Loss aversion, moral hazard, and stochastic contracts

I examine whether stochastic contracts benefit the principal in the setting of moral hazard and loss aversion. Incorporating that the agent is expectation-based loss averse and allowing the principal to add noise to performance signals, I find that stochastic contracts reduce the principal's implementation cost in comparison with deterministic contracts. Surprisingly, if performance signals are highly informative about the agent's action, stochastic contracts strictly dominate the optimal deterministic contract for almost any degree of loss aversion. The optimal stochastic contract pays a high wage whenever the principal observes good performance signals, while upon observing bad performance signals it adds a lottery that gives either the high wage or a low wage that serves as a harsh penalty to the agent. In the general case when the agent is both risk and loss averse, I show that if a penalty wage (i.e., a wage level at which the agent feels a substantial disutility) exists, the first best can be approximated closely but not attained. The findings have an important implication for designing contracts for loss-averse agents: the principal should insure the agent against wage uncertainty by employing stochastic contracts that increase the probability of a high wage.