We study the two-way relationship between fixed-rate mortgages (FRMs) and monetary policy in a panel of up to 35 countries over the last two decades. The dataset includes quarterly information on the composition of mortgage flows and stock by type of rate-fixation and monetary policy shocks cleaned of information effects. Using instrumental-variablel local projections, we find both path- and state-dependency in monetary transmission. Monetary policy shapes mortgage choice, increasing (decreasing) the share of FRMs during easing (tightening) cycles. Over time, this mechanism alters the composition of the outstanding mortgage stock which, in turn, affects the central bank's ability to stabilize the economy ex-post. A greater (lower) prevalence of FRMs weakens (strengthens) monetary policy transmission to key macro-variables.