Moral Hazard Model Research Articles

Risks with semi-infinite support: Characterizations and applications

There are many situations that we need to model as risky prospects whose values are censored below at 0, hence defined on semi-infinite support. As useful tools for such models, we derive analytic characterizations of risks such as certainty equivalent and risk premium, for gamma and lognormal distributions and utility functions that have constant risk aversion. As a main application, we consider an extension of the `linear contract, exponential utility, normally distributed risks' (LEN) moral hazard model to gamma distributed risks. We also discuss other potential applications, ranging from loan contracts to comparison of income distributions.

State subsidy and moral hazard in corporate financing

This paper investigates the impact of state subsidy on the behavior of the entrepreneur under asymmetric information. Several authors formulated concerns about state intervention as it can aggravate moral hazard in corporate financing. In the seminal paper of Holmstrom and Tirole (Q J Econ 112(3):663–691, 1997) a two-player moral hazard model is presented with an entrepreneur initiating a risky scalable project and a private investor (e.g. bank or venture capitalist) providing outside financing. The novelty of our research is that this basic moral hazard model is extended to the case of positive externalities and to three players by introducing the state subsidizing the project. It is shown that in the optimum, state subsidy does not harm, but improves the incentives of the entrepreneur to make efforts for the success of the project; hence in effect state intervention reduces moral hazard. Consequently, state subsidy increases social welfare which is defined as the sum of private and public net benefits. Also, the exact form of the state subsidy (ex-ante/ex-post, conditional/unconditional, refundable/nonrefundable) is irrelevant in respect of the optimal size and the total welfare effect of the project. Moreover, in case of nonrefundable subsidies state does not crowd out private investors; but on the contrary, by providing additional capital it boosts private financing. These results are mainly due to the special mechanism imbedded in our model by which the private investor is able to transform even the badly designed state subsidies into a success fee which is optimal from the incentive point of view.

Dynamic incentive contracts with termination threats

We consider a dynamic moral hazard model where the principal offers a series of short-run contracts. We study the optimal mix of two alternative instruments for incentive provision: a performance based wage (a “carrot”) and a termination threat (a “stick”). At any given point in time, these instruments are substitutes in the provision of incentives. We are particularly interested in the dynamic interaction of these two instruments. Both carrot and stick are used more intensively as the agent approaches the end of his finite life. The sharing of the surplus of the relationship plays a key role: a termination threat is included in the optimal contract if and only if the agent’s expected future gain from the relationship is sufficiently high, compared to the principal’s expected future gain. Also, a termination threat is more likely to be optimal if output depends more on “luck” than on effort, if the discount factor is high, or if the agent’s productivity is low. The model, provided that the optimal contract includes a termination threat, essentially provides an alternative explanation for upward-sloping wage profiles even in the absence of full-commitment.

Research on the Participant Behavior Selections of the Energy Performance Contracting Project Based on the Robustness of the Shared Savings Contract

The profits of the ESCO (Energy Services Company) and EU (Energy Using Organization) in the EPCP (energy performance contracting project) rely on the signing of the shared savings contract and the successful operation of the project, and the probability of the project’s success is decided by the complementary efforts of the ESCO and EU. However, the effort selection of the two sides face the bidirectional moral hazard caused by asymmetric information. Based on the robustness of shared savings contract, this paper establishes a bidirectional moral hazard model under asymmetric information to analyze the complementary efforts selection of the ESCO and EU with the given revenue sharing rules, and analyzes the differences of the complementary efforts under symmetric and asymmetric information conditions and the impacts of those efforts on the shared savings contract’s robustness by using a numerial simulation. The results show that compared with information symmetry, the bidirectional moral hazard will erode the project’s value under information asymmetry, the project’s success probability and the level of the parties’ efforts will decrease, which reveals the negative impact of asymmetric information on the robustness of the shared savings contract, and the significance of eliminating information asymmetry effectively as well as incentivizing the parties to increase the degree of complementary efforts to enhance the probability of the project’s success. Finally, policy recommendations regarding the introduction of incomplete contracts, promoting guaranteed savings contracts, and improving energy savings audits for the enhancement of the robustness of the shared savings contract are provided. This research will be helpful to improve the theoretical research on the contract’s robustness, perfect the design of the energy service contract, and formulate the related support policies.

