One issue with the Fed is how they look at inflation. Their favorite measure is the core PCE deflator. The problem? It has no assets in it. Here’s inflation as measured by PCE. Find the tech or housing bubbles. Oh right, they aren’t there.
As we continue with the reopening, one issue with the Fed will be actual inflation of food, travel, etc. We can see that in the data.
But the real problem is if the Fed keeps rates too low too long, an asset bubble can build without it showing up in inflation data.