> Home prices vary inversely with interest rates. This is true if all else is equal. In theory, however, the Fed is supposed to raise interest rates when the e

> Home prices vary inversely with interest rates. This is true if all else is equal. In theory, however, the Fed is supposed to raise interest rates when the economy is heating up, which implies buyers are being paid higher salaries, which implies their income (step 2 of your chain) is higher. In theory this could neutralize some or all of the effect of the interest rate increase.