Incentives for quality improvement efforts coordination in supply chains with partial cost allocation contract

In this paper, we consider quality improvement efforts coordination in a two-stage decentralised supply chain with a partial cost allocation contract. The supply chain consists of one supplier and one manufacturer, both of which produce defective products. Two kinds of failure cost occur within the supply chain: internal and external. The supplier and the manufacturer determine their individual quality levels to maximise their own profits. We propose a partial cost allocation contract, under which the external failure cost is allocated between the manufacturer and the supplier at different rates based on information derived from failure root cause analysis. If the quality levels of the supplier and the manufacturer are observable, we show that the partial cost allocation contract coordinates the supply chain, provided that the failure root cause analysis does not erroneously identify the manufacturer’s fault as the supplier’s, and the supplier does not take responsibility for the manufacture’s fault. In the single moral hazard model, where only the quality level of the supplier is unobservable, the optimal share rates require the supplier to take some responsibility for the manufacture’s fault. However, in the double moral hazard model, where quality levels of the supplier and the manufacturer are unobservable to each other, the optimal share rates require the supplier not to take responsibility for the manufacturer’s fault. It is noted that the root cause analysis conducted by the manufacturer may have its disadvantage in attributing the fault to the supplier when both sides are at fault. We also propose a contract based on the dual root cause analysis to reduce the supplier’s penalty cost. Numerical results illustrate that the partial cost allocation contract satisfies the fairness criterion compared with the traditional cost allocation contract.

The Importance of Legitimacy

Within organizations, there are typically limits to leaders' legitimacy. This article explores how organizations are structured in the face of such constraints. The concept of legitimacy is formalized in the context of a single-agent moral hazard model. The principal can give the agent monetary incentives; in addition, he can give the agent an order. The agent finds it costly to disobey orders provided they are legitimate. We find that it may be optimal for the principal to take costly actions to bolster legitimacy. We argue that many organizational phenomena can be understood as attempts to bolster legitimacy. Examples include: rejection of overqualified workers, bureaucracy, merger decisions, and above-market-clearing wages.

Optimal sales force compensation

We analyze a dynamic moral-hazard model to derive optimal sales force compensation plans without imposing any ad hoc restrictions on the class of feasible incentive contracts. We explain when the compensation plans that are most common in practice – fixed salaries, quota-based bonuses, commissions, or a combination thereof – are optimal. Fixed salaries are optimal for small revenue-cost ratios. Quota-based bonuses (commissions) should be used if the revenue-cost ratio takes intermediate (large) values. If firms face demand uncertainty, markets are rather thin, and the revenue-cost ratio large, firms should combine a commission with a quota-based bonus. If word-of-mouth advertising affects sales, a dynamic commission that increases over time can be optimal. When entering a new market or launching a new product, firms should install long-term bonus plans.

Optimal income taxation when asset taxation is limited

Several frictions restrict the government's ability to tax assets. First, it is very costly to monitor trades on international asset markets. Second, agents can resort to nonobservable low-return assets such as cash, gold or foreign currencies if taxes on observable assets become too high. This paper shows that limitations in asset taxation have important consequences for the taxation of labor income. We study a simple dynamic moral hazard model of social insurance with observable and nonobservable saving decisions. We find that optimal labor income taxes become less progressive when the ability to tax savings is limited.

Managerial Incentives, Moral Hazard and Risk Management

This paper examines how the structure of managerial compensation is affected by the possibility that managers trade derivatives for a speculation purpose. A simple moral hazard model shows that a strong pay-for-performance sensitivity is ineffective when shareholders cannot monitor the (speculative) use of derivative instruments. Intuitively, while a strong pay-performance sensitivity provides managerial incentives to increase shareholder value by exerting effort, it also creates perverse incentives to increase the firm's cash-flow risks by taking unproductive managerial actions. To test this prediction, I study the effect on the managerial compensation of a new accounting standard, Statement of Financial Accounting Standard No. 133 (FAS 133) which makes it harder for managers to hide the speculative use of derivatives. Following the issuance of FAS 133, derivative users (i.e., firms that traded derivatives before the issuance of FAS 133) increase the sensitivities of their CEO/CFO pay to the firm performance and to the cash-flow risks relative to other firms. Consistent with the model, the evidence suggests that the managerial pay-performance sensitivity is higher when managers cannot conceal information about the use of financial instruments.

