Persistent Private Information

This paper studies the design of optimal contracts in dynamic environments where agents have private information that is persistent. In particular, I focus on a continuous‐time version of a benchmark insurance problem where a risk‐averse agent would like to borrow from a risk‐neutral lender to stabilize his utility. The agent privately observes a persistent state variable, typically either income or a taste shock, and he makes reports to the principal. I give verifiable sufficient conditions showing that incentive‐compatible contracts can be written recursively, conditioning on the report and two additional state variables: the agent's promised utility and promised marginal utility of the private state. I then study two examples where the optimal contracts can be solved in closed form, showing how persistence alters the nature of the contract. Unlike the previous discrete‐time models with independent and identically distributed (i.i.d.) private information, the agent's consumption under the contract may grow over time. Furthermore, in my setting the efficiency losses due to private information increase with the persistence of the private information, and the distortions vanish as I approximate an i.i.d. environment.     

Stable and Coordinating Contracts for a Supply Chain with Multiple Risk‐Averse Suppliers

We analyze a decentralized supply chain with a single risk‐averse retailer and multiple risk‐averse suppliers under a Conditional Value at Risk objective. We define coordinating contracts and show that the supply chain is coordinated only when the least risk‐averse agent bears the entire risk and the lowest‐cost supplier handles all production. However, due to competition, not all coordinating contracts are stable. Thus, we introduce the notion of contract core, which reflects the agents' “bargaining power” and restricts the set of coordinating contracts to a subset which is “credible.” We also study the concept of contract equilibrium, which helps to characterize contracts that are immune to opportunistic renegotiation. We show that, the concept of contract core imposes conditions on the share of profit among different agents, while the concept of contract equilibrium provide conditions on how the payment changes with the order quantity.     

Implementation With Contingent Contracts

We study dominant strategy incentive compatibility in a mechanism design setting with contingent contracts where the payoff of each agent is observed by the principal and can be contracted upon. Our main focus is on the class of linear contracts (one of the most commonly used contingent contracts) which consist of a transfer and a flat rate of profit sharing. We characterize outcomes implementable by linear contracts and provide a foundation for them by showing that, in finite type spaces, every social choice function that can be implemented using a more general nonlinear contingent contract can also be implemented using a linear contract. We then qualitatively describe the set of implementable outcomes. We show that a general class of social welfare criteria can be implemented. This class contains social choice functions (such as the Rawlsian) which cannot be implemented using (uncontingent) transfers. Under additional conditions, we show that only social choice functions in this class are implementable.     

Channel Coordination for a Supply Chain with a Risk‐Neutral Manufacturer and a Loss‐Averse Retailer*

This articles considers a decentralized supply chain in which a single manufacturer is selling a perishable product to a single retailer facing uncertain demand. It differs from traditional supply chain contract models in two ways. First, while traditional supply chain models are based on risk neutrality, this article takes the viewpoint of behavioral principal–agency theory and assumes the manufacturer is risk neutral and the retailer is loss averse. Second, while gain/loss (GL) sharing is common in practice, there is a lack of analysis of GL‐sharing contracts in the supply chain contract literature. This article investigates the role of a GL‐sharing provision for mitigating the loss‐aversion effect, which drives down the retailer order quantity and total supply chain profit. We analyze contracts that include GL‐sharing‐and‐buyback (GLB) credit provisions as well as the special cases of GL contracts and buyback contracts. Our analytical and numerical results lend insight into how a manufacturer can design a contract to improve total supply chain, manufacturer, and retailer performance. In particular, we show that there exists a special class of distribution‐free GLB contracts that can coordinate the supply chain and arbitrarily allocate the expected supply chain profit between the manufacturer and retailer; in contrast with other contracts, the parameter values for contracts in this class do not depend on the probability distribution of market demand. This feature is meaningful in practice because (i) the probability distribution of demand faced by a retailer is typically unknown by the manufacturer and (ii) a manufacturer can offer the same contract to multiple noncompeting retailers that differ by demand distribution and still coordinate the supply chains.     

