Monetary and macroprudential policy with multi-period loans

We study the implications of multi-period loans for monetary and macroprudential policy, considering several realistic modifications -- variable vs. fixed loan rates, non-negativity constraint on newly granted loans, and occasionally binding collateral constraint -- to an otherwise standard DSGE model with housing and financial intermediaries. In line with the literature, we find that monetary policy is less effective when contracts are multi-period, but only under fixed rate mortgages or when borrowers cannot be forced to accelerate repayment of their loans. Moreover, the probability that the collateral constraint becomes slack depends on loan maturity only for fixed rate mortgages while the probability that the non-negativity constraint becomes binding grows with loan maturity regardless of the contract type. As a result, muti-period loans not only weaken monetary and macroprudential policy, but also introduce asymmetry into their transmission.