COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 742 "Aggregation and Linearity in the Provision of Intertemporal Incentives" Bengt Holmstrom and Paul R. Milgrom April 1985 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. |
