Dynamic delegation with a persistent state

In this paper, I study the dynamic delegation problem in a principal-agent model wherein an agent privately observes a persistently evolving state, and the principal commits to actions based on the agent's reported state. There are no transfers. While the agent has state-independent preferences, the principal wants to match a state-dependent target. I solve the optimal delegation in closed form, which sometimes prescribes actions that move in the opposite direction of the target. I provide a simple necessary and sufficient condition for that to occur. Generically, the principal fares strictly better in the optimal delegation than in the babbling outcome. Over time, the principal is worse off in expectation, but the agent is better or worse off depending on the shape of the principal's state-dependent target.