When I was at the University of Iowa, I was the Chester Phillips Professor. When my Dean, Gary Fethke (who I now appreciate as a perceptive and skilled administrator - but that's another story) told me he was going to make me a chaired professor (more like a stooled professor actually), he told me a story about Chester Phillips. Apparently Chester was thought to be the inventor of the money multiplier. I have no idea who else might lay claim to this dubious honor, but my response to Gary was something like: "That's too bad, the money multiplier is probably the most misleading piece of monetary economics known to humankind." Gary's response was something like: "Well, Steve, that's very interesting, but if you share that thought with any of the College donors you can be the Sam Schwartz Professor of toilet cleaning."
Yesterday, at the beginning of a lunchtime seminar at the St. Louis Fed, I was eating my tuna sandwich waiting for the seminar to start, and the money multiplier came up (don't remember how). I said something akin to what I said years ago to Gary Fethke. Then, David Levine frowned at me (the look that usually says: "I think you said something stupid, but I'm going to grill you to find out") and said: "What's wrong with a fractional reserve requirement?" At the time I was too tired to argue with David (which led to a later conflagration - another story), and just dropped it.
After some thought, here's a story that might help David. Suppose a world where every owner of a refrigerator has an account with the central bank. Call this account a reserve account, and require every refrigerator owner to hold reserves - say 10% of the market value of the refrigerator. Now, in our undergraduate Economics of Refrigerators class, we could tell a story like the following. Suppose that the central bank makes a transfer of more reserves to each refrigerator owner (lump sum, in proportion to existing reserves, whatever). Refrigerator owners find themselves with excess reserves, and they spend them on goods and services (the central bank provides a full array of transactions services associated with its reserve accounts). Ultimately the reserves are spent on more refrigerators, which increases required reserves, and there is a multiplier process. In equilibrium the nominal quantity of refrigerators rises - in this case by 10 times the increase in the quantity of reserves. The refrigerator multiplier is ten.
Now maybe you see the analogy at this point, but maybe not, so I'll explain it. The money multiplier story is no more than a description of the obvious truth that, under a fractional reserve requirement, if the reserve requirement binds, the nominal quantity of the objects that one must hold reserves against must expand by a fixed multiple of a reserve injection by the central bank. But that is as far as it goes. Sometimes undergraduate money and banking professors spend an enormous amount of time explaining the multiplier process, and there is essentially no economic content to it. It sounds like something magical and mysterious is going on, but the story is actually obvious, and misleading, for the following reasons:
1. It makes us think that what is important about central banking is the control of the quantity of "money" - some aggregation of assets that appear to serve a medium of exchange role. Liquidity is actually a matter of degree, and we can't arbitrarily draw the line between assets that have some "moneyness" property, and others that do not. Currency is exchanged in many types of transactions. Transactions deposits at banks are traded in other types of transactions. Transactions using different payments instruments have different arrangements for settlement. Treasury bills have liquidity value in part because they serve as collateral in some types of lending in financial markets. Reserves serve a transactions role in interbank clearing and settlement.
2. Transactions deposits at banks are not the same as outside money (just as refrigerators are not reserves) - one is a private liability backed by a bank's portfolio of assets, the other is a public liability backed by the central bank's portfolio of assets, and outside money is not a promise to any explicit payoffs.
3. A central banker whose intuition comes from money multiplier stories has no idea how to think about a banking system with no reserve requirements. Some central bankers are pretty smart though - in New Zealand and Canada, for example, they have figured this out.
4. Under the current regime where large amounts of excess reserves are being held by banks, a central banker with undergraduate money and banking intuition will again get lost.
5. There is only one question to which the money multiplier gives us a useful answer: How much will assets subject to the reserve requirement increase in nominal terms in the long run if there is an unbacked, one-time increase in reserves? But if I understand the neutrality money, I know the answer to the question anyway. Otherwise, the money multiplier is in general not policy invariant - i.e. the Lucas critique comes into play.
For more details, read the "Intermediation" section of this paper.