Collateralized debt as the optimal contract

In a simple risk-sharing environment with ex post private information, conditions are found under which a collateralized debt contract is the optimal allocation. The critical condition for optimality is that the borrower values the collateral good more highly than does the lender; otherwise the optimal contract does not resemble debt. Limited collateral can give rise to an endogenous borrowing constraint, driving a further wedge between the intertemporal marginal rates of substitution of the borrower and the lender. I argue that perhaps all debt contracts are implicitly collateralized.