A recent piece published by the St. Louis Fed concluded that inflation has been low because of a sharp decline in the velocity of money reflecting money hoarding by the public. This conclusion got a great deal of attention by the talking heads on financial tv. The problem is that the conclusion is very misleading because it used the monetary base (bank reserves plus outstanding currency) as the money supply rather than a measure of money actually used as such by the public such as M2 or M1.
Once upon a time, the monetary base and these measures of money moved together so dividing any of them into nominal GDP gave similar results for the various velocities. The financial crisis changed that dramatically. The Fed's purchases of securities created bank reserves as usual, but the banks didn't expand lending and investing sufficiently to maintain a similar growth rate for retail money. You might say that the banks 'hoarded' reserves, which caused money growth to slow. The velocity of M1 and M1 also declined (reflecting money hoarding), but not by nearly as much as the 'velocity' of bank reserves and the monetary base.
Very roughly speaking, in recent years, M2 has grown roughly 7 percent per year and its velocity has declined roughly 3 percent per year to yield an expansion of nominal GDP of roughly 4 percent per year (about half inflation and half real). By these rough estimates, one can say that the public has been 'hoarding' money-reflected in the 3 percent decline in velocity. But that is a much smaller bit of hoarding than implied by the St. Louis Fed's article. Much of the hoarding that has taken place has been the hoarding of reserves by the banking system which caused the money supply growth to be much lower than it would have been.
A more accurate way to explain what happened is not that the public has been doing massive hoarding, but that the hoarding of bank reserves by the banks has diminished money supply growth greatly and what growth we have had has been partially offset by the public hoarding of money. To imply that the shortfall in nominal GDP growth is entirely the fault of public money hoarding is wrong.