Risk Sharing under Limited Committment

In a model with capital accumulation, aggregate risk and competitive intermediaries, Abraham and Carceles-Poveda (2006) show that the constrained efficient allocations can be decentralized as a competitive equilibrium with endogenous borrowing limits if one also imposes an upper limit on the intermediaries' capital holdings. Since it is difficult to find any empirical evidence of such restrictions, the authors also characterize the equilibrium with no capital accumulation constraints. In the present paper, we compare the allocations with and without such constraints numerically. We find that both models behave qualitatively very similar. However, capital accumulation is higher in the absence of accumulation constraints, since the intermediaries do not internalize that fact that a higher aggregate capital increases the incentives to default. In this case, we also find that agents may enjoy a higher welfare in the long run in spite of the fact that this allocation is not constrained efficient.