Limited Liability Constraints Research Articles

Moral hazard and subjective evaluation

This study investigates optimal contracts to solve the moral hazard problem with subjective evaluation in a static environment with multiple agents wherein the principal observes agents' performances privately. Despite the limitations of feasible contracts that the principal can credibly offer, we show the irrelevance theorem that even under subjective evaluation, the principal can be as well off as if agents' performances are objective and verifiable, provided there are at least two risk-neutral agents whose actions satisfy a certain condition on their output distributions. Our irrelevance result encompasses a large class of moral hazard problems, including statistically correlated and technologically interdependent performance signals. We also extend the model to include multidimensional actions, limited liability constraints, and collusion among agents.

Effects of changes in preferences in moral hazard problems

This study examines the effects of changes in an agent's preferences over income and effort on the principal's costs. The incentive cost is fundamentally affected by two factors: the income-effort marginal rate of substitution at the first-best wage, and the degree of absolute risk aversion around it. Thus, a resulting increase in the first-best wage has mixed effects because both factors are altered simultaneously. When the limited liability constraint does not bind and if the utility is concave with respect to the inverse of the marginal utility, a decrease in the marginal rate of substitution, an increase in the degree of risk aversion, and an increase in the first-best wage will raise both incentive and agency costs. However, when the constraint binds and if the marginal rate of substitution at the minimum payment decreases, an increase in the degree of risk aversion and an increase in the first-best wage will raise agency cost. Even if the first-order approach is not valid, the results still hold under the log-submodularity of the marginal cost.

The Risk-Sharing Problem Under Limited Liability Constraints in a Single-Period Model

This work provides analysis of a variant of the Risk-Sharing Principal-Agent problem in a single period setting with additional constant lower and upper bounds on the wage paid to the Agent. The effect of the extra constraints on optimal contract existence is studied and leads to conditions on the underlying utility functions under which an optimum may be attained. Solution characterization is then provided along with the derivation of a Borch rule for Limited Liability. Finally, some applications, including the CARA utility case, are discussed.

Limited liability and non-responsiveness in agency models

This paper analyzes the optimal menu of contracts offered by a risk-neutral principal to a risk-averse agent under moral hazard, adverse selection, and limited liability. We show that a limited liability constraint causes pooling of the most efficient agent types. We also find sufficient conditions under which full pooling is optimal, regardless of the agent's risk aversion or type distribution. Our model suggests that offering a single contract is often optimal in environments with moral hazard, adverse selection, and in which the principal faces a limited liability constraint.

Optimal Risk Regulation of Monopolists with Subjective Risk Assessment

This study aims at characterizing the optimal regulation of risky activities when risk assessment is subjective as a result of ambiguity on the probability of an accident. The attitudes toward ambiguity held by stakeholders form subjective risk perceptions, which substantially affect the optimal intervention. To explore this issue, we construct a moral hazard model with the limited-liability constraint, where ambiguity is described by using the Choquet expected utility with a neo-additive capacity. We first show that the monopolist's optimism reduces the equilibrium preventive effort level and increases the optimal fine level, which is in contrast to the effect of less risk-aversion. We then extend the analysis to the case where the regulator can set a product price as another regulatory instrument. The optimal product price is increasing in the monopolist's degree of optimism. Furthermore, under such an optimal scheme, more optimism held by the monopolist does not necessarily reduce the level of preventive effort.

A Theory of Quota Contract with Risk-Averse Agents

This paper studies incentive contracts between a risk-neutral principal and a risk-averse sales agent in a standard moral-hazard model. We show that a quota-based contract can achieve a first-best outcome when the agent is risk-averse. Furthermore, we show that if the agent is sufficiently risk-averse, this contract also achieve a first-best outcome, even when the agent is protected by limited liability constraint.

Incentive-compatibility, limited liability and costly liquidation in financial contracting

This paper studies a financial contracting problem where a firm privately observes its cash flow and faces a limited liability constraint. The firm's collateral is piecemeal divisible and can only be liquidated continuously by resorting to the service of a costly third party, typically associated with bankruptcy. In this situation, multi-class collateralized debt is optimal, in which the firm makes several debt-like promises with a seniority structure. The decision over continuous and piecemeal liquidation depends on both the cost of introducing the third party and the firm's funding need. Allowing the firm to refinance ex-post through surreptitious liquidation may reduce the firm's ex-ante payoff, consistent with covenants in debt contracts prohibiting the sale of assets.

