RE:RE:RE:RE:RE:RE:RE:RE:RE:RE:RE:No buyers ,no sellers.. Well, shelter costs are measured too, you can find the data where I posted which includes "rent of primary residence". Shelter costs inflation from 2019 to 2021 was 2.85%.
The higher price of housing (as in buying) doesn't lead to direct and straight inflation to everyone. If you are going from renting to buying a house, the slope will be steeper. If you already own a home, you don't owe more even if your property value increases. Also, the rents move at a pace of their own, which will reflect the cost of financing more than the cost of purchasing a house/apartment complex.
Looking at the monthly cost of owning a property, even for a new buyer, right now, the increase in top line cost doesn't lead to dramatic monthly cost increases. In 2019, the base federal reserve rate was 2.25% and it is now 0%. Let's take that median price (290k in 2019 and 380k in 2021 using your number), assume cash down of 40k, use a 25 years term payment, a 5 years fixed rate, and see what the monthly payment would be at 3.75% and 1.50% (base rate + bank spread): In 2019, the payment would be 1 281$ and in 2021, 1 359$. That works out to an increase of 3% on the payment number, so basically, considering all the economic variables, the inflation on the payment has increased by 3% yearly. This is in line with what was measured for shelter costs in the CPI index from 2019. So, even if the value increase looks high, you also need to consider the financing cost, which has come down sharply from 2019 to get the impact on renters/owners.
When rates do increase, however, then unless the price for new homes come down, then the increase in rates will contribute to inflation on shelter prices. If interests rate go back to 3.75%, then that 1 359$ payment would surge to 1 742$, so if it happens over 2 years would mean around 12% increase/inflation. Since home values rarely tend to go down unless the economy is really bad, then as the rates increase, unless done really slowly, chances are shelter costs inflation will be higher going forward than from 2019 to 2021.
In the past, the banks have increased rates at times they shouldn't have and pushed the economy into economic downturns. Also, unless the economy strenghtens, and should inflation starts going back towards the 3ish % in April/May with a curve pointing down, imo, it will change the Fed's plan and they won't make the three forecast raises. That's pretty much the story of what happened between 2010 and 2015, they would forecast hikes and then push them further down the road time and time again.