Dynamic Incentive Contracts in Multiple Penalty Systems with No-commitment to Tenure-track Auditing

This paper generalizes Khalil's (1997) static model to a multiperiod one in the tenure-track auditing. Three penalty systems considered are full-transfer-dependent, partial-transfer-dependent, and transfer-independent ones. It is found that the equilibrium under the tenure-track auditing is also an equilibrium under the periodic auditing. The conditions under which the principal prefers the periodic auditing, or is indifferent between the two auditing schemes are derived. Incentive contracts may vary in different penalty systems. For instance, the equilibrium with principal’s sure ex post auditing exists only under the partial-transfer-dependent and transfer-independent penalty systems. And the equilibrium with the first-best contract as the first-period optimum appears merely under the transfer-independent penalty system.     

Portfolio delegation under short-selling constraints

Summary. In this paper we study delegated portfolio management when the manager’s ability to short-sell is restricted. Contrary to previous results, we show that under moral hazard, linear performance-adjusted contracts do provide portfolio managers with incentives to gather information. We find that the risk-averse manager’s effort is an increasing function of her share in the portfolio’s return. This result affects the risk-averse investor’s choice of contracts. Unlike previous results, the purely risk-sharing contract is now shown to be suboptimal. Using numerical methods we show that under the optimal linear contract, the manager’s share in the portfolio return is higher than what it is under a purely risk sharing contract. Additionally, this deviation is shown to be: (i) increasing in the manager’s risk aversion and (ii) larger for tighter short-selling restrictions. As the constraint is relaxed the deviation converges to zero.Received: 25 July 2002, Revised: 12 December 2004, JEL Classification Numbers: D81, D82, J33.Juan-Pedro Gómez: Correspondence toAn earlier version of the paper was circulated under the title “Providing Managerial Incentives: Do Benchmarks Matter?” We are grateful to an anonymous referee whose comments helped to improve the paper. We also thank comments by Viral Acharya, Alexei Goriaev, Ernst Maug, Kristian Rydqvist, Neil Stoughton, Rangarajan Sundaram, Fernando Zapatero and seminar participants at the 1999 SED meetings in Sardinia, the 1999 Workshop in Mutual Fund Performance at EIASM, Brussels, the 2000 EFA meetings in London, the Bank of Norway, the Stockholm Schools of Economics, the Norwegian School of Management and the 2001 WFA meetings in Tucson. Sharma gratefully acknowledges financial support from the Asociacion Mexicana de Cultura.     

Corporate insurance with optimal financial contracting

Summary. This paper attemps to rationalize the use of insurance covenants in financial contracts, and shows how external financing generates a demand for insurance by risk-neutral entrepreneurs. In our model, the entrepreneur needs external financing for a risky project that can be affected by an accident during its realization. Accident losses and final returns are private information to the firm, but they can be evaluated by two costly auditing technologies. We derive the optimal financial contract: it is a bundle of a standard debt contract and an insurance contract with franchise, trading off bankruptcy costs vs auditing costs. We then analyze how this optimal contract can be achieved by decentralized trading on competitive markets when insurance and credit activities are exogenously separated. With additive risks, the insurance contract involves full coverage above a straight deductible. We interpret this result by showing how our results imply induced risk aversion for risk-neutral firms. Received: December 14, 1998; revised version: August 11, 1999     

The Role of Bargaining Initiative Under no Commitment to Audit

This paper addresses the issue of the optimal contract design under costly state verification and no commitment to auditing when the contract offer comes from the uninformed party. Contrary to similar frameworks and to cases where the informed party retains the bargaining power, we find that the optimal contract is characterised neither by truth telling nor by mixed strategy equilibria. Depending on endogenous revenues and observation cost, a pooling equilibrium with either deterministic or random auditing occurs.     

The optimality of nominal contracts

Summary. This paper presents a model in which agents choose to use money as a medium of exchange, a means of payment, and a unit of account. The paper defines conditions under which nominal contracts, promising future payment of a fixed number of units of fiat money, prove to be the optimal contract form in the presence of either relative or aggregate price risk. When relative prices are random, nominal contracts are optimal if individuals have ex ante similar preferences over future consumption. When the aggregate price level is random, whether from shocks to the money supply or aggregate output, nominal contracts (perhaps coupled with equity contracts) lead to optimal risk-sharing if individuals have the same degree of relative risk aversion. Finally, nominal contracts may be optimal if the repayment of contracts is subject to a binding cash-in-advance constraint. In this case, a contingent contract increases the risk of holding excessive cash balances. Received: March 29, 1996; revised version: February 25, 1997     

How to allocate forward contracts: The case of electricity markets

Several regulatory authorities worldwide have imposed forward contract commitments on electricity producers as a way to mitigate their market power. In this paper we analyze the impact of such commitments on equilibrium outcomes in a model that reflects important institutional and structural features of electricity markets. We show that, when firms are asymmetric, the distribution of contracts among firms matters. In the case of a single dominant firm, the regulator can be confident that allocating contracts to that firm will be pro-competitive. However, when asymmetries are less extreme, certain contract allocations might yield anti-competitive outcomes by eliminating more competitive equilibria. Our analysis thus suggests that forward contracts should be allocated so as to (virtually) reduce asymmetries across firms.     