Moral Hazard: Base Models and Two Extensions

We analyze the optimal contract in static moral hazard situations, where the agent’s effort is not verifiable. We first present the main trade-offs of the principal–agent model. We cover the trade-off of incentives (motivation) vs risk sharing (efficiency), incentives vs rents (when the agent is protected by limited liability), incentives to a task vs incentives to another (in a multitask situation), and incentives to the agent vs incentives to the principal (when both exert a non-verifiable effort). Then, we discuss two recent extensions: how incorporating behavioral biases in the analysis of incentives and inserting the principal–agent problem in a matching market affect the predictions of the classical moral hazard model.

Analysis of Credit Risk Management in Small and Micro Businesses with Moral Hazard Model

Small micro enterprises have effectively promoted the economic growth and technological innovation and cre- ated a lot of financial income for our country, which are not only the main force of the economic growth in our country, but also the basic cell and lifeblood of the economy in our country, however, financing difficulty that small micro enter- prises suffer from is an inextricable problem which is hard to crack for a long time. Now, under the dual drive of the ex- ternal competitive pressure and the assessment of internal profit, domestic commercial banks see it as an opportunity of business development and transformation to vigorously develop small micro credit business in succession, therefore, they enlarge the input of manpower, material resources and financial resources increasingly and aim to develop a vast new world in the small business. However, the credit risk problem of small micro enterprise has hindered the advance of com- mercial bank. Management of credit risk in small and micro enterprise will directly restrict healthy and rapid development of small credit business. Therefore, scientific and effective credit risk management for small and micro enterprise has be- come an imperative issue for domestic commercial banks to develop small credit business. This paper, based on moral hazard model, analyzes the deeply-rooted cause of the credit risk in small micro enterprise and further puts forward to the relevant strategies to solve the financing obstacles of small micro enterprise combining with domestic commercial banks' traditional experience in credit risk management.

Rater Bias and Incentive Provision

The tendency of supervisors to judge an employee as either good or bad and then to seek out evidence supporting that earlier established opinion is regarded as one of the major problems of performance appraisal. We investigate the implications of this rater bias in a dynamic moral hazard model with a wealth-constrained agent. Although rater bias weakens the agent's incentives to exert effort in late periods, at the same time it strengthens implicit incentives in early periods. Under the optimal contract, as long as rater bias is not overly strong, its adverse effect on late-period incentives is fully offset by exploitation of stronger early-period incentives and thereby leaves the principal's profits unchanged

Bundling and Quality Assurance

We consider a repeated moral hazard model of product quality choice by a multiproduct firm selling experience goods with imperfect private monitoring. When consumers receive imperfect private signals of product quality, consuming two products from the same firm improves monitoring. Monitoring by consumers has a positive externality on other consumers, but consumers ignore this when making their purchase decisions. Product bundling improves product quality by constraining consumers to purchase both goods and monitor more effectively. The social and private value of bundling is even larger if (1) consumers can only attribute a negative signal to a pair of complementary products and not to a specific product, and (2) if one of the two goods is a durable and the other is a complementary nondurable.

Minimum taxation as a luxury good

This paper investigates the use of minimum tax thresholds to avoid income tax evasion. We analyze a moral-hazard model in which, given the endogenous audit probability, taxpayers may choose to comply or not with their tax obligation. The main result is that the imposition of a minimum tax, whereby taxpayers need to pay a tax on wealth no lower than a certain amount, can be Pareto efficient. The result hinges upon a critical level of wealth endowment: wealthy economies should ask for a minimum tax payment from all taxpayers; poor economies should only rely on income taxation, and allow taxpayers to be able to get away with their tax obligations. Minimum taxation, therefore, is like a luxury good and only rich economies can afford it.

BEHAVIORAL HAZARD IN HEALTH INSURANCE.

