On Repeated Moral Hazard with a Present Biased Agent

This paper introduces time inconsistent preferences into a moral hazard setting where the agent is risk-averse. We derive a necessary optimality condition on the consumption allocation that is different from the so-called Inverse Euler Equation of Rogerson (1985). Specifically, inverse marginal utility is not a martingale, rather it follows a partial adjustment process. If the bias for the present is sufficiently large the optimal allocation will leave the agent with the desire to borrow. We extend the analysis to the case in which the principal does not know if the agent is time consistent or not. Finally, we show that in a setting with a risk-neutral agent and limited liability everything is as if the principal faces a time consistent agent.