Productivity Shocks, Discount Rate and Incentives

In this paper we analyze a repeated Principal Agent model, formulated as a Multi-Objective Optimization problem. We approximate its Pareto Frontier by using a recently proposed Multi-Objective Optimization Evolutionary Algorithm named RankMOEA. We focus on the effects of changes of productivity shocks and discount rates on the aforementioned Pareto Frontier. Our numerical results indicate that as the discount rate increases, the Principal Agent relationship generates higher values; the spread in the Agent´s future (current) compensation between the low and high productivity shocks increases (decreases); and the Agent chooses, in general, higher effort levels. On the other hand, when the structure of productivity shocks is such that the Agent´s effort yields higher (lower) production levels, the Principal (Agent) tends to benefit because in those cases the Agent (Principal) assumes more risk.