CAR –
I agree that there are many other factors, that is my whole point. You pointed out several, including demographics and other loan conditions besides interest rates. Therefore one cannot conclude that a 1% rate increase results in a X% price decrease. (or that it necessarily automatically results in a price decrease at all).
In the 2006 to 2010 time frame, rates declined in the context of declining GDP, growing unemployment, tightening of lending standards, and the gravity of market fundamentals (prices outstripped rents and incomes). It is obvious in hindsight that those factors trumped changes in interest rates.
If interest rates were to rise in the context of a growing economy, declining unemployment, and loosening lending standards, prices may or may not rise.
I am not insisting that rising rates always result in rising prices. I am simply pointing out that rising rates do not necessarily result in lower prices as borne out by the examples above.
People seem to believe in the model of an inverse relationship between prices and interest rates when in reality there is historically as much or more evidence of the opposite being true.