Wealth effects and agency costs

We analyze how the agent's initial wealth affects the principal's expected profits in the standard principal–agent model with moral hazard.We show that if the principal prefers a poorer agent for all specifications of action sets, probability distributions, and disutility of effort, then the agent's utility of income must exhibit a coefficient of absolute prudence less than three times the coefficient of absolute risk aversion for all levels of income, thus strengthening the sufficiency result of Thiele and Wambach (1999). Also, we prove that there is no condition on the agent's utility of income alone that will make the principal prefer richer agents. Moreover, we show that, for an interesting class of problems, the principal prefers a relatively poorer agent if agent's wealth is sufficiently large. Finally, we discuss how alternative ways of modeling the agent's outside option affects the principal's preferences for agent's wealth.     

Precautionary retirement and precautionary saving

The paper analyzes the lifetime utility maximization problem of an agent who chooses her saving and timing of retirement in the presence of labor income risk in a simple setting where a pure redistributive pension scheme is in place. In this context, a precautionary motive for retirement, which pushes old workers to replace an uncertain labor income with certain pension payments, and to retire early is identified. The conditions for precautionary retirement and saving to arise are then characterized and interpreted in two settings. In the first setting, utility only depends on income, and a sufficiently low level of absolute prudence is necessary for precautionary retirement. A sufficiently high level is necessary however for precautionary saving, which can coexist with precautionary retirement only for intermediate values of absolute prudence. In the second setting, agent utility also depends on leisure, and three conditions allow the precautionary motive for retirement and saving to jointly operate: prudence, an index of absolute prudence sufficiently low and cross-prudence in leisure.     

Optimal consumption and the timing of the resolution of uncertainty

As is well-known, consumers want to accumulate precautionary savings in the face of income risks when their marginal utility is convex (prudence). In this paper, we explore the effect of the timing of the resolution of income uncertainty on savings. An agent faces uncertainty about his income at date t+2. What is the effect of being informed that the uncertainty will be resolved at date t+1 on the consumption at date t? We show that the effect is positive, if and only if, marginal utility is convex (prudence), when either the risk free rate is equal to the rate of pure preference for the present, or when the utility function is HARA. The intuition is that an early resolution of uncertainty allows for time-diversifying the risk. It therefore plays a role similar to a reduction of the income risk, whose effect on savings is negative under prudence.     

On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Decreasing absolute prudence: Characterization and applications to second-best risk sharing

In this paper, we provide two basic properties of utility functions u which exhibit decreasing absolute prudence i.e. (− u/u″)′ ≤ 0. These properties are used to examine the allocation of risks in an economy when some agents bear non-transferable risks. We show that it is fair Pareto-efficient to let those with a non-transferable risk bear relatively less of the transferable risk in the economy if and only if absolute prudence is decreasing. In another model, there is a complete set of contingent markets, but some agents have no direct access to them. We examine the fair efficient allocation of risk in a pool gathering a trader and a non-trader. Decreasing absolute prudence provides an upper bound to the share of the pool's risk that should be borne by the trader.     

Survey measures of risk aversion and prudence

This paper utilizes a thought experiment conducted by the Bank of Italy to estimate absolute and relative risk aversion along with absolute and relative prudence for a broad cross-section of Italian households. Upper and lower bounds are calculated for each parameter, and comparisons are made across socio-demographic groups. Evidence is found of decreasing absolute risk aversion, decreasing absolute prudence, increasing relative risk aversion, and increasing relative prudence.     

Unemployment insurance with hidden savings

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini (1997) [1]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.     

Prudence, Intertemporal Substitution, and Savings under Uncertainty

This paper derives the relations between the coefficient of absolute prudence, the equivalent precautionary premium, risk aversion to concentration, and the normality and shift of current consumption under uncertainty, without the time-separable utility assumption. Examples show that Kimball's coefficient of absolute prudence does not fully characterize precautionary saving or saving behavior under uncertainty. It is proved that, whereas a higher rate of intertemporal substitution and a larger coefficient of absolute prudence imply more savings when current consumption is normal, a larger coefficient of intertemporal substitution and a smaller coefficient of absolute prudence imply more savings when current consumption is inferior. Received July 17, 2001; revised version received November 20, 2001     

Greater prudence and greater downside risk aversion

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=−u^?/u^″, is related to downside risk aversion, which is indicated by a positive value for u^?. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.     

The impact of prudence on optimal prevention

Summary. What are the determinants of the optimal level of effort to reduce the probability of a loss to occur? Whereas most of the literature on this question focused on risk aversion, we show that the concept of prudence (i.e., a positive third derivative of the utility function) is essential to answer this question. We explain in this paper that prudence and prevention tend to be opponents rather than allies contrary to the intuition attached to everyday language.Received: 7 November 2003, Revised: 3 August 2004, JEL Classification Numbers: D61, D81. Correspondence to: Christian Gollier     

Prudence and prevention: an economic laboratory experiment

In an economic laboratory experiment, we study the relationship between prudence and prevention in general decision situations. Previous theoretical research on this relationship posits a negative impact of prudence on the optimal level of prevention. Overall, we find both risk-averse and prudent behaviour among our subjects. Moreover, prudent subjects chose significantly less prevention than nonprudent subjects, confirming the theoretical results of one-period models in the literature. Our findings might have implications for health policy if prudence – rather than irrational decision behaviour, as previously assumed – is responsible for low levels of preventive effort.     

