The Uselessness of the Money Multiplier as Brilliantly Elucidated by Nick Rowe

Not long after I started blogging over two and a half years ago, Nick Rowe and I started a friendly argument about the money multiplier. He likes it; I don’t. In his latest post (“Alpha banks, beta banks, fixed exchange rates, market shares, and the money multiplier”), Nick attempts (well, sort of) to defend the money multiplier. Nick has indeed figured out an ingenious way of making sense out of the concept, but in doing so, he has finally and definitively demonstrated its total uselessness.

How did Nick accomplish this remarkable feat? By explaining that there is no significant difference between a commercial bank that denominates its deposits in terms of a central bank currency, thereby committing itself to make its deposits redeemable on demand into a corresponding amount of central bank currency, and a central bank that commits to maintain a fixed exchange rate between its currency and the currency of another central bank — the commitment to a fixed exchange rate being unilateral and one-sided, so that only one of the central banks (the beta bank) is constrained by its unilateral commitment to a fixed exchange rate, while the other central bank (the alpha bank) is free from commitment to an exchange-rate peg.

Just suppose the US Fed, for reasons unknown, pegged the exchange rate of the US dollar to the Canadian dollar. The Fed makes a promise to ensure the US dollar will always be directly or indirectly convertible into Canadian dollars at par. The Bank of Canada makes no commitment the other way. The Bank of Canada does whatever it wants to do. The Fed has to do whatever it needs to do to keep the exchange rate fixed.

For example, just suppose, for reasons unknown, the Bank of Canada decided to double the Canadian price level, then go back to targeting 2% inflation. If it wanted to keep the exchange rate fixed at par, the Fed would need to follow along, and double the US price level too, otherwise the US dollar would appreciate against the Canadian dollar. The Fed’s promise to fix the exchange rate makes the Bank of Canada the alpha bank and the Fed the beta bank. Both Canadian and US monetary policy would be decided in Ottawa. It’s asymmetric redeemability that gives the Bank of Canada its power over the Fed.

Absolutely right! Under these assumptions, the amount of money created by the Fed would be governed, among other things, by its commitment to maintain the exchange-rate peg between the US dollar and the Canadian dollar. However, the numerical relationship between the quantity of US dollars and quantity of Canadian dollars would depend on the demand of US (and possibly Canadian) citizens and residents to hold US dollars. The more US dollars people want to hold, the more dollars the Fed can create.

Nick then goes on to make the following astonishing (for him) assertion.

Doubling the Canadian price level would mean approximately doubling the supplies of all Canadian monies, including the money issued by the Bank of Canada. Doubling the US price level would mean approximately doubling the supplies of all US monies, including the money issued by the Fed. Because the demand for money is proportional to the price level.

In other words, given the price level, the quantity of money adjusts to whatever is the demand for it, the price level being determined unilaterally by the unconstrained (aka “alpha”) central bank.

To see how astonishing (for Nick) this assertion is, consider the following passage from Perry Mehrling’s superb biography of Fischer Black. Mehrling devotes an entire chapter (“The Money Wars”) to the relationship between Black and Milton Friedman. Black came to Chicago as a professor in the Business School, and tried to get Friedman interested in his idea the quantity of money supplied by the banking system adjusted passively to the amount demanded. Friedman dismissed the idea as preposterous, a repetition of the discredited “real bills doctrine,” considered by Friedman to be fallacy long since refuted (definitively) by his teacher Lloyd Mints in his book A History of Banking Theory. Friedman dismissed Black and told him to read Mints, and when Black, newly arrived at Chicago in 1971, presented a paper at the Money Workshop at Chicago, Friedman introduced Black as follows:

Fischer Black will be presenting his paper today on money in a two-sector model. We all know that the paper is wrong. We have two hours to work out why it is wrong.

Mehrling describes the nub of the disagreement between Friedman and Black this way:

“But, Fischer, there is a ton of evidence that money causes prices!” Friedman would insist. “Name one piece,” Fischer would respond.The fact that the measured money supply moves in tandem with nominal income and the price level could mean that an increase in money casues prices to rise, as Friedman insisted, but it could also mean that an increase in prices casues the quantity of money to rise, as Fischer thought more reasonable. Empirical evidence could not decide the case. (p. 160)

Well, we now see that Nick Rowe has come down squarely on the side of, gasp, Fischer Black against Milton Friedman. “Wonder of wonders, miracle of miracles!”

But despite making that break with his Monetarist roots, Nick isn’t yet quite ready to let go, lapsing once again into money-multiplier talk.

