Collateral premia and risk sharing under limited commitment

A competitive general equilibrium model with complete collateralized contracts under limited commitment is proposed and analyzed. With limited aggregate collateral, risk sharing is imperfect. There exists a minimal spanning set of finite collateralized contracts that generates the feasible space and that contains more than the complete set of collateralized Arrow securities. Examples show that exogenously restricting feasible contracts has a significant impact on agents’ welfare. I prove that constrained optimal allocations can be decentralized as a general equilibrium with collateral constraints, and vice versa. Because a capital good serves as collateral, it has an additional value, called collateral premium. The collateral premium is zero if and only if risk sharing is perfect. This is a testable implication of the model.