The data is out there, but really it's common sense. On the margin, a buyer purchases a house with a monthly payment he/she can afford. The monthly payment is determined based on the purchase price of the house and the interest rate. The higher the rate, the higher the payment. If rates raise, the margin buyer will no longer be able to purchase the same priced house. Prices must fall to clear the market. Yes, increased wages could help make up for the gap. Wages do not have to rise with interest rates (stagflation).
The last real period of rising mortgage rates was in the 70s. You can pretty clearly see that home prices were rising in spite of rising financing costs.
