Bob Murphy has a new article addressing criticism of the “money multiplier” model taught in many textbooks.  He does a nice job pushing back against some claims in a Bank of England report.  For instance, the BOE says:

A related misconception is that banks can lend out their reserves. Reserves can only be lent between banks, since consumers cannot have access to reserves accounts at the [central bank]

Murphy correctly points out that banks can lend out reserves, and then adds this:

Now it’s true that even here the authors of the Bank of England study could object that we don’t call it “reserves” when a member of the public holds currency, even though those same $20 bills were considered reserves when they sat in Acme’s vault.

But this is obviously a matter of semantics, not economics. For an analogy, consider this puzzle: would it be wrong to say that a department store “sells its inventory” to members of the public? After all, we only call it “inventory” when the store owns it—the “inventory” turns into “merchandise” when the customer walks out of the store. But clearly, there is nothing wrong economically with saying that a department store sells its inventory to the public. Likewise, there is nothing wrong with saying that a commercial bank, in granting new loans, lends out some of its reserves.

I like that analogy.  The BOE report also says:

While the money multiplier theory can be a useful way of introducing money and banking in economic textbooks, it is not an accurate description of how money is created in reality. Rather than controlling the quantity of reserves, central banks today typically implement monetary policy by setting the price of reserves—that is, interest rates.

This is rather misleading.  Prior to 2008, central banks like the Fed often controlled interest rates by adjusting the quantity of reserves.  Thus one could just as well say that central banks adjusted the quantity of reserves to a level that moved interest rates to a level that was expected to produce 2% inflation.  In that case, both the quantity of reserves and the interest rate are “endogenous”.  Today, central banks implement policy both by adjusting the quantity of reserves (QE) and by adjusting the interest rate paid on reserves.

I am even more skeptical of the value of the money multiplier than are the authors of the BOE study.  But I don’t accept their specific reasoning:

In reality, neither are reserves a binding constraint on lending, nor does the central bank fix the amount of reserves that are available. As with the relationship between deposits and loans, the relationship between reserves and loans typically operates in the reverse way to that described in some economics textbooks. Banks first decide how much to lend depending on the profitable lending opportunities available to them—which will, crucially, depend on the interest rate set by the [central bank]. It is these lending decisions that determine how many bank deposits are created by the banking system.

To me, this seems to confuse real and nominal variables.  Let’s step back a bit and look at how “the” money multiplier is just one of a virtually infinite number of money multipliers:

money multiplier = (broad money supply)/monetary base

Importantly, both money supplies in this ratio are nominal variables.  There are similar ratios for the annual production of crude oil in dollars and the monetary base, the value of common stock and the monetary base, the nominal value of revenue earned in the washing machine industry and the monetary base, and indeed any nominal variable divided by the monetary base.

There’s also a concept called “money neutrality”, which predicts that a one-time permanent change in the monetary base will not affect any real variables in the long run, including any of the various multipliers.  Thus a permanent doubling of the monetary base will, other things equal, permanently double the nominal output of the zinc mining industry, or the toaster manufacturing industry.

In these thought experiments, monetary policy is not having any long run real effects on any industry, including the banking industry.  The nominal amount of bank loans is thus determined by the central bank even as the real quantity is determined by industry specific factors, just as the real quantity of zinc and toaster output is determined by real factors specific to those two industries.  When the BOE says, “It is these lending decisions that determine how many bank deposits are created by the banking system.” they have to be referring to the real amount of bank lending, otherwise the claim makes no sense.  Does anyone seriously believe that bank “lending decisions” determined the nominal size of Zimbabwe’s banking industry during its hyperinflation?  But the money multiplier is comparing two nominal variables.

The money multiplier taught in textbooks is not “wrong” as long as the textbook explains that the multiplier changes over time.  But it’s also not useful.  Knowing that changes in the monetary base impact M1 or M2 is not helpful, because knowing the path of the broader aggregates adds almost nothing useful that we don’t already know by looking at the variables that really matter.

In my view, the only “multiplier” that is useful is NGDP/monetary base.  This ratio is generally not called a multiplier, however, it’s usually called “base velocity” (itself a very misleading term).