Repeated Moral Hazard with Persistence
This paper considers the optimal contract when the current (hidden) action of an agent has a persistent effect on the future outcome. In this setting, the current outcome is not only a signal of the current action taken by the agent, but also conveys information about his past actions. The optimal contract in a two-effort choice, two-period setting is characterized analytically and numerically. In particular, it is shown that persistence tends to make compensation less responsive to the first-period outcome. At the extreme, there are cases where the agent is perfectly insured against the first-period outcome: the agent obtains the same utility regardless of the first-period outcome. The model is extended to a setting with three effort choices, a three-period setting, and an N-period setting with two-period persistence. Also discussed is an application of our model to the optimal unemployment insurance program. Some empirical evidence is then presented.
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