Optimal Retention in Agency Problems

This paper studies the interaction between a single long-lived principal and a series of short-lived agents in the presence of both moral hazard and adverse selection. We assume that the principal can influence the agents' behavior only through her choice of a retention rule; this rule is further required to be sequentially rational (i.e., no precommitment is allowed). We provide general conditions under which equilibria exist where (a) the principal adopts a "cut-off" rule under which agents are retained only when the reward they generate exceeds a critical bound; and (b) agents separate according to type, with better agents taking superior actions. We show that in equilibrium, a retained agent's productivity is necessarily declining over time, but that retained agents are also more productive on average than untried agents due to selection effects. Finally, we show that for each given type, agents of that type are more productive in the presence of adverse selection than when there is pure moral hazard (i.e., when that type is the sole type of agent in the model); nonetheless, adding uncertainty about agent-types cannot benefit the principal except in uninteresting cases.