Informed Principal, Moral Hazard, and Limited Liability

I consider a moral hazard problem with risk neutral parties, limited liability, and an informed principal. The contractible outcome is correlated to both the principal's private information and the agent's hidden action. In contrast to a model without a privately informed principal or without limited liability, I show that the first-best payoff cannot be implemented by any equilibrium mechanism. Furthermore, limited liability precludes the existence of equilibrium refinements such as (Strongly) Neologism proofness.