We study the impact of the Federal Reserve's pandemic-era Mortgage-Backed Security purchases (QE4) on housing markets and consumer inflation. Using mortgage market segmentation, we generate a cross-sectional interest rate instrument to capture areas more heavily affected by Fed purchases in the conforming mortgage market. We find QE4 substantially decreased mortgage rates, raised house prices and rents, and lowered local unemployment. We interpret these results through a quantitative spatial model, and estimate substantial impacts of mortgage purchases on aggregate house prices and consumer inflation. Our findings suggest that unconventional monetary policy can meaningfully stimulate housing demand and economic activity, but may also amplify inflationary pressures and housing affordability tradeoffs.