Implementing high‐powered contracts to motivate intertemporal effort supply

We characterize the optimal contract between a principal and a risk‐neutral, wealth‐constrained agent when an adverse selection problem follows a moral hazard problem. The optimal contract in this setting often is more steeply sloped for the largest output levels than is the optimal contract in either the standard moral hazard setting or the standard adverse selection setting. The large incremental rewards for exceptional performance motivate the agent to deliver substantial effort both before and after he acquires privileged information about the production environment.     

Stairway to heaven or highway to hell: Liquidity,sweat equity,and the uncertain path to ownership

We study a setting in which a principal contracts with an agent to operate a firm over an infinite time horizon when the agent is liquidity constrained and privately observes the sequence of cost realizations. We formulate the principal’s problem as a dynamic program in which the state variable is the agent’s continuation utility, which is naturally interpreted as his equity in the firm. The optimal incentive scheme resembles what is commonly regarded as a sweat equity contract, with all rents back loaded. Payments begin when the agent effectively becomes the owner, and from this point on, all production is efficient. These features are shown to be similar to features common in real‐world work‐to‐own franchising agreements and venture capital contracts.     

Market participation in delegated and intrinsic common‐agency games

We study how competition in nonlinear pricing between two principals (sellers) affects market participation by a privately informed agent (consumer). When participation is restricted to all or nothing (“intrinsic” agency), the agent must choose between both principals' contracts and selecting her outside option. When the agent is afforded the additional possibilities of choosing only one contract (“delegated” agency), competition is more intense. The two games have distinct predictions for participation. Intrinsic agency always induces more distortion in participation relative to the monopoly outcome, and equilibrium allocations are discontinuous for the marginal consumer. Under delegated agency, relative to monopoly, market participation increases (respectively, decreases) when contracting variables are substitutes (respectively, complements) on the intensive margin. Equilibrium allocations are continuous for the marginal consumer and the range of product offerings is identical to both the first‐best and the monopoly outcome.     

Contracting for information under imperfect commitment

We study optimal contracting under imperfect commitment in a model with an uninformed principal and an informed agent. The principal can commit to pay the agent for his advice but retains decision‐making authority. Under an optimal contract, the principal should (i) never induce the agent to fully reveal what he knows—even though this is feasible—and (ii) never pay the agent for imprecise information. We compare optimal contracts under imperfect commitment to those under full commitment as well as to delegation schemes. We find that gains from contracting are greatest when the divergence in the preferences of the principal and the agent is moderate.     

Overcompensation as a Partial Solution to Commitment and Renegotiation Problems: The Case of Ex Post Moral Hazard

In a Costly State Verification world, an agent who has private information regarding the state of the world must report what state occurred to a principal, who can verify the state at a cost. An agent then has what is called ex post moral hazard: he has an incentive to misreport the true state to extract rents from the principal. Assuming the principal cannot commit to an auditing strategy, the optimal contract is such that: (1) the agent's expected marginal utility when there is an accident (high‐ and low‐loss states) is equal to his marginal utility when there is no accident; (2) the lower loss is undercompensated, while the higher loss is overcompensated; and (3) the welfare of the agent is greater under commitment than under no‐commitment. Result 2 is contrary to the results obtained if the principal can commit to an auditing strategy (higher losses underpaid and lower losses overpaid). The reason is that by increasing the difference between the high and the low indemnity payments, the probability of fraud is reduced.     

Optimal Incentive Contracts When Agents Can Save, Borrow, and Default

The standard Principal–Agent (PA) model assumes that the principal can control the agent's consumption profile. In an intertemporal setting, however, Rogerson (1985, Econometrica53, 69–76) shows that given the optimal PA contract, the agent has an unmet precautionary demand for savings. Thus the standard PA model is invalid if the agent has access to credit markets. In this paper we generalize the standard PA model to allow for saving and borrowing by the agent. We show that the impact of such access critically depends upon the treatment of default. If default is not permitted, efficiency is strictly reduced by the introduction of credit markets, and the equilibrium level of borrowing or saving is indeterminate in the model. If default is allowed, however, the optimal contract depends upon the level of bankruptcy protection in the economy, which is described by a minimum level of wage income. We show that there is an optimal intermediate range of bankruptcy protection. Within this range, allowing default increases efficiency in the economy relative to the case of no default. Also, the model predicts specific levels of consumer debt, interest rates, and default rates as functions of the level of bankruptcy protection level. Journal of Economic Literature Classification Numbers: D80, G21, G28, J30.     

