Robust Contract Designs: Linear Contracts and Moral Hazard

31 Dec 2019


Yimin Yu, Xiangyin Kong

Published in Operations Research, September 2020

Incentive contracts are ubiquitous in our society. The main idea is that employee efforts are typically not observable to firms or principals. As a result, to incentivize employees to exert efforts, firms often offer performance-based compensations. The issues of designing effective and least cost incentive contracts are important both for microeconomics, business, and practice.

However, the existing economics literature typically shows that optimal incentive contracts are complex and nonlinear. This raises a fundamental question in agency theory: why linear or commission-based contracts are so common in practice, while classical agency theory often prescribes more complicated contract forms? Holmstrom and Milgrom, Nobel prize laureates in economics, conjectured that issues of robustness lie at the heart of explaining any incentive scheme which is expected to work well in practical environments.

In this research, Yimin Yu, Associate Professor, Department of Management Sciences and co-author Xiangyin Kong consider incentive contracts under model uncertainty. Model uncertainty refers to the decision-makers' ambiguity or uncertainty over the right models, and is common due to the limited data in practice.

“Interestingly, we find that when the agent is risk-neutral, the optimal robust contract is a (piecewise) linear contract: paying the agent a base payment and a fixed share or commission of the realized output,” says Yu.

“In other words, a linear contract is robust to the change of the underlying environments.”

Yu and Kong provide a new explanation and micro-foundation on why linear based contracts as well as quota-based piecewise linear contracts are so common in practice, particularly in salesforce and CEO compensations. Consistent with the conjecture of Holmstrom and Milgrom, they show that model uncertainty and the worst-case criterion can be the driving factors of the popularity of linear rules due to their robustness. As the optimal robust contact is simple and intuitive, they provide guidelines and insights on how to design incentive contracts in practice.