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. The optimal contract in a two-effort choice, two-period setting is characterized analytically and numerically. In particular, we show 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 three periods. We also present a computational method to characterize an N-period model with two-period persistence.