Complete Markets, Enforcement Constraints and Intermediation

Alvarez and Jermann (2000) show that the constrained efficient allocations of endowment economies with complete markets and limited commitment can be decentralized with endogenous borrowing limits on the Arrow securities. In a model with capital accumulation, aggregate risk and competitive intermediaries, we show that such a decentralization is not possible unless one imposes an upper limit on the intermediaries' capital holdings. Since there is no empirical evidence of such restrictions, we also characterize the equilibrium with no capital accumulation constraints. We show that this allocation solves a similar system of equations to the one of the constrained optimal solution, a result which considerably simplifies the equilibrium computation. In addition, capital accumulation is higher in this case, since the intermediaries do not internalize that fact that a higher aggregate capital increases the incentives to default. Finally, this also implies that agents may enjoy a higher welfare in the long run in spite of the fact that this allocation is not constrained efficient