The First-Order Approach to Moral Hazard Problems with Hidden Saving : The Case of CARA Utility

This paper examines the first order approach to moral hazard problems in which the agent can secretly save and borrow. The paper shows that hidden saving constrains the concavity of the agent's problem even for CARA utility and additively separable effort disutility in an important way: Consumption utility in the second period will be jointly concave in effort and saving if and only if the negative consumption utility is log-convex in effort. We derive two sets of sufficient conditions for the validity of the first order approach in this setup. First, we strengthen the classic approach by Mirrlees (1979) and Rogerson (1985). We obtain a second set of conditions by using the theory of total positivity (Karlin 1968)