact of changes in the initial cost of lending on the contract terms.     

Operating efficiency and output insensitive employment contracts for capital management

Summary This paper considers a problem in which an agent is hired to manage a capital investment and subsequently receives private information regarding the productivity of the capital investment. The capital manager must decide whether to invest capital supplied by the firm (the principal), or to divert these investment funds to perquisite consumption. If the manager decides to invest, the manager must then select the level of operating efficiency (productivity) of the capital investment, this latter choice being unobservable and constrained by the (maximal) productivity of the investment. In this setting we demonstrate that the optimal employment contract, from the perspective of the firm hiring the manager, is the contract whichminimizes the dependence of the manager's compensation on firm output. This contract pays the manager a fixed wage whenever output from the investment exceeds the wage and provides the manager with all of the projects rents whenever output falls below this level. Thus, we provide a setting in which fixed wage contracts are the optimal incentive contract even when agents are risk neutral and contracts can be costlessly written on future output.We would like to thank the participants in the Princeton Economics and Finance Workshop and the Ohio State University Finance Workshop for their comments on an earlier draft of this paper. The second author gratefully acknowledges the research support of the Georgia State College of Business Administration Research Council.     

Optimal growth and cycles in overlapping generations models

Summary This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.We thank C. Blackorby, J. Blot, P. Cartigny and one anonymous referee for helpful comments and suggestions which generally improved the exposition of the paper. We would also like to thank the participants of the Population and demography session of the European Economic Association 10th Annual Congress (Prague, The Czech Republic, September 1–4, 1995).     

When to fire a CEO: optimal termination in dynamic contracts

Existing models of dynamic contracts impose that it is both optimal and feasible for the contracting parties to bind themselves together forever. This paper introduces optimal termination in dynamic contracts. We modify the standard dynamic agency model to include an external labor market which, upon the dissolution of the contract, allows the firm to return to the labor market to seek a new match. Under this simple closure of the model, two types of terminations emerge. Under one scenario, the agent is fired after a bad output and he becomes too poor to be punished effectively. Under the second scenario, the agent is forced out after a good output and he becomes too expensive to motivate.     

Why it Pays to Conceal: On the Optimal Timing of Acquiring Verifiable Information

Abstract. We consider optimal contracts when a principal has two sources to detect bad projects. The first one is an information technology without agency costs (IT_P), whereas the second one is the expertise of an agent subject to moral hazard, adverse selection and limited liability (IT_A). First, we show that the principal does not necessarily benefit from access to additional information and thereby may prefer to ignore it. Second, we discuss different timings of information release, i.e., a disclosure contract offered to the agent after the principal announced the result of IT_P , and a concealment contract where the agent exerts effort before IT_P is checked. We find that concealment is superior whenever the quality of IT_P is sufficiently low. Then, IT_P is almost worthless under a disclosure contract, while it can still be exploited to reduce the agent's information rent under concealment. If the quality of IT_P improves, disclosure can be superior as it allows to adjust the agent's effort to the updated expected quality of the project. However, even for a highly informative IT_P , concealment can be superior as it mitigates the adverse selection problem.