Relational Incentive Contracts with Hidden Action and Unequal Discounting

We analyze relational incentive contracts with hidden action when the principal and the agent have different discount factors, and identify a new agency cost that exists only when they cannot commit themselves to long-term contracts and the agent is more patient than the principal. We show that there is a new trade-off between rent extraction and incentive provision, and the optimal contract may be non-stationary, even without private information or limited-liability constraints. We characterize the condition under which the trade-off exists, as well as the condition for the optimality of non-stationary contracts.

A note on optimal contracting with public ex post information under limited liability

Riordan and Sappington (J Econ Theory 45:189–199, 1988) show that in an agency relationship in which the agent’s type is correlated with a public ex post signal, the principal may attain first best (full surplus extraction and efficient output levels) if the agent is faced with a lottery such that each type is rewarded for one signal realization and punished equally for all the others. Gary-Bobo and Spiegel (RAND J Econ 37:431–448, 2006) show that there exist locally incentive compatible lotteries such that limited liability constraints are satisfied, only if these constraints are satisfied when that kind of lottery is used. We explore how lotteries should be designed to attain not only local but also global incentive compatibility when the agent is protected by limited liability. The main issue with global incentive compatibility rests with intermediate types being potentially attractive reports to both lower and higher types. A lottery including three levels of profit (rather than only two) is found to be optimal under limited liability, in that it is most likely to be globally incentive compatible, if local incentive constraints are strictly satisfied. Conditions for first-best implementation are identified.

Why Do Firms Hire Using Referrals? Evidence from Bangladeshi Garment Factories

I argue that firms use referrals from current workers to mitigate a moral hazard problem. I develop a model in which referrals relax a limited liability constraint by allowing the firm to punish th...

Dynamic relational contracts under complete information

This paper considers a long-term relationship between two agents who both undertake an action or investment that produces a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. Agents have quasi-linear preferences. Two cases are considered: where agents are risk averse but where limited liability constraints do not bind, and where agents are risk neutral and subject to limited liability constraints. We ask how to structure the investments and division of the surplus over time to avoid expropriation. In the risk-averse case, the dynamics of actions and surplus may or may not be monotonic depending on whether or not a first-best allocation can be sustained. Agents may underinvest but never overinvest. If the first-best allocation is not sustainable, there is a trade-off between risk sharing and surplus maximization; surplus may not be at its constrained maximum even in the long run and the “amnesia” property of pure risk-sharing models fails to hold. In contrast, in the risk-neutral case there may be an initial phase in which one agent overinvests and the other underinvests. Both actions and surplus converge monotonically to a stationary state, where surplus is maximized subject to the self-enforcing constraints.

Delegation and nonmonetary incentives

In many contracting settings, actions costly to one party but with no direct benefits to the other (money-burning) may be part of the explicit or implicit contract. A leading example is bureaucratic procedures in an employer–employee relationship. We study a model of delegation with an informed agent, where the principal may impose money-burning on the agent as a function of the agent's choice of action, and show that money-burning may be part of the optimal contract. This result holds even if action-contingent monetary transfers are possible, as long as transfers from the principal to the agent are bounded from below (as in limited liability or minimal wage requirements). In fact, the optimal contract can involve a combination of both efficient monetary incentives and inefficient nonmonetary incentives through money burning. Our model delivers some results novel to the delegation literature. First, money-burning is more likely if the principal is more “sensitive” to the choice of action than the agent. This is consistent with the perception that there is more bureaucratization in large organizations. Second, money-burning is more likely if the agent's limited liability constraint is tighter relative to his participation constraint. This implies that a higher minimum wage distorts employment contracts towards using socially wasteful nonmonetary incentives, leading to a Pareto inferior outcome as the agent is still held down to his reservation value through increased money burning.

Relational contracts, limited liability, and employment dynamics

This paper studies a relational contracting model in which the agent is protected by a limited liability constraint. The agent's effort is his private information and affects output stochastically. We characterize the optimal relational contract and compare the dynamics of the relationship with that under the optimal long-term contract. Under the optimal relational contract, the relationship is less likely to survive, and the surviving relationship is less efficient. In addition, relationships always converge to a steady state under the optimal long-term contract, but they can cycle among different phases under the optimal relational contract.