A fundamental implication of standard moral hazard models is overuse of low-value medical care because copays are lower than costs. In these models, the demand curve alone can be used to make welfare statements, a fact relied on by much empirical work. There is ample evidence, though, that people misuse care for a different reason: mistakes, or "behavioral hazard." Much high-value care is underused even when patient costs are low, and some useless care is bought even when patients face the full cost. In the presence of behavioral hazard, welfare calculations using only the demand curve can be off by orders of magnitude or even be the wrong sign. We derive optimal copay formulas that incorporate both moral and behavioral hazard, providing a theoretical foundation for value-based insurance design and a way to interpret behavioral "nudges." Once behavioral hazard is taken into account, health insurance can do more than just provide financial protection - it can also improve health care efficiency.

A solvable continuous time dynamic principal–agent model

I study the provision of incentives in a continuous time dynamic moral hazard model with hidden actions and hidden states. I consider a principal–agent model with linear production and exponential utility, whose explicit solution allows me to show how allocations are distorted for incentive reasons, and how access to hidden savings further alters allocations. I solve the model by applying a stochastic maximum principle, where the co-state variables from the agent's optimization problem become state variables for the principal's problem of choosing an optimal contract. I show that the main effect of moral hazard is a distortion on the effort margin, with a smaller effect on the intertemporal consumption allocation. Access to hidden savings shuts down the intertemporal distortions and increases the effort distortion. I also show how the optimal contracts can be implemented via a constant equity share, a constant flow payment, and a constant tax on savings.

Executive Compensation: A Modern Primer

This article studies traditional and modern theories of executive compensation, bringing them together under a simple unifying framework accessible to the general-interest reader. We analyze assignment models of the level of pay, and static and dynamic moral-hazard models of incentives, and compare their predictions to empirical findings. We make two broad points. First, traditional theories find it difficult to explain the data, suggesting that compensation results from “rent extraction” by CEOs. However, more modern “shareholder value” theories, that arguably better capture the CEO setting, do deliver predictions consistent with observed practices, suggesting that these practices need not be inefficient. Second, seemingly innocuous features of the modeling setup, often made for tractability or convenience, can lead to significant differences in the model's implications and conclusions on the efficiency of observed practices. We close by highlighting apparent inefficiencies in executive compensation and additional directions for future research. (JEL G38, M12, M48, M52)

Quantifying the social welfare loss in moral hazard models

The main aim of this paper is to measure the social welfare loss for a continuous moral hazard model when a set of minimal assumptions are fulfilled. By using a new approach, we are able to reproduce the results of Balmaceda, Balseiro, Correa, and Stier-Moses (2010) pertaining to the social welfare loss for discrete and continuous models respectively. Previous studies rely on the validity of the first-order approach at the expense of strong assumptions, in particular the convexity of the distribution function condition while we do not make such a restrictive assumption in our developments. In addition, we obtain new bounds for the social welfare loss that are both tight and easy to compute.

Unraveling in a repeated moral hazard model with multiple agents

This paper studies an infinite-horizon repeated moral hazard problem where a single principal employs several agents. We assume that the principal cannot observe the agents’ effort choices; however, agents can observe each other and can be contractually required to make observation reports to the principal. Observation reports, if truthful, can serve as a monitoring instrument to discipline the agents. However, reports are cheap talk so that it is also possible for agents to collude, i.e., where they shirk, earn rents, and report otherwise to the principal. The main result of the paper constructs a class of collusion-proof contracts with two properties. First, equilibrium payoffs to both the principal and the agents approach their first-best benchmarks as the discount factor tends to unity. These payoff bounds apply to all subgame perfect equilibria in the game induced by the contract. Second, while equilibria themselves depend on the discount factor, the contract that induces these equilibria is independent of the discount factor.

Executive Compensation: A Modern Primer

This article studies traditional and modern theories of executive compensation, bringing them together under a simple unifying framework accessible to the general-interest reader. We analyze assignment models of the level of pay, and static and dynamic moral hazard models of incentives, and compare their predictions to empirical findings. We make two broad points. First, traditional theories find it difficult to explain the data, suggesting that compensation results from rent extraction by CEOs. However, more modern shareholder value theories that arguably better capture the CEO setting do deliver predictions consistent with observed practices, suggesting that these practices need not be inefficient. Second, seemingly innocuous features of the modeling setup, often made for tractability or convenience, can lead to significant differences in the model's implications and conclusions on the efficiency of observed practices. We close by highlighting apparent inefficiencies in executive compensation and additional directions for future research.