Changes in probability distributions and the form of compensation contracts

Abstract

We consider a standard principal-agent setting where the first-order approach to the effort choice problem applies. We decompose the effect of a change in the probability distribution of performances on the form of the optimal contract into three additive components. We also consider the specific cases of a linear likelihood ratio, a rightward or leftward translation of the likelihood ratio, and CRRA utility. The results shed light on the differences between the optimal contracts derived in the literature, notably depending on whether a linear likelihood ratio or a lognormally distributed performance measure is assumed.Keywords Executive compensation · First-order approach · Likelihood ratio · Performance measure · Principal-agent modelTo provide effort incentives, a "principal" can offer a compensation contract to an "agent". When the measure of performance of the agent is a noisy version of his effort, the literature has developed settings where the optimal contract can be expressed as a function of risk preferences and the probability distribution of performances. However, we still lack tools to analyze the effect of changes in the probability distribution of performances on the form of the optimal compensation contract.This paper studies a standard model of incentive provision, where the problem of a principal is to induce a risk averse agent to exert a certain level of effort at the minimum possible cost. Crucially, we assume that the first-order approach to the agent's effort