Optimal information acquisition and monetary policy

I study optimal monetary policy with an expectational AS curve and private agents who optimally choose their amount of information pertinent to predicting policy. Shocks with time-varying variance (ARCH) induce interesting information acquisition (IA) dynamics; optimal IA affects optimal policy and vice versa. Under discretion, IA dynamics cause time-varying effectiveness of policy because of the expectational AS curve; policy may be rendered completely ineffective. In policy game equilibrium, a fall in the shock’s variance typically induces less IA and raises welfare. In one exceptional case the opposite occurs, a result which does not require implausible unstable equilibria. An agent becoming informed increases the endogenous component of economic volatility; IA therefore has a negative externality. Under commitment policy’s effectiveness is again time-varying, but policy is never completely ineffective: commitment enables the central bank to credibly limit policy’s volatility; this limits private agents’ incentive to become informed, so limits expectation-induced policy neutrality.     

Bounding the benefits of stochastic auditing: The case of risk-neutral agents

Summary. In the context of a costly-state-verification model with a risk-neutral agent having limited liability, it has been postulated that allowing stochastic auditing reduces the asymmetric information problem to a trivial one: i.e., the first best can be approached arbitrarily closely with feasible contracts. This paper proves the postulate to be false: the surplus from feasible contracts is bounded strictly below the first-best surplus level. The bound is straightforward to compute in examples. The paper thus removes a justification for the restriction to deterministic auditing commonly made in the literature. Received: July 18, 1997; revised version: February 23, 1998     

Exclusion via Non‐Exclusive Contracts

We establish that non‐linear vertical contracts can allow an incumbent to exclude an upstream rival in a setting that does not rely on the exclusivity of the incumbent's contracts with downstream firms or any limits on distribution channels available to the incumbent or rival. The optimal contract we describe is a three‐part quantity discounting contract that involves the payment of an allowance to a downstream distributor and a marginal wholesale price below the incumbent's marginal cost for sufficiently large quantities. The optimal contract is robust to allowing parties to renegotiate contracts in case of entry.     

Limited observability as a constraint in contract design

Limited observability is the assumption that economic agents can only observe a finite amount of information. Given this constraint, contracts among agents are necessarily finite and incomplete in comparison to the ideal complete contract that we model as infinite in detail. We consider the extent that finite contracts can approximate a complete contract. The objectives of the paper are: (i) to identify properties of agents’ preferences that determine whether or not finiteness of contracts causes significant inefficiency; (ii) to evaluate the performance of finite contracts against the ideal optimal contract in a bilateral bargaining model.     

Share contracts and macroeconomic externalities

Weitzman's analysis of the share economy contrasts fixed-wage and fixed-share contracts; this paper notes that neither is an optimal labor contract, rendering the comparison suspect. Given this comparison, though, share contracts may be superior to wage contracts in an economy characterized by a “macroeconomic externality,” whereby firm-level employment decisions affect the demand for other firms' goods.     

A Simple Model of Contract Enforcement Institutions

We demonstrate that in highly productive economies contract enforcement institutions are endogenously established, and partnership contracts correct inefficient land allocation. In less productive economies, however, such institutions are not established, and partnership contracts are not formed. In economies with intermediate productivity levels, multiple Nash equilibria exist; that is, contract enforcement institutions are established in the high Nash equilibrium whereas they are not formed in the low Nash equilibrium. In this case, institutional quality can be diverse across economies. We also prove that improvement in institutional quality reduces within‐country inequality. All these outcomes are consistent with cross‐country observations.     

Optimal incentive contracts with multiple agents

A setting in which a single principal contracts with two agents who possess perfect private information about their own productivity is considered. With correlated productivities, each agent's private information also provides a signal about the other agent's productivity. In contrast to the setting in which there is only one agent, it is shown that such private information may be of no value to the agents. It is only if the agents are risk-averse that their private information may allow them to command rents. Moreover, when the agents are constrained only to reveal their private information truthfully as a Nash equilibrium, the Pareto optimal incentive scheme may induce the agents to adopt strategies other than truth-telling. This leads to the consideration of truth-telling equilibria that are not Pareto dominated in the subgame played by the agents. Among all such equilibria, the one preferred by the principal restricts one agent to tell the truth as a dominant strategy and the other as a Nash response to truth.     

