When QE was first suggested a few years ago, the doomsayers and inflation-phobes predicted hyperinflation would result from the large amount of money printing involved in QE. One reason inflation didn't increase was as follows.
As Joseph Huber and James Robertson explain in their work "Creating New Money", the freedom that private banks have to create money from thin air and lend it out means that those banks can undercut existing savers. As Huber & Robertson put it:
"Allowing banks to create new money out of nothing enables them to cream off a special profit. They lend the money to their customers at the full rate of interest, without having to pay any interest on it themselves. So their profit on this part of their business is not, say, 9% credit-interest less 4% debit-interest = 5% normal profit; it is 9% credit-interest less 0% debit-interest = 9% profit = 5% normal profit plus 4% additional special profit."
But if the existing rate for a zero or near zero risk loan is about 0%, then the scope for the above undercutting is much reduced! Huber and Robertson's "creaming off" becomes much less profitable.
Put another way, the excess amount of base money currently sloshing around at the start of 2016 will not be inflationary until central banks attempt to impose a significant rise in interest rates. And at that point they may well find their efforts thwarted by the "Huber & Robertson" phenomenon.
A recent article by Christopher Phelan of the Minneapolis Fed deals with the potential for that excess supply of reserves to be inflationary.
George Selgin also wrote an article about the "excess reserves" scenario. He actually considered what would happen if there was an economy where the only form of money was central bank money and privately issued money (i.e. fractional reserve banking) was then allowed. But that comes to the same thing as the above "excess reserves" scenario. Selgin's conclusion was that there'd be excess inflation for a while - until the stock of reserves (in real terms) was down to the minimum that private banks needed.
One solution to the latter form of inflation would be to force private banks to hold a larger stock of reserves.