Optimal Dynamic Contracting: the First-Order Approach and Beyond
We explore the conditions under which the "first-order approach" (FO-approach) can be used to characterize profit maximizing contracts in dynamic principal-agent models. The FO-approach works when the resulting FO-contract satisfies a particularly strong form of monotonicity in types, a condition that is satisfied in most of the solved examples used to motivate its use. The main result of our paper is to show that, except for non-generic choices of the stochastic process governing the types' evolution, monotonicity and incentive compatibility are necessarily violated by the FO-optimal contract if the frequency of interactions is sufficiently high (or equivalently if the discount factor, time horizon and type persistence is sufficiently large). This suggests that the applicability of the FO-approach is problematic in environments in which expected continuation values are important relative to per period payoffs. We explore the features of optimal dynamic contracts in generic environments by solving a simple example, and by studying a class of easily solvable approximately optimal contracts.