Moral Hazard Contracting and Private Credit Markets

This paper studies the impact of credit markets on optimal contracting, when the agent's “interim preference” over upcoming contracts is private information because personal financial decisions affect it via the wealth effect. The main result is a severe loss of incentive provision: equilibrium contracts invariably cause the agent to shirk (i.e., exert minimal effort) if the agent's private financial decision precedes moral hazard contracting. The basic intuition is that committing on another private variable, other than the effort level, exposes the parties to further exploitation of efficient risk‐sharing by relaxing the incentive constraint that was binding ex ante, unless the risk‐sharing was fully efficient to begin with.     

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.     

INFORMATION SHARING IN COMMON AGENCY: WHEN IS TRANSPARENCY GOOD?

When should principals dealing with a common agent share their individual performance measures about the agent's unobservable effort for producing a public good? In a model with two principals who offer linear incentive schemes, we show that information sharing always increases total expected welfare if the principal who is less informed about the agent's effort also cares more about the agent's output. If the less‐informed principal cares somewhat (but not too much) less than the other principal about the agent's output, information sharing reduces total expected welfare. In our model the efficient information regime emerges as an equilibrium outcome. (JEL: D82, D86, M52)     

道德风险下带有Knight不确定的最优动态契约设计

本文从概率统计模型本身的不确定性是本质的、不能消除掉的角度出发, 研究了Knight不确定下连续时间委托-代理问题, 其中主要考虑了代理人的道德风险对契约执行过程以及契约存续情况的影响.首先, 建立了代理人延续价值以及委托人预期利润的动态方程.其次, 运用次线性期望下的随机最优性原理, 以更加准确、深刻的方法去刻画实际委托人和代理人经济行为, 进而得到委托人效用值函数的Hamilton-Jacobi-Bellman (HJB) 方程, 并求得委托人对代理人最优支付以及代理人最优努力水平的表达式.最后, 通过理论解的数值模拟, 分析了Knight不确定对委托人和代理人最优策略以及最优契约的影响.     

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.     

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.     

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.     

A Polynomial Optimization Approach to Principal–Agent Problems

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.     

An Efficient Dynamic Mechanism

This paper constructs an efficient, budget‐balanced, Bayesian incentive‐compatible mechanism for a general dynamic environment with quasilinear payoffs in which agents observe private information and decisions are made over countably many periods. First, under the assumption of “private values” (other agents' private information does not directly affect an agent's payoffs), we construct an efficient, ex post incentive‐compatible mechanism, which is not budget‐balanced. Second, under the assumption of “independent types” (the distribution of each agent's private information is not directly affected by other agents' private information), we show how the budget can be balanced without compromising agents' incentives. Finally, we show that the mechanism can be made self‐enforcing when agents are sufficiently patient and the induced stochastic process over types is an ergodic finite Markov chain.     

Random Choice and Private Information

We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter's perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent's beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well‐calibrated or rational.     

DRIVE AND TALENT

We analyze ways in which heterogeneity in responsiveness to incentives (“drive”) affects employees' incentives and firms' incentive systems in a career concerns model. On the one hand, because more driven agents work harder in response to existing incentives than less driven ones—and therefore pay is increasing in perceived drive—there is a motive to increase effort to signal high drive. These “drive‐signaling incentives” are strongest with intermediate levels of existing incentives. On the other hand, because past output of a more driven agent will seem to the principal to reflect lower ability, there is an incentive to decrease effort to signal low drive. The former effect dominates early in the career, and the latter effect dominates towards the end. To maximize incentives, the principal wants to observe a noisy measure of the agent's effort—such as the number of hours he works—early but not late in his career. (JEL: C70, D82, D23)     

BUILDING REPUTATION FOR CONTRACT RENEWAL: IMPLICATIONS FOR PERFORMANCE DYNAMICS AND CONTRACT DURATION

We study how career concerns affect the dynamics of incentives in a multi‐period contract, when the agent's productivity is a stochastic function of his past productivity and investment. We show that incentives are stronger and performance is higher when the contract approaches its expiry date. Contrary to common wisdom, long‐term contracts may strengthen reputational effects whereas short‐term contracting may be optimal when investment has persistent, long‐term effects.     

