jats:pThis paper investigates the macroeconomic dynamics of consumption and real interest rates when there are constraints on debt finance, used both for insurance against income shocks and transferability of resources over time. We amend a standard continuous‐time deterministic model, with patient and impatient household sectors, introducing sector level income shocks. Shocks that push the impatient sector towards its leverage limit increase precautionary saving and result in a substantial but transient decline of the real interest rate relative to the deterministic benchmark. We discuss the resulting dynamics of consumption, leverage and interest rates, and implications for macroeconomic modelling and policy.</jats:p>