Specific knowledge and performance measurement

I examine optimal incentives and performance measurement in a model where an agent has specific knowledge (in the sense of Jensen and Meckling) about the consequences of his actions for the principal. Contracts can be based both on “input” measures related to the agent's actions and an “output” measure related to the principal's payoff. Whereas input‐based pay minimizes income risk, only output‐based pay encourages the agent to use his knowledge efficiently. In general, it is optimal to use both kinds of performance measures. The results help to explain some empirical puzzles and lead to several new predictions.     

Tax incentives for inefficient executive pay and reward for luck

I study the economic consequences of tax deductibility limits on salaries for the design of incentive contracts. The analysis is based on an agency model in which the firm’s cash flow is a function of the agent’s effort and an observable random factor beyond the agent’s control. According to my analysis, limiting the tax deductibility of fixed wages has two consequences. The principal rewards the agent on the basis of the observable random factor and adjusts the amount of performance-based pay in the optimal incentive contract. The new contract can have weaker or stronger work incentives than without the tax. The theoretical findings have implications for empirical compensation research. First, the analysis shows that reward for luck can be the optimal response to recent tax law changes, whereas earlier empirical literature has attributed this phenomenon to managerial entrenchment. Second, I demonstrate that a simple regression analysis that fails to control for separable measures of luck is likely to find an increased pay for performance sensitivity as a response to the introduction of tax deductibility limits on salaries even if the pay for performance sensitivity has actually declined.     

Bank monitoring incentives and optimal ABS

The paper examines a continuous-time delegated monitoring problem between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian “contagion.” Moral hazard induces a foreclosure bias unless the bank is compensated with the right incentive-compatible contract. Fees are paid when the bank’s performance is on target and liquidation arises when the bank’s performance is sufficiently poor. I show that the optimal contract can be implemented with a whole loan sale involving both credit risk retention based on ABS credit default swaps and credit enhancement in the form of a reserve account. The optimal securitization bears out rulemaking recently proposed in the wake of the Dodd-Frank Act on a number of controversial provisions. I argue that further efficiency gains could be reaped by extending the role of the “premium capture” account into a liquidity buffer capturing performance-based compensation as a way of increasing skin in the game over the life of the transaction.     

Options in Compensation: Promises and Pitfalls

We derive the optimal compensation contract in a principal–agent setting in which outcome is used to provide incentives for both effort and risky investments. To motivate investment, optimal compensation entails rewards for high as well as low outcomes, and it is increasing at the mean outcome to motivate effort. If rewarding low outcomes is infeasible, compensation consisting of stocks and options is a near‐efficient means of overcoming the manager's induced aversion to undertaking risky investments, whereas stock compensation is not. However, stock plus option compensation may induce excessively risky investments, and capping pay can be important in curbing such behavior.     

Optimal information transmission in a holdup problem

This article examines the optimal contract in a bilateral trade model with unobservable relationship‐specific investment and renegotiation. In such a setting, a contract plays an additional role that it does not have in the standard holdup model, namely that of transmitting information between the parties. The article shows that a partial‐disclosure contract may be optimal and describes the optimal contract. If the investment is cooperative and the information between the trading parties is asymmetric, the optimal contract generally cannot result in the first best, but dispensing with either of these assumptions makes the first‐best achievable.     

Demand for the truth in principal–agent relationships

Consider the following puzzle: If earnings management is harmful to shareholders, why don’t they design contracts that induce managers to reveal the truth? To answer this question, we model the shareholders–manager relationship as a principal–agent game in which the agent (the manager) alone observes the economic outcome. We show that the limited liability (LL) of the agent, defined as the agent’s feasible minimum payment, might explain the demand for earnings management by the principal. Specifically, when the LL level is high (low), a contract that induces earnings management may be less (more) costly than a truth-revealing contract. This finding offers a new explanation of the demand for earnings management.     

