Dynamic Financing with Imperfect Monitoring
37 Pages Posted: 20 Aug 2019 Last revised: 21 Aug 2019
Date Written: June 1, 2019
We study a contracting problem in continuous time where the principal hires an agent to conduct an R&D project for which progress towards success is binary. Under general concave payoffs, we explicitly derive the optimal dynamic incentive contract. In the first best scenario where incentives between the agent and principal are aligned, the optimal contract is constant. In contrast, when incentive compatability is a binding constraint, the optimal contract is explicitly characterized by the unique solution of an ordinary differential equation. The duration of employment is also uniquely specified by an endogenous threshold. The principal is patient near that threshold and his continuation value may in fact be negative in a neighborhood of the threshold. Importantly, due to the lumpy nature of the project completion, the optimal incentive-pay is two-dimensional: a flow payments during the R&D phase, and a lump-sum reward upon successful completion of the project. Finally, in numerical simulations, we find that the optimal contract features a miniscule level of flow payments, where most of the agent’s benefit come from the lump-sum reward when the project is successful. This theoretical feature of our model agrees with empirical evidence that CEO compensation is tied to the success of research agendas taking place over a long time horizon.
Keywords: Dynamic continuous-time contracts, Moral hazard, Imperfect monitoring
JEL Classification: G14, G18, D83, G01
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