I know higher rates mean lower home prices (generally) b/c people think monthly payments when buying a home.
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This makes sense intuitively, but is not borne out by historical experience. For example, housing prices increased dramatically during the 70s and early-80s even though rates were increasing, because rents were tracking (high) inflation. Folks bought as a hedge against future inflation despite the high interest rates.
That may or may not happen this time around. It’s too early to tell. I think higher interest rates will hurt the housing “recovery” for a while… but longer term it’s hard to say.