Efficient Risk Sharing with Limited Commitment and Storage

We extend the model of risk sharing with limited commitment by introducing both a public and a private (unobservable and/or non-contractible) storage technology. Positive public storage relaxes future participation constraints, hence it can 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. At the steady state, 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. Finally, we find that, in contrast with the limited-commitment model without storage, past income affects consumption growth negatively both in our model with storage and in data from Indian villages.