Scott Sumner  

One multiplier to rule them all! (apologies to Nick Rowe)

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There's a vigorous debate about the money multiplier taking place in the blogosphere. On one side is everyone from MMTers, to new monetarists, to market monetarists. On the other is Nick Rowe. And I'm sort of in the middle, but leaning against Nick. (Generally I'm most comfortable in Nick's position, where everyone is against me.)

The money multiplier is technically defined as M/B, where M is some monetary aggregate and B is the monetary base. As a practical matter, the multiplier is not useful unless the ratio is somewhat stable, or at least varies predictably in response to changes in the base. And even that's merely a necessary condition for it being useful, not a sufficient condition. Nick seems to have a slightly different definition of multiplier:

And please don't be a knuckle-dragger and assume the money multiplier refers to the multiplier effect of an initial decision by the central bank only. Yes, the textbook usually illustrates the money multiplier with an example where the initial shock comes from the central bank, just as it usually illustrates the keynesian multiplier with an example where the initial shock comes from fiscal policy. But the money multiplier, just like the keynesian multiplier, multiplies anything that gets the ball rolling.
I'm not sure exactly what Nick is referring to here, but I imagine it is something like the following. Suppose a drug dealer shows up at a boatyard and spends $1,000,000 in cash on a new yacht. The boat dealer then deposits the cash in a bank, and the deposit multiplier (different from the money multiplier, but related) does its magic.

That sort of example is subject to the same sort of criticism as the fiscal multiplier. Recall that government spending tends to provide an upward impetus to total spending, but it quickly dissipates if velocity is unchanged. And its hard to see how a one time increase in government spending has any persistent impact on V. Similarly the drug money boosts deposits and M1 in the short run, but the effect quickly dissipates if the drug dealer rebuilds up to his desired cash balances. In other words, unless C/D changes permanently, the effect is minor (especially when expected future AD is what matters.) That's not to say either Nick's claim or the Keynesian claim is "wrong", just that one must be careful for essentially identical reasons.

In theory there are an almost infinite number of money multipliers. Indeed if money is neutral, then you could argue in favor of any ratio X/B representing a sort of "money multiplier." After all, a once and for all increase in the base is supposed to cause a proportional increase in all nominal aggregates, indeed all nominal variables of any kind (measured in dollar terms.) So if M2 is 10 times the size of the base, and the nominal value of all real estate is 100 times the size of the base, the a given increase in the monetary base should (ceteris paribus) cause M2 to rise by 10 times that much, and it should cause the nominal value of all real estate to rise by 100 times the increase in the base, at least in the long run. And that's generally what happens in response to exogenous increases in the base (In the short run prices are sticky and things get much more complicated.)

Here I'd like to suggest that within the near infinite set of all X/B ratios, there is only one of interest to monetary economists, the ratio of the policy target to the base. Because multiplier opponents like David Glasner, and multiplier supporters like Nick Rowe, and moderates like myself all seem to find NGDP an acceptable monetary target, I'd argue that NGDP/B is the only multiplier of interest.

The more common name for this money multiplier is "velocity," and more precisely "base velocity." I have to be precise, because there are lots of different definitions of velocity (M1 velocity, M2 velocity, etc.), which vary wildly in magnitude. And that's because velocity isn't really about velocity, it's about 1/V, aka money demand (as a share of national income.)

Although velocity is not stable enough to make money supply targeting a good policy, it's a useful pedagogical device, a way of getting students to visualize concepts such as the neutrality of money. If everyone could agree to stop calling NGDP/B "velocity", and start calling it "the money multiplier," I'd have a much more positive view of the money multiplier.

I do understand Nick's perspective. Whereas I think of money in terms of its role as the medium of account (the "MOA," which is the monetary base in our system) he thinks of money in terms of its role as a medium of exchange. That means he thinks the broader aggregates, not the narrow base, have the key causal role to play in determining NGDP and the price level. If I looked at things that way I'd probably be more sympathetic to the multiplier, at least as a pedagogical device.