The money issued by the Bank of Canada (mostly currency, with a very small quantity of reserves) is a very small share of the total Canadian+US money supply. What exactly that share would be would depend on how exactly you define “money”. Let’s say it’s 1% of the total. The total Canadian+US money supply would increase by 100 times the amount of new money issued by the Bank of Canada. The money multiplier would be the reciprocal of the Bank of Canada’s share in the total Canadian+US money supply. 1/1%=100.

Maybe the US Fed keeps reserves of Bank of Canada dollars, to help it keep the exchange rate fixed. Or maybe it doesn’t. But it doesn’t matter.

Do loans create deposits, or do deposits create loans? Yes. Neither. But it doesn’t matter.

The only thing that does matter is the Bank of Canada’s market share, and whether it stays constant. And which bank is the alpha bank and which bank is the beta bank.



So in Nick’s world, the money multiplier is just the reciprocal of the market share. In other words, the money multiplier simply reflects the relative quantities demanded of different monies. That’s not the money multiplier that I was taught in econ 2, and that’s not the money multiplier propounded by Monetarists for the past century. The point of the money multiplier is to take the equation of exchange, MV=PQ, underlying the quantity theory of money in which M stands for some measure of the aggregate quantity of money that supposedly determines what P is. The Monetarists then say that the monetary authority controls P because it controls M. True, since the rise of modern banking, most of the money actually used is not produced by the monetary authority, but by private banks, but the money multiplier allows all the privately produced money to be attributed to the monetary authority, the broad money supply being mechanically related to the monetary base so that M = kB, where M is the M in the equation of exchange and B is the monetary base. Since the monetary authority unquestionably controls B, it therefore controls M and therefore controls P.

The point of the money multiplier is to provide a rationale for saying: “sure, we know that banks create a lot of money, and we don’t really understand what governs the amount of money banks create, but whatever amount of money banks create, that amount is ultimately under the control of the monetary authority, the amount being some multiple of the monetary base. So it’s still as if the central bank decides what M is, so that it really is OK to say that the central bank can control the price level even though M in the quantity equation is not really produced by the central bank. M is exogenously determined, because there is a money multiplier that relates M to B. If that is unclear, I’m sorry, but that’s what the Monetarists have been saying all these years.

Who cares, anyway? Well, all the people that fell for Friedman’s notion (traceable to the General Theory by the way) that monetary policy works by controlling the quantity of money produced by the banking system. Somehow Monetarists like Friedman who was pushing his dumb k% rule for monetary growth thought that it was important to be able to show that the quantity of money could be controlled by the monetary authority. Otherwise, the whole rationale for the k% rule would be manifestly based based on a faulty — actually vacuous — premise. The post-Keynesian exogenous endogenous-money movement was an equally misguided reaction to Friedman’s Monetarist nonsense, taking for granted that if they could show that the money multiplier and the idea that the central bank could control the quantity of money were unfounded, it would follow that inflation is not a monetary phenomenon and is beyond the power of a central bank to control. The two propositions are completely independent of one another, and all the sturm und drang of the last 40 years about endogenous money has been a complete waste of time, an argument about a non-issue. Whether the central bank can control the price level has nothing to do with whether there is or isn’t a multiplier. Get over it.

Nick recognizes this:

The simple money multiplier story is a story about market shares, and about beta banks fixing their exchange rates to the alpha bank. If all banks expand together, their market shares stay the same. But if one bank expands alone, it must persuade the market to be willing to hold an increased share of its money and a reduced share of some other banks’ monies, otherwise it will be forced to redeem its money for other banks’ monies, or else suffer a depreciation of its exchange rate. Unless that bank is the alpha bank, to which all the beta banks fix their exchange rates. It is the beta banks’ responsibility to keep their exchange rates fixed to the alpha bank. The Law of Reflux ensures that an individual beta bank cannot overissue its money beyond the share the market desires to hold. The alpha bank can do whatever it likes, because it makes no promise to keep its exchange rate fixed.

It’s all about the public’s demand for money, and their relative preferences for holding one money or another. The alpha central bank may or may not be able to achieve some targeted value for its money, but whether it can or can not has nothing to do with its ability to control the quantity of money created by the beta banks that are committed to an exchange rate peg against the money of the alpha bank. In other words, the money multiplier is a completely useless concept, as useless as a multiplier between, say, the quantity of white Corvettes the total quantity of Corvettes. From now on, I’m going to call this Rowe’s Theorem. Nick, you’re the man!