It's a complicated relationship. The prices of assets are related to the price of debt (the cheaper the debt, the more expensive the asset). Housing is an asset

It's a complicated relationship. The prices of assets are related to the price of debt (the cheaper the debt, the more expensive the asset). Housing is an asset that pays a coupon (rent), so it acts a bit like a bond. Bonds have been riding the coattails of decreasing interest rates for the last 40 years - if interest rates increase then stocks, houses, bonds etc are going to deflate. While inflation with low interest rates might increase the value of assets - inflation that leads to higher interest rates might actually do the opposite. So it ends up being a choice of the central bank which way to push this thing (although there is a lean towards keeping interest rates lower for longer because of the size of the U.S. government debt interest payments)