The Price of Unobservability: Moral Hazard and Limited Liability

Abstract

This article studies a principal-agent problem with discrete outcome and effort space. The principal and the agent are risk neutral and the latter is subject to limited liability. For a given monitoring technology, we consider the maximum possible ratio between the first best social welfare to the social welfare arising from the principal's optimal pay-for-performance contract (the price of unobservability). Our main results provide tight bounds for this price. Key parameters to these bounds are number of possible efforts, the likelihood ratio evaluated at the highest outcome, and the ratio between costs of the highest and the lowest efforts. The paper provides insights on how costly moral hazard and limited liability could be from the social point of view.

Keywords: Moral hazard, Limited Liability, Price of Anarchy, Welfare Loss

JEL Classification: J21, J34, D21