The nature of tournaments

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen in J Polit Econ 89:841?C864, 1981). We find that it is often optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (1) R is small relative to P (where R is risk aversion and P is absolute prudence); (2) the distribution of shocks to output is asymmetric and the asymmetry takes a particular form; (3) the principal faces a limited liability constraint; and (4) there is agent heterogeneity of a particular form.     

Background risk and the demand for state-contingent claims

Summary. We consider the demand for state-contingent claims, in the presence of an independent zero-mean, non-hedgeable background risk. An agent is defined to be generalized risk averse if he/she chooses a demand function for contingent claims with a smaller slope everywhere, given a simple increase in background risk. We show that the conditions for standard risk aversion, that is positive, declining absolute risk aversion and prudence, are necessary and sufficient for generalized risk aversion.Received: 13 February 2002, Revised: 10 February 2003, JEL Classification Numbers: D52, D81, G11. Correspondence to: Guenter FrankeWe are grateful to Louis Eeckhoudt, Christian Gollier, Harris Schlesinger and an unknown referee for valuable comments.     

Theories of behavior in principal-agent relationships with hidden action

In a laboratory experiment, we investigate behavior in a principal-agent situation with moral hazard. We evaluate the predictive success of two theories. One is the standard agency theory, which assumes that the agent will accept any contract offer that satisfies his participation constraint, typically requiring zero expected utility. The other is the “fair-offer” theory suggested by Keser and Willinger [2000. Principals’ principles when agents’ actions are hidden. International Journal of Industrial Organization 18 (1), 163-185], which requires that the principal provide full insurance against losses to the agent and leave him a share of at most 50% of the generated surplus. The treatment variable of our experiment is the cost of effort. As effort costs increase, expected net surplus of a contract decreases. We observe that fair-offer theory generally predicts observed contract offers better than standard agency theory. However, the predictive success of the fair-offer theory decreases, while the one of standard agency theory increases with decreasing expected net surplus.     

Erratum to “Negotiation and take it or leave it in common agency”: [Journal of Economic Theory 111 (2003) 88-109]

The no-externalities condition provided in the text is not sufficient for Theorems 3 and 4 when effort is not fully contractable. In the case where the principals cannot contract at all on agent's effort, the condition in the text requires that for any set of alternatives offered by the principal there is one that is at least as good as all other alternatives in the set for the agent no matter what the other principal does, no matter what effort the agent takes, and no matter what the agent's type. In fact, a stronger condition is required. For any set of alternatives offered by a principal, each of the choices within this set that is at least as good for the agent as any other choice within the set must remain so no matter what actions the other principals take, no matter what effort the agent takes, and no matter what the agent's type.     

Redistributing Gains from Globalisation*

This paper analyses the effects of redistribution in a model of international trade with heterogeneous firms in which a fair‐wage effort mechanism leads to firm‐specific wage payments and involuntary unemployment. The redistribution scheme is financed by profit taxes and gives the same absolute lump‐sum transfer to all workers. International trade increases aggregate income and income inequality, ceteris paribus. If, however, trade is accompanied by a suitably chosen increase in the profit tax rate, it is possible to achieve higher aggregate income and a more equal income distribution than in autarky, provided that the share of exporters is sufficiently high.     

Wealth Inequality and Asset Pricing

In an Arrow–Debreu exchange economy with identical agents except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the risk-free rate. We first show that wealth inequality raises the equity premium if and only if the inverse of absolute risk aversion is concave in wealth. We then show that the equilibrium risk-free rate is reduced by wealth inequality if the inverse of the coefficient of absolute prudence is concave. We also prove that the combination of a small uninsurable background risk with wealth inequality biases asset pricing towards a larger equity premium and a smaller risk-free rate.     

EMERGENCE OF LEADERSHIP IN TEAMS*

This paper provides a simple model to explain the emergence of leadership in an unstructured team. Each agent has partial information about the productivity of the team. Each agent may invest a productive effort in one of two periods. If one agent voluntarily moves first and the other waits for the second period, and if the first‐move action successfully transmits his type, the first mover effectively exercises leadership in affecting the effort choice of the second mover. We prove that, if each agent holds stochastically independent information, leadership emerges with positive probabilities in Cho–Kreps stable outcomes.     

GRANTING AN EXIT OPTION TO CONDUCT AN AUDIT

We study a principal–agent relationship with auditing in which information from an audit is ‘soft’– by conducting an audit, the principal observes the agent's private information, but cannot obtain verifiable evidence on the information. Moreover, the principal's auditing effort is unverifiable in our model. Therefore, besides the agent's misreporting incentive, there is the principal's incentive to accuse the truthful agent even without auditing. If the principal's auditing effort is verifiable, granting no exit option to the agent is optimal although the principal can still accuse a truthful agent after the audit. We show that when the principal's auditing effort is unverifiable, granting an exit option to the agent and auditing are complementary. Without granting an exit option to the agent, no auditing is optimal, and the principal grants an exit option to conduct a sincere audit, which in turn mitigates the agent's misreporting incentive. Our analysis also reveals that, when the cost of auditing is sufficiently large, the principal conducts more sincere audits with a smaller amount of penalty.     

The wisdom of the minority

We consider a simple variant of the canonical model of social learning and show that in many situations it is optimal for an agent to abandon her own information and follow the minority rather than the majority. This possibility depends on two economically meaningful requirements: agents are differentially informed and observe only the number of agents having chosen each option, such as consumers observing only market shares. We show that minority wisdom arises when information is sufficiently heterogeneous and the well informed are not overly abundant, yet the conditions necessary are not overly restrictive. In fact, it is possible for the minority to be wise even when the minority consists of a lone dissenter and a majority of citizens are well informed.