Who Shares Risk with Whom and How? Endogenous Matching and Selection of Risk Sharing Equilibria

I examine a model in which agents first form risk-sharing pairs, and then repeatedly share income risks under limited commitment. Agents of different occupations differ in income autocorrelations, i.e. how their current incomes correlate with past ones. I show that agents with high autocorrelation are hard to share risks with. Two equilibrium outcomes can occur: either 1) agents match positive assortatively, or 2) agents from different occupations do match together, but in order to sustain such matches, agents share risks unevenly favoring the relatively less autocorrelated. Either equilibrium features substantial inequality across occupations and low total welfare, compared to what would happen if the agents could be forced into a specific matching. This model emphasizes the interplay between matching and risk sharing, and has implications for evaluating policies. For instance, uniform increases in everyone's low income levels (minimal wages) may hurt some agents. Increases in occupation-specific common income shocks could improve overall risk sharing and reduce inequality. My results are also robust to forms of heterogeneity other than income autocorrelations, such as heterogeneous opportunities to rematch or migrate.