Optimal Long-term Contracting with Learning

This paper introduces profitability uncertainty into an infinite-horizon variation of the classic Holmstrom and Milgrom (1987) model, and studies optimal dynamic contracting with endogenous learning. The agent's potential belief manipulation leads to the hidden information problem, which makes incentive provisions intertemporally linked in the optimal contract. We reduce the contracting problem into a dynamic programming problem with one state variable, and characterize the optimal contract with an ordinary differential equation. In the benchmark case of Holmstrom and Milgrom (1987) without learning, the optimal effort is constant, and the optimal contract is linear. In contrast, in our model with endogenous learning, the optimal effort policy becomes history dependent, and decreases over time on average. Moreover, we show that the optimal contract exhibits an option-like feature in that the incentives rise after good performance shocks.