Efficient Risk Sharing with Limited Commitment and Storage

We extend the model of risk sharing with limited commitment (Kocherlakota, 1996) 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. 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. We compare the dynamics of consumption in simulated data and data from Indian villages, and find that past incomes matter in a similar way in our model with storage and the data but not in the basic limited-commitment model.