Saturday, April 17, 2010

The Money Multiplier

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.


  1. Welcome to the econoblogosphere, by the way! (I only found your very good blog via David Andolfatto and Stephen Gordon. (For some reason you don't seem to show up on Economics Roundtable )

    I have been reading through your papers on "New Monetarism" with pleasure. There's a lot there I like. But I think you are missing some lessons that were learned by some Old Monetarists/Old Keynesians. I'm thinking particularly of the "disequilibrium money" approach, for want of a better name. Clower/Yeager, etc.

    I'm going to take issue with you on this post. Here's some points for starters:

    1. Demand deposits are media of exchange, and refrigerators aren't. Milton Friedman's analogy between money and durable goods is OK as far as it goes, but it doesn't go very far. In a monetary exchange economy, an excess demand for the medium of exchange will cause an excess supply of all other goods; an excess demand for refrigerators will not cause an excess supply of all other goods. (Yes, I am contradicting Walras' Law).

    2. Yes, there are degrees of liquidity. But sometimes, and in this case, a difference in degree becomes a difference in kind. That good which is the most liquid behaves in a qualitatively different way from all others. In nearly all cases, we convert even liquid assets like T-bills into money before we buy something else.

    3. Demand deposits do (often) serve as media of exchange, just like currency. commercial banks net out offsetting transactions at the central clearing house; only the difference is settled in reserves. So demand deposits (unlike refrigerators), really are special, and are like currency.

    4. Suppose refrigerators required 10% reserves. If I buy a new $100 fridge I have to include the opportunity cost of holding an extra $10 in reserves, as part of the cost of owning a new fridge. Not a big deal, especially in the limit as required reserves go to 0%. But, if an *individual* commercial bank extends an extra $100 in loans, by creating an extra $100 in demand deposits, what happens? The borrower did not take out a $100 loan just so he could hold an extra $100 in deposits. He (presumably) borrowed the $100 so he could spend it. And when he spends it the proceeds will almost certainly be deposited in a different bank. So our first bank loses $100 in reserves, *regardless of whether the required reserve ratio is 10%, 0%, or 100%*. At the margin, it is as if an individual bank faces a 100% reserve ratio. So the cots of making a $100 loan, and expanding deposits by $100, at the margin, is the cost of losing (or needing to borrow) $100 in extra reserves. So the supply (i.e. the supply price, or supply curve) of reserves affects deposit creation even under 0% desired reserve ratio. And it does so to a far greater extant than a 10% reserve ratio on fridges affects the demand for fridges. It is as if there were 100% required reserve ratio on fridges, at the margin.

    I know I must be about the last economist alive who still thinks there's some truth in the old textbook story. But there it is!

  2. Hi Nick. Thanks for reading my stuff, and I appreciate the comments. I didn't mean to have you take the refrigerator analogy too literally - I just wanted to use some arbitrary asset (and make the story funny) and I was in the kitchen at the time. Steve

  3. Hi Steve:

    FYI, the originator of the money multiplier was:

    Crick, W.F. (1927), The genesis of bank deposits, Economica, vol 7, 1927, pp 191–202.

    I got the citation from the wikipedia article on fractional reserves.

    Also, my personal favorite money multiplier analogy starts with the observation that a checking account dollar is actually a call option on a green paper dollar, with a strike of zero and no expiration. Option pricing theory says that the issue of options does not systematically reduce the value of the base security, since options do not affect the assets and liabilities of the issuer of the base security. In the same way, the quantity of checking account dollars does not affect the value of green paper dollars, since the Fed's assets and liabilities are unaffected by the actions of private banks.

  4. With respect to Nick Rowe's comment: A bank creating a chequing account to balance a new loan needs central bank cash on hand to the extent that cheques its customer writes are not offset by cheques that its customers deposit. And this need for central bank cash could be higher or lower than a reserve requirement.
    Glad to see your new blog,
    Another Canadian!

  5. Yes, that's a good point. Bank liabilities are being exchanged all the time using checks (cheques in Canadian English), debit cards, and other means. Some of this may involve "on us" transactions - e.g. I may write you a check, and we both have accounts at the Bank of Montreal. For other transactions, there needs to be interbank settlement, which is done through interbank exchanges (by Fedwire in the US, or through LVTS in Canada) of reserves. There is thus a transactions demand for reserve balances. However, note that the transactions are made only during the trading day. Overnight the reserves just sit - they are doing nothing but potentially earning interest. Typically in Canada, overnight reserves are essentially zero (not right now, but these are unusual times). In the US, what counts toward required reserves, and the reserves that the Fed pays interest on, are an average of reserves held overnight over a 2-week period.

  6. Money, banks, loans, reserves, capital, and loan officers

    I like this comment (Posted by: JKH | November 29, 2009 at 05:32 PM)

  7. Interesting. I'll write on bank capital sometime soon.

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