An Analytically Solvable Principal-Agent Model


Book Description

We analyze a principal-agent model with moral hazard where the principal is risk neutral and the agent is risk averse or risk neutral. The agents' actions determine the probability distribution over outcomes, where some probability distributions require more effort than others. We analyze a family of effort disutility functions with arguably desirable properties. For a canonical class of such functions and arbitrary outcome spaces, the model is explicitly solvable. Optimal contracts combine debt with a monotonic sharing rule for the surplus created. When the agent is risk neutral, the contract is a pure debt contract. For agents with unit degree of relative risk aversion, the surplus is divided in fixed shares.




Essays on Principal-agent Models


Book Description

This dissertation consists of three chapters on principal-agent models. Chapter 2 studies an optimal contract design problem in a principal-framework whereas chapter 3 is an empirical investigation of the incentive contracts in the market of top executives. Chapter 4 is a theoretical chapter exploring welfare impacts of the structure in a top-level bureaucracy. In the first chapter, I consider a dynamic moral hazard model where the principal offers a series of short-run contracts. I study the optimal mix of two alternative instruments for incentive provision: a performance based wage (a "carrot") and a termination threat (a "stick"). At a given point in time, these instruments are substitutes in the provision of incentives. I am 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 her 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. Having inspired from chapter 2, chapter 3 of the dissertation is an empirical study of the contracts of Chief Executive Officers (CEO). Direct pay for performance and a threat of termination when performance is low are two important instruments to incentivize CEOs. This chapter is an empirical analysis of the use of these two incentive devices and how they depend on tenure and managerial ability. For managers promoted from within a firm, ability is proxied by their age at the time of promotion. For managers hired from outside, I instead rely on constructed measures of "reputation", based on media citations over time windows of different length. Using a sample of firms, listed in S & P 1500 over the period 1998-2008, I find that CEO compensation and the threat of forced turnover are used as incentive devices throughout tenure. Even though the results indicate that pay increases as the CEO is more senior in her tenure, there is no strong evidence that termination threat follows a particular time pattern. For outsider CEOs, a better reputation increases pay and decreases the likelihood of forced turnover, with stronger effects for more current reputational measures. Regarding the impacts of reputation on the tenure-pay relationship, only more current measures have a significant and negative effect. Managerial ability, as proxied by age-at-promotion for insiders and as proxied by reputation for outsiders, decreases the likelihood of forced turnover. More current reputation measures, as in the case of total pay, have a larger impact of likelihood of turnover. Chapter 4 investigates the welfare implications of multiple principals in the highest level of bureaucracy. An agent has to carry out two separate tasks, which can either be organized by two separate principals, or combined under one principal. The relationship between the top level (the principals) and the lower level (agent) of the bureaucracy is a "principal-agent problem". The existence of multiple principals generates a "common agency". The analysis reveals that the optimal hierarchy depends on the existence of "rents" from office that the principals enjoy. If there are no rents, the two systems are equally welfare-efficient. A single-principal model dominates common agency otherwise.













Wealth Effects in the Principal Agent Model


Book Description

This paper addresses the question of how the principal's surplus and agency costs depend on the agent's wealth. Our main results are: If the agent has an additively separable utility function in income and effort and his degree of absolute prudence is smaller than three times the agent's degree of absolute risk aversion, then the principal's expected pay-off is smaller the richer the agent. For general utility functions, this result also holds if the first order approach is applicable and one further technical assumption is satisfied. If, however, the participation constraint does not bind, then richer agents are cheaper.