A brief excerpt:
It is important to understand that housing is a key transmission mechanism for Federal Open Market Committee (FOMC) policy. There are several channels according to economist Frederick Mishkin: Housing and the Monetary Transmission Mechanism
By raising or lowering short-term interest rates, monetary policy affects the housing market, and in turn the overall economy, directly or indirectly through at least six channels: through the direct effects of interest rates on (1) the user cost of capital, (2) expectations of future house-price movements, and (3) housing supply; and indirectly through (4) standard wealth effects from house prices, (5) balance sheet, credit-channel effects on consumer spending, and (6) balance sheet, credit-channel effects on housing demand.
So, when the FOMC raises rates, housing is a key target. For example, higher rates change the trade-off between buying and renting, and also changes the calculation for investors. Higher rates have already slowed down the “home ATM” (Mortgage Equity Withdrawal) and will likely impact demand (not yet!).
There is much more in the article.