Crowding Effects and Work Ethics

Abstract. This paper analyses optimal contracts in a principal–agent model where the agent is intrinsically motivated, and there is an endogenous relationship between the structure of incentive payments and intrinsic motivation (crowding effects). The analysis shows that crowding effects have implications for the optimal contract, and that, under some conditions, the principal can make better achievements without implementing any economic incentives. Furthermore, it is shown that when high‐powered incentives reduce intrinsic motivation (crowding‐out), the first‐best solution in a principal–agent framework is unattainable.     

Coordination of Supply Chains with Risk‐Averse Agents

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.     

Inventory‐Related Compensation in Decentralized Organizations

We consider a principal agent problem in a decentralized organization. The agent holds private precontracting information with respect to an uncertain demand in a single period setting. Being head of a profit center, his only task is to determine the optimal order quantity. We show that using a profit share as the only performance measure to incentivize the agent creates agency costs. In fact, offering a menu of profit‐sharing contracts to the agent to pick from, requires rent payments to motivate the agent to always choose the desired contract. This result still holds if a fixed payment is added. Using an inventory‐related component as a third measure, however, allows one to solve the agency problem and to achieve first best outcomes. Precisely, each contract needs to specify a bonus or a penalty conditioned on the inventory level at the end of the selling season combined with a profit share and a fixed pay. The paper not only demonstrates that first best can be achieved in the described setting, it also provides a theoretical explanation for the observed practice of using inventory‐related compensation elements, such as service‐level agreements, in organizations.     

GETTING IT DONE: DYNAMIC INCENTIVES TO COMPLETE A PROJECT

A principal wants an agent to complete a project. The agent undertakes unobservable effort, which affects in each period the probability that the project is completed. We characterize the contracts that the principal sets, with and without commitment. With full commitment, the contract involves the agent's value and wage declining over time, in order to give the agent incentives to exert effort. The best sequentially rational equilibrium for the principal also involves the agent's wage declining over time, while the worst sequentially rational equilibrium for the principal has a constant wage (and is in fact the unique stationary equilibrium). The best (weakly) renegotiation‐proof equilibrium for the principal is achieved by a constant wage that maximizes the principal's payoff, conditional on wages being constant. We compare these solutions to the efficient outcome.     

JEEA‐FBBVA Lecture 2012: USE AND ABUSE OF AUTHORITY: A BEHAVIORAL FOUNDATION OF THE EMPLOYMENT RELATION

Employment contracts give a principal the authority to decide flexibly which task his agent should execute. However, there is a tradeoff, first pointed out by Simon (1951, Econometrica, 19, 293–302), between flexibility and employer moral hazard. An employment contract allows the principal to adjust the task quickly to the realization of the state of the world, but he may also abuse this flexibility to exploit the agent. We capture this tradeoff in an experimental design and show that principals exhibit a strong preference for the employment contract. However, selfish principals exploit agents in one‐shot interactions, inducing the latter to resist entering into employment contracts. This resistance to employment contracts vanishes if fairness preferences in combination with reputation opportunities keep principals from abusing their power, leading to the widespread, endogenous formation of efficient long‐run employment relations. Our results inform the theory of the firm by showing how behavioral forces shape an important transaction cost of integration—the abuse of authority—and by providing an empirical basis for assessing differences between the Marxian and the Coasian view of the firm, as well as Alchian and Demsetz's (1972, American Economic Review, 62, 777–795) critique of the Coasian approach.     

Existence of Optimal Mechanisms in Principal‐Agent Problems

We provide general conditions under which principal‐agent problems with either one or multiple agents admit mechanisms that are optimal for the principal. Our results cover as special cases pure moral hazard and pure adverse selection. We allow multidimensional types, actions, and signals, as well as both financial and non‐financial rewards. Our results extend to situations in which there are ex ante or interim restrictions on the mechanism, and allow the principal to have decisions in addition to choosing the agent's contract. Beyond measurability, we require no a priori restrictions on the space of mechanisms. It is not unusual for randomization to be necessary for optimality and so it (should be and) is permitted. Randomization also plays an essential role in our proof. We also provide conditions under which some forms of randomization are unnecessary.     

