Screening risk-averse agents under moral hazard:: single-crossing and the CARA case

Principal-agent models of moral hazard have been developed under the assumption that the principal knows the agent's risk-aversion. This paper extends the moral hazard model to the case when the agent's risk-aversion is his private information, so that the model also exhibits adverse selection. We characterize the optimal menu of contracts; while its detailed properties depend on the setting, we show that some of them must hold for all environments. In particular, the power of incentives always decreases with risk-aversion. We also characterize the relationship between the outside option and the optimal contracts. We then apply our results to testing for asymmetric information in insurance markets.