A correction to your analysis. Rate cuts will more likely reduce the housing portion of the CPI. The CPI housing segment doesn't measure housing prices, they, instead, measure homeowner's equivalent rent, where the BLS estimates what it would cost the homeowner to rent an equivalent piece. There are some quirks, but basically it tracks mortgage payments. So, if house prices go up but the cost of carrying the mortgage due to lower rates goes down, the housing inflation could be neutral or negative. This is why during near zero rates and 3% mortgage rates, housing inflation was low despite a house price boom.
A correction to your analysis. Rate cuts will more likely reduce the housing portion of the CPI. The CPI housing segment doesn't measure housing prices, they, instead, measure homeowner's equivalent rent, where the BLS estimates what it would cost the homeowner to rent an equivalent piece. There are some quirks, but basically it tracks mortgage payments. So, if house prices go up but the cost of carrying the mortgage due to lower rates goes down, the housing inflation could be neutral or negative. This is why during near zero rates and 3% mortgage rates, housing inflation was low despite a house price boom.