Optimality and Renegotiation in Dynamic Contracting

We characterize the optimal renegotiation-proof contract in a dynamic Principal-Agent model in which the type of the agent may change stochastically over time. Contrary to the case with constant types, the ex ante optimal contract may be renegotiation-proof even if types are highly correlated. The marginal benefit of having some pooling of types in the first period is not monotonic in their persistence level, but the equilibrium level of pooling is non-decreasing in persistence; and, for any level persistence, it is always optimal to partially screen the types by offering a menu of choices to the agent. Despite the non-linearity of the problem, the optimal equilibrium allocation is unique.