Robustness and Separation in Multidimensional Screening

A principal wishes to screen an agent along several dimensions of private information simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principal's problem, in which she knows the marginal distribution of each component of the agent's type, but does not know the joint distribution. Any mechanism is evaluated by its worst‐case expected profit, over all joint distributions consistent with the known marginals. We show that the optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single crossing) on the structure of preferences within each component. The proof technique involves a generalization of the concept of virtual values to arbitrary screening problems. Sample applications include monopoly pricing and a stylized dynamic taxation model.     

Progressive Learning

We study a dynamic principal–agent relationship with adverse selection and limited commitment. We show that when the relationship is subject to productivity shocks, the principal may be able to improve her value over time by progressively learning the agent's private information. She may even achieve her first‐best payoff in the long run. The relationship may also exhibit path dependence, with early shocks determining the principal's long‐run value. These findings contrast sharply with the results of the ratchet effect literature, in which the principal persistently obtains low payoffs, giving up substantial informational rents to the agent.     

Two New Conditions Supporting the First‐Order Approach to Multisignal Principal–Agent Problems

This paper presents simple new multisignal generalizations of the two classic methods used to justify the first‐order approach to moral hazard principal–agent problems, and compares these two approaches with each other. The paper first discusses limitations of previous generalizations. Then a state‐space formulation is used to obtain a new multisignal generalization of the Jewitt (1988) conditions. Next, using the Mirrlees formulation, new multisignal generalizations of the convexity of the distribution function condition (CDFC) approach of Rogerson (1985) and Sinclair‐Desgagné (1994) are obtained. Vector calculus methods are used to derive easy‐to‐check local conditions for our generalization of the CDFC. Finally, we argue that the Jewitt conditions may generalize more flexibly than the CDFC to the multisignal case. This is because, with many signals, the principal can become very well informed about the agent's action and, even in the one‐signal case, the CDFC must fail when the signal becomes very accurate.     

Social Connections and Incentives in the Workplace: Evidence From Personnel Data

We present evidence on the effect of social connections between workers and managers on productivity in the workplace. To evaluate whether the existence of social connections is beneficial to the firm's overall performance, we explore how the effects of social connections vary with the strength of managerial incentives and worker's ability. To do so, we combine panel data on individual worker's productivity from personnel records with a natural field experiment in which we engineered an exogenous change in managerial incentives, from fixed wages to bonuses based on the average productivity of the workers managed. We find that when managers are paid fixed wages, they favor workers to whom they are socially connected irrespective of the worker's ability, but when they are paid performance bonuses, they target their effort toward high ability workers irrespective of whether they are socially connected to them or not. Although social connections increase the performance of connected workers, we find that favoring connected workers is detrimental for the firm's overall performance.     

Large Matching Markets as Two‐Sided Demand Systems

This paper studies two‐sided matching markets with non‐transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed‐point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.     

INFORMATION GATHERING IN ORGANIZATIONS: EQUILIBRIUM,WELFARE, AND OPTIMAL NETWORK STRUCTURE

We model an organization as a game in which all agents share a common decision problem and some level of coordination is necessary between individual actions. Agents have individual private information concerning the task they have to perform, and they share this private information through pairwise channels of communication. We analyze how this communication pattern, modeled by means of a network structure, affects individual behavior and aggregate welfare. In the unique equilibrium of this Bayesian game, each agent's optimal action depends on a properly defined knowledge index that measures how the aggregation of information helps him to infer higher‐order beliefs about other's information after communication. Adding communication channels is not always beneficial for the organization because it can lead to mis‐coordination. We single out the geometry of interagent communication links that the manager could implement in order to improve the organization's performance.     

Multiple Temptations

We use a preference‐over‐menus framework to model a decision maker who is affected by multiple temptations. Our two main axioms on preference—exclusion and inclusion—identify when the agent would want to restrict his choice set and when he would want to expand his choice set. An agent who is tempted would want to restrict his choice set by excluding the normatively worst alternative of that choice set. Simultaneously, he would want to expand his choice set by including a normatively superior alternative. Our representation identifies the agent's normative preference and temptations, and suggests the agent is uncertain which of these temptations will affect him. We provide examples to illustrate how our model improves on those of Gul and Pesendorfer (2001) and Dekel, Lipman, and Rustichini (2009).     

The Law of Demand and Risk Aversion

This note proposes a necessary and sufficient condition on a utility function to guarantee that it generates a demand function satisfying the law of demand. This condition can be interpreted in terms of an agent's attitude towards lotteries in commodity space. As an application, we show that when an agent has an expected utility function, her demand for securities satisfies the law of demand if her coefficient of relative risk aversion does not vary by more than 4.