Efficient risk sharing and separation

This paper extends the model of risk sharing with limited commitment to feature separation. Partners face idiosyncratic income and match quality shocks, share risk subject to limited commitment, and separate whenever they are better off doing so. We characterise analytically the sets of shock realisations where constrained-efficient separations occur and the dynamics of consumption while the risk-sharing partnership continues. The separation probability typically jumps as parameter values change continuously, and an additional inefficient equilibrium emerges. A key reason is complementarity between risk sharing and staying together today and in the future. Income inequality affects consumption inequality via its effect on separations, and consumption inequality can optimally exceed income inequality for any history of income realisations. Both partial risk sharing and separation are relevant for many applications, including the interaction between partners in a household and countries in an economic union.