Delegation and Nonmonetary Incentives

In many contracting settings, actions costly to one party but with no direct benefits to the other (money-burning) may be part of the explicit or implicit contract. A leading example is bureaucratic procedures in an employer-employee relationship. We study a model of delegation with an informed agent, where the principal may impose money-burning on the agent as a function of the agent’s choice of action, and show that money-burning may be part of the optimal contract. This result holds even if action-contingent monetary transfers are possible, as long as transfers from the principal to the agent are bounded from below (as in limited liability or minimal wage requirements). In fact, the optimal contract can involve a combination of both efficient monetary incentives and inefficient nonmonetary incentives through money burning. Our model delivers some results novel to the delegation literature. First, money-burning is more likely if the principal is more sensitive to the choice of action than the agent. This is consistent with the perception that there is more bureaucratization in large organizations. Second, money-burning is more likely if the agent’s limited liability constraint is tighter relative to his participation constraint. This implies that a higher minimum wage distorts employment contracts towards using socially wasteful nonmonetary incentives, leading to a Pareto inferior outcome as the agent is still held down to his reservation value through increased money burning.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2700851

A General Equilibrium Analysis of Personal Bankruptcy Law

We analyze an economy where principals (lenders, asset owners, franchisors) and agents (borrowers, tenants, franchisees) match and contract subject to moral hazard. Bankruptcy law defines the limited liability constraint in these contracts. We provide a Walrasian characterization of stable allocations and use it to analyze the distributional impact of changing bankruptcy law. We show (i) weakening liability law leads to a redistribution of debt from poor to rich agents; (ii) it makes rich agents better o and poor agents and principals worse o; (iii) exemption limits Pareto-dominate other bankruptcy laws if project size is fixed, and (iv) means testing (as used in the new US bankruptcy law) which is ex post pro-poor in intent makes the poor worse o ex ante.

Characterizing optimal wages in principal-agent problems without using the first-order approach

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA.

Optimal Incentive Contracts and Information Cascades

We examine information aggregation regarding industry capital productivity from privately informed managers in a dynamic model with optimal incentive contracts. Information cascades always occur if managers enjoy limited liability: when beliefs regarding productivity become endogenously extreme (optimistic or pessimistic), learning stops. There is no learning if initial beliefs are extreme, or if agency conflicts are severe. In contrast to the literature, cascades occur even when signals have unbounded precision or when there are rich action spaces. Relaxing limited liability constraints is not sufficient to avoid cascades; we provide sufficient conditions for efficient information aggregation through incentive contracts.

Optimal collusion with limited liability

Collusion sustainability depends on firms' aptitude to impose sufficiently severe punishments in case of deviation from the collusive rule. We extend results from the literature on optimal collusion by investigating the role of limited liability. We examine all situations in which either structural conditions (demand and technology), financial considerations (a profitability target), or institutional circumstances (a regulation) set a lower bound, possibly negative, to firms' profits. For a large class of repeated games with discounting, we show that, absent participation and limited liability constraints, there exists a unique optimal penal code. It commands a severe single-period punishment immediately after a firm deviates from the collusive stage-game strategy. When either the participation constraint or the limited liability constraint bind, there exists an infinity of multi-period punishment paths that permit firms to implement the optimal collusive strategy. The usual front-loading scheme is only a specific case and an optimal punishment profile can take the form of a price asymmetric cycle. We characterize the situations in which a longer punishment does not perform as a perfect substitute for more immediate severity. In this case the lowest discount factor that permits collusion is strictly higher than without the limited liability constraint, which hinders collusion.

Calibrated Incentive Contracts

This paper studies a dynamic agency problem which includes limited liability, moral hazard, and adverse selection. The paper develops a robust approach to dynamic contracting based on calibrating the incentive properties of simple benchmark contracts that are attractive but infeasible, due to limited liability constraints. The resulting dynamic contracts are detail-free and satisfy robust performance bounds independently of the underlying process for returns, which need not be i.i.d. or even ergodic. [PUBLICATION ABSTRACT]

Are tournaments optimal over piece rates under limited liability for the principal?

A highly acclaimed result is that tournaments are superior to piece rates when the agents are risk averse and their production activities are subject to a relatively large common shock. The reason is that tournaments allow the principal to trade insurance for lower income to the agents. Our analysis shows that this celebrated result does not carry over to the case when a limited liability (bankruptcy) constraint limits the payments the principal can make, provided that the liquidation value of the firm is sufficiently small. This finding has important implications for the vast number of limited liability firms. Even though limited liability becomes an issue for different ranges of liquidation values under the two schemes, tournaments are still superior when the liquidation value of the firm is intermediate or large, even though the limited liability constraint is still binding for intermediate values. Surprisingly, uncertainty in the price of output strengthens the need for tournaments by expanding the range of liquidation values over which tournaments are dominant, because price uncertainty introduces additional bankruptcy risk. These findings provide insight into policy implications in the contracting out of services by state and local governments, in procurement, in rent-seeking contests and in tournaments used by HMOs.