Performance Evaluation under Adverse Selection and Correlation Ambiguity

We develop a model wherein a risk-neutral but ambiguity-averse principal contracts with a risk-averse agent who has a risky project. Both the agent and the principal can observe the project output and a public signal. The correlation between the output and the public signal is private information to the agent but is an ambiguous random variable to the principal. Then, apart from moral hazard, the optimal contract takes into consideration both adverse selection and ambiguity aversion simultaneously. Due to the classic trade-off between rent and efficiency, the principal lowers contract power for the agent with a low correlation project (the l-type agent) and compensates her for luck. However, aversion to correlation ambiguity counteracts with this rent reducing effect by making the principal weight the l-type agent more. Consequently, although ambiguity lessens the principal's value, it could improve social welfare by increasing efficiency of the l-type agent. We further extend the model by incorporating an aggregate signal whose variance depends on the ambiguous distribution of all the projects and allowing the agents to be ambiguity-averse. In this case, the principal has to respect the agent's model choice and compensates her for ambiguity premium, which again decreases contract power. With ambiguity-sharing, the pair of optimal separating contracts is metamorphosed compared to those in the baseline model.