Time of the essence

In most industries, ranging from information systems development to construction, an overwhelming proportion of projects are delayed beyond estimated completion time. This fact constitutes somewhat of a puzzle for existing theory. The present paper studies project delays and optimal contracts under moral hazard in a setting with time to build. Within this setup, project delays are found to be most likely to happen at early stages of development and intimately connected to the degree of commitment of the procurer and the class of contracts that can be enforced. The first-best, optimal spot contracting and optimal long-term contract scenarios are analyzed, as well as commonly encountered additional constraints on the long-term contract.     

Limited attention and the optimal incompleteness of contracts

A decision-maker's limited attention is allocated between writingnew contracts and directing current contracts. More time spentwriting a new contract makes the contract more complete. A morecomplete contract performs better and generates higher returns.The optimal allocation of attention implies two types of contracts,relational and market. A relational contract, which is directedperiodically, is optimally less complete than a market contract,which is not directed. The completeness of relational contractsdecreases with the ability to direct contracts, since changingcircumstances can be dealt with later. In addition, the completenessof relational contracts increases with the ability to writenew contracts, since more complete relational contracts aredirected less frequently and leave more time for writing newcontracts. The optimal allocation of attention to relationalcontracts is socially efficient even though it does not maximizethe discounted expected returns of the firm.     

Layoffs,wages and unemployment insurance

The influence of unemployment insurance on wage and layoff behavior is analyzed in the context of optimal labor contracts. Responses of contract terms to changes in economic parameters are shown to depend in general on the nature of the initial contract, the degree of workers' risk aversion, and the resolution of bargaining conflict. Layoffs are not necessarily reduced by an increase in experience rating or a reduction in the UI benefit. Product demand fluctuations tend to induce procyclical employment fluctuations but not wage fluctuation. An implication of optimal contracts with private insurance suggests a reason for government intervention in UI provision.     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

Measurement distortion and missing contingencies in optimal contracts

Summary Theory suggests that optimal contracts should include many contingencies to achieve optimal risk sharing. However, in practice, few contracts are as complex as theory suggests. This paper develops a model which is consistent with this observation. The lack of risk sharing results from the interplay of two factors. First, contingencies must be based on information produced by measurement systems, which may be manipulable. Second, when two parties to a contract meet, they often have incomplete information. The type of contract offered may reveal information about the party who proposes it. Different types of agents have different preferences over contingent contracts, because they have different abilities to manipulate the measurement system. These differences in preferences allow the parties to signal their types through the contracts they offer. Noncontingent contracts may be chosen in equilibrium because they are the only contracts which do not give any type an incentive to distort the measurement system and, hence, do not reveal information about the party proposing the contract.We have benefited from conversations with Oliver Hart, Rick Lambert, Michael Riordan and Jean Tirole and the comments of Michel Habib, Nick Yannelis and two anonymous referees. Financial support from the National Science Foundation under grants SES-8920048 and SES-8720589 is gratefully acknowledged.     

Double Moral Hazard,Monitoring, and the Nature of Contracts

generalized double-sided moral-hazard model, with risk-averse parties who mutually monitor each other (to get a reasonable idea of outcome/effort). The model considers trade-off between monitoring costs and moral hazard costs, which are endogenously determined by the extent of monitoring. Using this model, we formally prove a generalized version of Coase's conjecture – that the optimal contract minimizes the agency and risk costs. We then show how varying assumptions about the feasibility or cost of monitoring of the outcome or the worker's effort lead to different contracts being optimal. The analysis is then used to explain the nature of contracts observed in practice under many different situations. We will give an explanation as to why industrial workers typically work under wage contracts, while share contracts are common in agriculture and will explain why profit sharing is more common for senior managers than for the production workers. Received September 19, 2000; revised version received October 30, 1997     

A note on long-term contracts

The purpose of this paper is three-fold: (i) to interpret Townsend's (1982) long-term contract model as a labor contract model where a value of job matching for a worker is a private information, (ii) to contrast Townsend's long-term contract model with Holmstrom's (1983) long-term contract model in a common framework, and (iii) to explore the effect of workers' mobility on the contract configuration of the two models.Both Holmstrom and Townsend construct models in which a single-period contract is not viable, but a long-term contract is. However, reasons for this characteristic in the two models are quite different. This paper proposes a simple framework of labor contracts with illustrates the essential difference of the two models, and the role of mobility costs. Mobility costs in the two types of long-term contracts are shown to be beneficial for both workers and the firm. Results of comparative statics show how contract configurations in two models are influenced by changes in mobility costs.