Income Risk and Household Debt with Endogenous Collateral Constraints

We present a heterogeneous-agent model with incomplete markets, in which household debt need to be collateralized by durable holdings and the lowest attainable labor income. Labor income is risky and households decide how much non-durables to consume, on their position of secured debt and the durable stock. Consumers value durables not only as collateral for their debt but also derive utility from their durable stock. We show that an interest spread between the borrowing and lending rate implies local convexities in the policy functions for non-durable consumption and especially durable holdings which are important quantitatively. Moreover, an increase in income risk decreases average household debt because of the buffer-stock saving motive