The velocity of money and money demand at the zero lower bound

I have been confused with the relationship between the money demand and the velocity of money.

The quantity theory of money implies that the greater the money demand is the slower the velocity of money will be at the given money market equilibrium, assuming other conditions remain the same. In other words, the more money the people demand, the longer at their hands the money will stay.

However, somewhat the situation in the U.S. economy does not seem to fit this theory. Even though the velocity of money is very low, the interest rate is also quite low and most of the expanded Fed monetary base stays within the Fed vaults, indicating the demand for money is low. It appears the quantity theory of money is being violated.

I realized that the problem of my first intuition lies within something basic in economics that most undergraduate students are struggling with : the difference between movement along the curve and shift of the curve. I suspect the following description shows what is happening.

1) The Fed has increased monetary base and set its interest rate target at zero, and so M1 and M2 have increased accordingly.

2) Since the quantity of money in the market has increased and the interest rate has fallen to zero, the quantity of money demanded by people has increased as much as that along the money demand curve. As a result, the velocity of money has fallen.

3) However, this increased quantity of money is not large enough to restore full employment given the assumption that the money demand itself has fallen, i.e., the money demand curve has shifted downward drastically. The nominal interest rate at zero is not low enough.

4) Therefore, the current velocity of money is not slow enough to keep the newly printed money at people's hands so that they will be able to consume and invest. The newly printed money has disappeared too quickly to the Federal Reserve vaults to stimulate the economy.

If my speculation is right, then we really don't have to expect hyperinflation will occur sooner or later. The money supply is still too tight and the money demand is too low.