The issue for housing prices vis-a-vis interest rates is the degree to which rents increase along with interest rates (which eventually reflect the general level of price inflation). If rates rise meaningfully more than rents then housing prices will fall. If rents rise more or less as much as interest rates then housing prices will be largely unaffected even if rates rise (see the 70s and early-80s for an example of this).
If the value (V) of a perpetual stream of cashflows (CF) is denoted by:
V=CF/(R-G)
where R is the interest rate and G is the growth in the cash flows, you can see that if G (re: rents) is increasing at the same rate as R (rates)… the denominator stays the same and the value is unchanged even as rates rise.
So, the issue of the impact of higher interest rates on housing prices must be discussed in the context of the degree to which rents follow the general level of inflation (the latter will drive interest rates).
