The aim of this paper is to show how housing tenure (rented vs. owner-occupied) affects monetary policy. I propose a dynamic stochastic general equilibrium model with housing, both owned and rented. First, I analyze how, in the model, preference parameters, fiscal incentives, and institutional factors determine the rental market share and the residential debt-to-GDP ratio. Then, within this framework, I study how the transmission and optimality of monetary policy differ depending on these factors. From a positive perspective, impulse responses illustrate differences in the monetary transmission mechanism. I find that of all factors, tax incentives generate the largest differences. In normative terms, results show that when the relative size of the rental market is larger, monetary policy is more stabilizing. An optimal monetary policy analysis also suggests that in this case, monetary policy should respond more aggressively to inflation and disregard output, because the financial accelerator effects are weaker.