**Optimal Dynamic Contracting: the First-Order Approach and Beyond**

We study a dynamic principal-agent model in which the agent's types are serially correlated. In these models, the standard approach consists of first solving a relaxed version in which only local incentive compatibility constraints are considered, and then in proving that the local constraints are sufficient for implementability. We explore the conditions under which this approach is valid and can be used to characterize the profit maximizing contract. We show that the approach works when the optimal allocation in the relaxed problem is monotonic in the types, a condition that is satisfied in most solved examples. Contrary to the static model, however, monotonicity is generally violated in many interesting economic environments. Moreover, when the time horizon is long enough and serial correlation is sufficiently high, global incentive compatibility constraints are generically binding. By fully characterizing a simple two period example, we uncover a number of interesting features of the optimal contract that cannot be observed in spatial environments in which the standard approach works. Finally, we show that even in complex environments, approximately optimal allocations can be easily characterized by focusing on a particular class of contracts in which the allocation is forced to be monotonic.