By Árpád Ábrahám and Sarolta Laczó
We extend the model of risk sharing with limited commitment (Kocherlakota, 1996) by introducing both a public and a private (non-contractible and/or non-observable) storage technology. Positive public storage relaxes future participation constraints and may hence improve risk sharing, contrary to the case where hidden income or effort is the deep friction. The characteristics of constrained-efficient allocations crucially depend on the storage technology’s return. In the long run, if the return on storage is (i) moderately high, both assets and the consumption distribution may remain time-varying; (ii) sufficiently high, assets converge almost surely to a constant and the consumption distribution is time-invariant; (iii) equal to agents’ discount rate, perfect risk sharing is self-enforcing. Agents never have an incentive to use their private storage technology, i.e., Euler inequalities are always satisfied, at the constrained-efficient allocation of our model, while this is not the case without optimal public asset accumulation.
From my experience, the risk-free interest rate does not matter much for outcomes in models with risk sharing with borrowing contraints, as long as this interest rate is within reasonable bounds. This paper shows that this should not hold for extensions of the model. And those extensions are quite relevant, as people do have assets that can be verified and others that do not have to be reported or in some cases are not permissible. It becomes then an important question which interest rate is then appropriate for these models.