Aggregation and Linearity in the Provision of Intertemporal Incentives

One of the main findings of the principal-agent literature has been that incentive schemes should be sensitive to all information that bears on the agent's actions. As a manifestation of this principle, incentive schemes tend to take quite complex (non-linear) forms. In contrast, real world schemes are often based on aggregate information with a rather simple structure. This paper considers the optimality of linear schemes that use only aggregated information. The hypothesis is that linear schemes are to be expected in situations where the agent has a rich set of actions to choose from, because richness in action choice allows the agent to circumvent highly nonlinear schemes. We show that optimal compensation schemes are indeed linear functions of appropriate accounting aggregates in a multi-period model where the agent can observe and respond to his own performance over time. Furthermore, when profits evolve according to a controlled Brownian motion (with the agent at the controls) the optimal compensation scheme is linear in profits. The optimal scheme can be computer as if the principal could only choose among linear rules in a corresponding static problem. Applications of this ad hoc principle appear quite promising and are briefly illustrated.