Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending: A Recursive Formulation

This paper studies the effect of secret access to the credit market in the dynamic moral hazard model. We first show that in our model the efficient allocation improves welfare with respect to the case where the agents can self insure only through borrowing and lending. This contrasts previous findings for hidden information models. We then provide a tractable recursive framework to study the optimal allocation in this setting. The recursive structure is based on a generalized first order approach, whose validity must be verified ex-post. Thanks to the recursive formulation, the verification procedure turns out to be numerically parsimonious. Finally, we study some of the main qualitative properties of the efficient allocation. Hidden asset accumulation changes dramatically the long run properties of the efficient allocation. The immiseration pattern typical of the standard moral hazard model is replaced by properties qualitatively similar to those of self insurance. We find that the intertemporal discrepancies with respect to self insurance are important but essentially of quantitative nature.