It’s Not What You Pay it’s the Way that You Pay it and that’s What Gets Results: Jockeys’ Pay and Performance

Management scholars and economists have recently set out the requirements of a system to elicit good performance when it is necessary to align the interests of the principal and agent. We analyse pay and performance in an occupation — jockeys — replete with moral hazard possibilities. We are able to do this because, most unusually, a measure of pure individual performance exists for an unbalanced panel of some 50 individuals for 8 years. Three hypotheses are tested. First, in line with classic agency theory, we expect monitoring mechanisms and incentive contracts to be used to align the interests of principals and agents. Second, pay and performance should be positively associated, subject to the first hypothesis being confirmed. Third, a limited number of jockeys were paid via an alternative mechanism involving very large non-contingent retainer fees. This serves as our counterfactual payment system. In line with agency theory we expect worse performance under such a system than under an incentive contract. The three hypotheses are confirmed: incentive contracts generate superior performance to non-contingent payment systems. Our evidence suggests that ‘it’s not what you pay it’s the way that you pay it … and that’s what gets results’. It is maddening that society confers its blessings on traditional academic pursuits but views the study of horseracing as utter frivolity (Beyer, 1983).     

Impatience versus Incentives

This paper studies the dynamics of long‐term contracts in repeated principal–agent relationships with an impatient agent. Despite the absence of exogenous uncertainty, Pareto‐optimal dynamic contracts generically oscillate between favoring the principal and favoring the agent.     

Acquisition of Telecommunications Bandwidth Under Economies of Scale in Size and Duration of Contracts*

Significant advances in information technology have brought about increased demand for bandwidth. Buyers of bandwidth often encounter bandwidth prices that are decreasing over time. Additionally, bandwidth prices at any point in time are decreasing in total bandwidth purchased and length of contracts. Therefore, buyers face complex decisions in terms of the number of contracts to buy, their bandwidth, and their lengths. In this article, we formulate models for the acquisition of bandwidth from a buyer's perspective. We begin with a model that allows varying contract durations under deterministic demand and without allowing shortages or overlapping contracts. We then formulate a simpler model, which restricts contract lengths over the planning horizon to be equal. We also solve the problem under probabilistic demand and allowing for shortages, which are satisfied by buying additional bandwidth at a premium. We perform numerical sensitivity analysis to compare the results of the models and illustrate the results with numerical examples. The numerical analyses illustrate that using relatively simple equal‐length contracts produces approximately the same results as the more complicated unequal‐length contract strategy.     

The Impact of Contracts and Competition on Upstream Innovation in a Supply Chain

We consider a supply chain with an upstream supplier who invests in innovation and a downstream manufacturer who sells to consumers. We study the impact of supply chain contracts with endogenous upstream innovation, focusing on three different contract scenarios: (i) a wholesale price contract, (ii) a quality‐dependent wholesale price contract, and (iii) a revenue‐sharing contract. We confirm that the revenue‐sharing contract can coordinate supply chain decisions including the innovation investment, whereas the other two contracts may result in underinvestment in innovation. However, the downstream manufacturer does not always prefer the revenue‐sharing contract; the manufacturer's profit can be higher with a quality‐dependent wholesale price contract than with a revenue‐sharing contract, specifically when the upstream supplier's innovation cost is low. We then extend our model to incorporate upstream competition between suppliers. By inviting upstream competition, with the wholesale price contract, the manufacturer can increase his profit substantially. Furthermore, under upstream competition, the revenue‐sharing contract coordinates the supply chain, and results in an optimal contract form for the manufacturer when suppliers are symmetric. We also analyze the case of complementary components suppliers, and show that most of our results are robust.     

