Efficient allocations with moral hazard and hidden borrowing and lending: A recursive formulation

We propose a tractable recursive framework to study the optimal allocation of consumption and effort in a dynamic setting with moral hazard where agents have secret access to the credit market or to storage. The recursive structure is based on a generalized first-order approach, whose validity must be verified ex post. Thanks to the recursive formulation of the optimal contract, the verification procedure turns out to be numerically parsimonious as it can be performed using standard dynamic programming techniques with only one endogenous state variable: The agent's level of assets. We study the performance of our ex post verification test in practice by solving numerically three representative infinite horizon examples.