If one assumes a constant money multiplier, then the dramatic increase in the monetary base since mid-2008 implies a huge (and frighteningly inflationary) increase in the money supply.
The growth of the Fed’s balance sheet, which has been funded by an increase in commercial banks’ reserve balances at the Fed, has sparked fears that the “money multiplier” mechanism would translate those reserves into an explosion in bank lending, bank deposits, and inflation. None of these things has happened, because the money multiplier no longer makes sense given the institutional framework of the contemporary banking system. In spite of being almost totally divorced from reality, the money multiplier is still taught in undergraduate economics textbooks, with much resulting confusion.While there have been quite a number of changes in the "institutional framework," which textbooks (and professors) may not want to treat in detail, the most basic flaw in the analysis which is being attributed to "undergraduate economics textbooks" is naively assuming a constant money multiplier.
I don't think that is a fair accusation. Indeed, the only reason why money multipliers are interesting to talk about in class is that they can change. In normal times, it makes sense for banks to hold as few reserves as they can get away with (they can lend excess reserves on the "interbank" loan market, and if they're short, they can borrow them, too). But in unusual times, the calculation changes and banks respond to a riskier environment by holding more reserves, which reduces the money multiplier.
This issue normally enters an undergraduate economics course in a discussion of the Great Depression. Milton Friedman and Anna Schwartz showed that the money multiplier fell during the banking panics of the early 1930's. Because of the fall in the money multiplier, the money supply actually was decreasing even as the Fed increased the monetary base. This example has become part of the case the Fed bungled the depression. Both the Mankiw and Abel and Bernanke intermediate macroeconomics textbooks discuss this case immediately after algebraically deriving the money multiplier.
The sudden increase in the monetary base (blue line) occurred in late 2008. In the same period, deposits (red) also rose, but much less dramatically, which means there was a large increase in the reserve ratio.
Fed announced on October 6, 2008 that it would begin paying interest on reserves. This is is the dominant factor in the increase in both the quantity of reserves and the reserve ratio. Interest on reserves does indeed represent a significant change in the institutional framework which isn't included in traditional textbook treatments.
However, looking a little more closely at the graph one can see that reserves began to increase in September. Reserves rose from $9bn on Sept. 10, to $47bn on Sept. 17 and $104bn on Sept. 24 - a more than tenfold increase over two weeks. Those two weeks, of course, were the absolute worst days of the financial panic of 2008 (Lehman declared bankruptcy on Sept. 15). At a time when the interbank lending market suddenly appeared risky, it is not surprising that banks would exercise more caution and increase reserves, thereby reducing the money multiplier. And that is likely quite consistent with what students read in their undergraduate economics textbooks.