COLLATERAL CONSTRAINTS IN A MONETARY ECONOMY

This paper reviews the role of collateral constraints in transforming small monetary shocks into large persistent output fluctuations. We do this by introducing money in the heterogeneous‐agent real economy of Kiyotaki and Moore (1997). Money enters in a cash‐in‐advance constraint and money supply is managed via open‐market operations. We find that a monetary shock generates persistent movements in aggregate output, the amplitude of which depends upon whether or not debt contracts are indexed. If only nominal contracts are traded, money shocks can trigger large output fluctuations. In this case a money expansion triggers a boom, whereas money contractions generate recessions. In contrast, if contracts are indexed then amplification is not only smaller; it can also generate the reverse results. When the possibility of default and renegotiation is considered, the model can generate asymmetric business cycles with recessions milder than booms. Finally, monetary shocks generate a highly persistent dampening cycle rather than a smoothly declining deviation. (JEL: E32, E43, E44, E52)     

EQUILIBRIUM INCENTIVE CONTRACTS AND EFFICIENCY WAGES

We analyze the optimal (efficiency) wage contract when output is contractible but firms neither observe the workers' effort nor their match‐specific productivity. Firms offer wage contracts that optimally trade off effort and wage costs. As a result, employed workers enjoy rents, which in turn creates unemployment. Nonetheless, the incentive power of the equilibrium wage contract is constrained efficient in the absence of taxes and unemployment benefits. We also show that more high‐powered incentive contracts tend to be associated with higher equilibrium unemployment rates. (JEL: E24, J30, J41)     

Agency Models With Frequent Actions

The paper analyzes dynamic principal–agent models with short period lengths. The two main contributions are: (i) an analytic characterization of the values of optimal contracts in the limit as the period length goes to 0, and (ii) the construction of relatively simple (almost) optimal contracts for fixed period lengths. Our setting is flexible and includes the pure hidden action or pure hidden information models as special cases. We show how such details of the underlying information structure affect the optimal provision of incentives and the value of the contracts. The dependence is very tractable and we obtain sharp comparative statics results. The results are derived with a novel method that uses a quadratic approximation of the Pareto boundary of the equilibrium value set.     

Channel Coordination with a Risk‐Neutral Supplier and a Downside‐Risk‐Averse Retailer

We investigate how a supply chain involving a risk‐neutral supplier and a downside‐risk‐averse retailer can be coordinated with a supply contract. We show that the standard buy‐back or revenue‐sharing contracts may not coordinate such a channel. Using a definition of coordination of supply chains proposed earlier by the authors, we design a risk‐sharing contract that offers the desired downside protection to the retailer, provides respective reservation profits to the agents, and accomplishes channel coordination.     

Motivating Retail Marketing Effort: Optimal Contract Design

We study a distribution channel where a manufacturer relies on a sales agent for selling the product, and for investing in the most appropriate marketing effort. The agent's effort is hard to monitor. In addition, the cost of effort is the agent's private information. These impose challenges to the manufacturer in its endeavor to influence the agent's marketing effort provisions and to allocate profit between the two parties. We propose two contract forms. The franchise fee contract is a two‐part price schedule specifying a variable wholesale price and a fixed franchise fee. The retail price maintenance contract links the allowed retail price that the agent charges customers with total payment to the manufacturer and sales level. Under information asymmetry, for implementing either contract form, the manufacturer needs to offer a menu of contracts, hoping to invoke the “revelation principle” when the agent picks a certain contract from that menu. We show that the two contract forms perform differently, and each party's preference toward a particular contract form is linked with the total reservation profit level and/or the sales agent's cost type. We provide managerial guidelines for the manufacturer in selecting a better contract form under different conditions.     

风险控制能力差异下的薪酬契约研究

道德风险和逆向选择问题是委托代理理论的研究重点，也是企业薪酬机制设计的核心。本文在道德风险和逆向选择同时存在的框架下，创新性地将利润风控能力作为能力差异的体现引入异质经理人，求解出单一契约和两种契约情况下薪酬契约的显式最优解，并对结果进行了数值模拟验证。本文与单一契约相比，两种契约情况下股东的期望收益较高，对低能力经理的激励降低，对高能力经理的激励上升，但高能力经理的效用由于受到契约的扭曲反而会下降。股东还可针对高能力经理设计单一契约，但当低能力经理所占的比例足够高时，设计两种契约将成为股东的最优选择。本文的研究结果可为私募基金等重视经理风控能力的行业提供薪酬契约设计方面的参考。