Think of it this way. M1 is equal to the base times the M1 money multiplier. So if you think M1 and M1 velocity are what really matters, there is good reason to pay attention to the money multiplier. If not, then not.

PS. Between 1929:2 and 2007:2 the base rose by 120 fold and GNP rose by 138 fold in the US. I view that base increase as mostly exogenous, as it mostly reflected the exogenous monetary policy decision to switch from gold to cash as a MOA. The reason GNP grew a bit faster is that base velocity rose from 14.9 to 17.1, presumably due to lower reserve requirements (currency velocity actually fell). Since then base velocity has collapsed to less than 5, due to zero interest rates plus interest on reserves. Will velocity rise again when rates normalize? That depends on what they do with IOR. I'd guess it will rise, but not all the way back.

PPS. Nick starts off his post as follows:

Alone again or, just me and the money multiplier, against the world of trendy sophisticates who have put aside such childish things. It brings out the reactionary contrarian in me. And the world needs more reactionary contrarians, to help provide negative feedback against the faddish bubble multiplier of popular theory.
As a defender of Fama's monetary views, which I would characterize as "banks don't matter, it's all about the currency stock," you know where I stand on the trendy sophisticates/reactionary divide. There is nothing less sophisticated than cash, except perhaps coins. It breaks my heart that I cannot stand shoulder to shoulder with Nick on this issue.

BTW, I don't believe Nick actually views his opponents as "trendy sophisticates," as the arms of sophisticates tend to be too short for their knuckles to drag on the ground.


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CATEGORIES: Macroeconomics , Money



COMMENTS (5 to date)
Nick Rowe writes:

Scott: "I'm not sure exactly what Nick is referring to here, but I imagine it is something like the following. Suppose a drug dealer shows up at a boatyard and spends $1,000,000 in cash on a new yacht. The boat dealer then deposits the cash in a bank, and the deposit multiplier (different from the money multiplier, but related) does its magic."

Yep, that is one example of what I have in mind (only a permanent fall in desired C/D). Or it might be a shock from the banks. But it all depends on how the central bank reacts. The central bank's job is to stamp out those multipliers.

MikeDC writes:

@ Nick,
Why would the CB want to stamp out those multipliers?

Doesn't the multiplier reflect the actual ground level productive activity in the economy? The velocity of the money out of the back reflects the combined judgement of the bank about its lending opportunities and the borrower about their borrowing against their future productive opportunities (e.g. a guy shows up for a home or business loan because he thinks he'll be able to cover the loan, and the bank lends the money because the bank thinks he's right).

But that multiplier is purely "descriptive" and changing based on the assumptions of the market participants. The CB obviously can't operate on a micro level and have any better info about whether person X and Bank 2 are correct in their assumptions.

At best, can operate on those assumptions. They can see velocity is falling like a rock and take a stance of easier money, such that they put a financial gun to banks/individuals heads that says "keep lending and keep producing, or we'll inflate away your accumulated wealth". Or they can do the opposite and say "money is flowing too quickly and too easily, you're not actually going to be able to collect/pay these loans. So we're going to slow the pace of money growth, and if you're dumb enough to keep making these sorts of transactions, you're going to get hurt".

In both cases, of course, the central bank is at the sledgehammer level and the individual is at the ant level. It's very easy to make a mistake and screw things up pretty substantially.

Scott Sumner writes:

Nick, That's right, and I probably should have emphasized that there is much I agree with in your post, as well as your other recent posts.

MikeDc, I'll try to speak for Nick, but am not certain how he'd answer. A change in money demand and/or the multiplier might make lots of sense from a microeconomic perspective, but the macro effects might still be quite harmful due to sticky wages and prices. That's what makes money different, everything else is priced in money terms (or as Nick would emphasize, everything else is purchased with money.)

Having said that, there are cases where one would want to accommodate those shocks, it all depends on the impact on NGDP.

willy2 writes:

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Lorenzo from Oz writes:

If you go back to Irving Fisher's original equation, what he is really on about is turnover, but he already had a 'T' for transactions in his equation. Hence velocity as a substitute, causing endless confusion if one actually understands the scientific concept of velocity.

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