Mediated audits

I study optimal contracting where the principal can verify the agent's private information via auditing but cannot contractually commit to audit frequency. Optimal contracting requires sophisticated communication: the agent reports his information to a mediator, who randomly selects a contract. Mediation allows for fine‐tuning the information flow, because the principal observes the selected contract but not the agent's report. Simply offering a menu of contracts is, in general, not optimal. I characterize optimal mediated contracts, determine conditions for when auditing is profitable, and analyze contractual distortions. Mediated contracts can be implemented via negotiated rulemaking procedures, and potentially via sequential communication.     

Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model

ABSTRACT

We discuss an optimal excess-of-loss reinsurance contract in a continuous-time principal-agent framework where the surplus of the insurer (agent/he) is described by a classical Cramér-Lundberg (C-L) model. In addition to reinsurance, the insurer and the reinsurer (principal/she) are both allowed to invest their surpluses into a financial market containing one risk-free asset (e.g. a short-rate account) and one risky asset (e.g. a market index). In this paper, the insurer and the reinsurer are ambiguity averse and have specific modeling risk aversion preferences for the insurance claims (this relates to the jump term in the stochastic models) and the financial market's risk (this encompasses the models' diffusion term). The reinsurer designs a reinsurance contract that maximizes the exponential utility of her terminal wealth under a worst-case scenario which depends on the retention level of the insurer. By employing the dynamic programming approach, we derive the optimal robust reinsurance contract, and the value functions for the reinsurer and the insurer under this contract. In order to provide a more explicit reinsurance contract and to facilitate our quantitative analysis, we discuss the case when the claims follow an exponential distribution; it is then possible to show explicitly the impact of ambiguity aversion on the optimal reinsurance.     

Investing in a relationship

A principal can make an investment anticipating a repeated relationship with an agent, but the agent may appropriate the returns through ex post bargaining. I study how this holdup problem and efficiency depend on the contracting environment. When investment returns are observable, informal contracts ex post can be more efficient than formal contracts, as they induce higher investment ex ante: the principal invests not only to generate direct returns, but also to improve relational incentives. Unobservability of returns increases the principal's ability to appropriate the returns but reduces her ability to improve incentives. The optimal information structure depends on bargaining power.     

Delegation and incentives

This article analyzes the relation between authority and incentives. It extends the standard principal‐agent model by a project selection stage in which the principal can either delegate the choice of project to the agent or keep the authority. The agent's subsequent choice of effort depends both on monetary incentives and the selected project. We find that the consideration of effort incentives makes the principal less likely to delegate the authority over projects to the agent. In fact, if the agent is protected by limited liability, delegation is never optimal.     

The effects of costly exploration on optimal investment timing

This paper investigates a principal–agent model in which an owner (principal) optimizes a contract with a manager (agent) who has been delegated to undertake an investment project. In the model, we explore the effects of costly exploration by which the manager learns the real value of development cost. We show that high exploration cost can lead to a pooling policy not contingent on project type. Further, and more notably, we show that, in the presence of asymmetric information, higher exploration cost leads to wealth transfer from owner to manager and can ultimately improve social welfare.     

Information and delay in an agency model

This article studies how delay in contracting depends on an exogenous signal. The agent whose cost is his private information may produce in the first period or be delayed until the second period. A signal about the cost of the agent is available between the two periods. The quality of the good can vary; in the benchmark case of no signal, the principal offers the standard Baron‐Myerson contract and there is no delay. Delay is determined by the considerations at the margin and may increase or decrease with a better signal. The value of information can be negative, as a better signal may aggravate the principal's commitment problem. A better signal may also increase the agent's rent and decrease social welfare.     

Dynamic programming approach to principal–agent problems

We consider a general formulation of the principal–agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following. We first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. As a consequence, we have reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be addressed by standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically on the recent extensions to the second order case.     

Contracting with private rewards

The canonical moral hazard model is extended to allow the agent to face endogenous and noncontractible uncertainty. The agent works for the principal and simultaneously pursues outside rewards. The contract offered by the principal thus manipulates the agent's work–life balance. The participation constraint is slack whenever it is optimal to distort the agent's work–life balance away from life compared to a symmetric-information benchmark. Then, the agent's expected utility is high and he faces flatter incentives. Such contracts may be optimal when the two activities are strong substitutes in the agent's cost function or when reservation utility is low.