This paper investigates the mortgage channel of monetary policy transmission to home purchasing behaviors of first-time home buyers and incumbent homeowners. Between 2009 and 2019, the first-time home buyer share of home purchases fell from 35% to 22%, a period in which mortgage rates fell from nearly 7% to 3.5%. First, I construct a new mortgage rate-specific monetary policy shock to use as an IV for mortgage rate changes which predicts future mortgage rates better than existing monetary policy shocks. Next, I find new empirical evidence that a negative 25 basis point mortgage rate shock lowers the first-time buyer share of home purchases by 80 b.p. in the first three months after the shock. These results are more pronounced in CBSAs with higher shares of high LTV constrained borrowers which tend to be areas with more severe housing crises. Finally, I construct a lifecycle model with a housing ladder, heterogeneous agents, and a system of housing-related taxes calibrated to my empirical findings. I find that a one-time unanticipated negative one p.p. transitory shock to mortgage rates causes potential first-time home buyers to face a 0.12% consumption-equivalent welfare losses and purchase their first home 0.1 years later while incumbent home owners receive welfare gains of 0.1%.