There has never been a money multiplier

In an interesting talk last week, San Francisco Fed president John Williams spoke about the need to modernize economics education. His remarks on the death of the “money multiplier” caught my eye:

The breakdown of the standard money multiplier has been especially pronounced during the crisis and recession. Banks typically have a very large incentive to put excess reserves to work by lending them out… If a bank were suddenly to find itself with a million dollars in excess reserves in its account, it would quickly try to find a creditworthy borrower and earn a return on that one million dollars…

But, this hasn’t happened—not at all. The Federal Reserve has added $1.5 trillion to the quantity of reserves in the banking system since December 2007. Despite a 200% increase in the monetary base—that is, reserves plus currency—measures of the money supply have grown only moderately….

Why has the money multiplier broken down? Well, one reason is that banks would rather hold reserves safely at the Fed instead of lending them out in the still struggling and risky economy. But, once the economy improves sufficiently, won’t banks start lending more actively in order to earn greater profits on their funds? And won’t that get the money multiplier going again? And can’t the resulting huge increase in the money supply overheat the economy, leading to higher inflation? The answer is no, and the reason for this is a profound, but largely unappreciated change in the inner workings of monetary policy….

I’m referring to the 2008 legislation that allowed the Fed to pay interest on bank reserves…

John Williams is an outstanding macroeconomist, far more knowledgeable that I am—and when he attributes the death of the money multiplier to interest on reserves, I’m hesitant to disagree with him. But as far as I can tell, this dramatically overstates the impact of interest on reserves. In reality, the “money multiplier” broke down because it never really existed in the first place.

Here’s the textbook story: as the Fed pumps reserves into the system, banks suddenly have the ability to increase their lending and create new money. Since the reserve requirement on checking accounts is 10%, any increase in bank reserves will lead to money creation ten times the size of the initial injection.

Casual observation suggests some problems with this story. After all, money market funds share many of the characteristics of checking accounts, and yet they have a reserve requirement of zero. Shouldn’t that make the money multiplier infinity? Since the money supply clearly isn’t infinity, there must be something other than reserve requirements limiting money creation.

And that’s the key point: even in normal times, the cost of meeting the reserve requirement accounts for only a small portion of the cost of creating money. If you’re accepting checking deposits and lending them out when the riskless nominal interest rate is 4%, you’re losing 10%*4% = 0.4% each year because the reserve requirement forces you to hold base money rather than T-bills. That’s not trivial, but it’s hardly overwhelming: the much more challenging part of a bank’s job is finding a decent borrower. If the reserve requirement falls from 10% to 5%, and the cost of holding reserves declines from 0.4% to 0.2% (if the riskless rate stays the same), you’re not going to suddenly find twice as many places to lend the money.

I’ve been over this before, but let’s try another analogy. Suppose you live on an isolated island filled with peanut farms, where peanuts are turned into peanut butter with tiny, handheld machines. There are lots of peanuts, but not many machines; since each machine can only produce a certain amount of peanut butter each month, local economists observe a extraordinarily close relationship between the supply of machines and the supply of peanut butter. They call this relationship the “peanut butter multiplier”.

Suddenly, unexpected visitors descend on the island with a boatload of peanut butter machines. There are now so many machines that the supply of peanuts can’t keep up. Many machines sit idle, and economists are shocked to see the “peanut butter multiplier” disappear. The ratio of peanut butter production to peanut butter machines plummets.

Obvious enough, right? Now that peanuts are the scarce input rather than machines, the direct relationship between machines and peanut butter production no longer holds. But the mechanics of the “money multiplier” are really no different: like the machines in my story, bank reserves are one input for money creation. They’re not the only input, however, or even the most important one; you can’t have peanut butter without peanuts, and you can’t have money creation without creditworthy borrowers.

It’s true that historically, there has been a direct relationship between reserves and deposit creation. Excess reserves have stayed at roughly zero, as banks hold precisely the amount necessary to satisfy their reserve requirements. But that’s just an artifact of how monetary policy is conducted: at the margin, the only reason banks hold reserves is that they need to meet reserve requirements, and as long as the federal funds rate is greater than zero (so that reserves are costly), they will limit their holdings to the bare minimum that’s acceptable under the rules. Since the federal funds rate was always significantly greater than zero until the last few years, there were no excess reserves. And now there are:

Technically, the federal funds rate is still a little higher than zero. With interest on reserves, however, there is now zero cost to holding reserves—in fact, the cost is slightly negative, as mysterious technical issues prevent banks from arbitraging away the (small) gap between the rate paid on reserves and the federal funds rate. Now that reserves are costless to hold, textbook microeconomics tells us that the relationship between reserves and money creation will break down: the reserve requirement is no longer a binding constraint, and the other costs of taking and lending deposits will determine banks’ activity.

Is there any reason to think this would be different if there was no interest on reserves, and the federal funds rate fell to zero? Not at all. We’d see the same pattern: with the rate at zero, reserves would no longer be a costly input, and other costs would dominate instead.

Lest you think this is all overconfident theorizing on my part, let’s consider the obvious empirical example: Japan. In 2001, Japan began its policy of quantitative easing, which resulted in an enormous increase in the supply of base money. Interest on reserves, however, wasn’t paid until 2008. What happened in the meantime? A 2003 paper asking “Who Killed the Japanese Money Multiplier?” makes the outcome clear enough.

I often see articles attributing the breakdown of the money multiplier to some special feature of the current economic climate: interest on reserves, or banks’ reluctance to lend during a recession. In truth, the reason is much simpler. The money multiplier has never been a deep structural relationship. The apparent “multiplier” in the data is no more profound than the relationship between peanut butter machines and peanut butter. When an input is scarce, output will move with it. When the input is no longer scarce, output will not.

No surprises here.


Filed under macro

26 responses to “There has never been a money multiplier

  1. bpabbott

    Isn’t Williams just saying that there is no profit for the banks in making loans?

  2. Scott Sumner

    This one has me scratching my head:

    1. Aren’t you confusing the money multiplier with the deposit multiplier? The money multiplier is not one over the reserve ratio.

    2. We’ve always known that the money multiplier is positively related to interest rates, and becomes very low at near-zero rates. That’s in all the textbook explanations of the multiplier, isn’t it? Japan wasn’t a surprise, the same thing happened in the US during the 1930s.

    Perhaps we can agree on this; There is no reason to make the money multiplier an important part of monetary analysis.

    • “Aren’t you confusing the money multiplier with the deposit multiplier? The money multiplier is not one over the reserve ratio.”

      I am guilty of oversimplifying a little on this score. It is true, of course, that when the Fed adds to the monetary base, much of new base money will eventually be held as currency, not reserves—so the money multiplier is definitely not the same as the deposit multiplier.

      But the base money creation associated with QE has mainly taken the form of increased reserves—the demand for currency hasn’t increased in a remotely commensurate way. At least as far as I know, the mechanism underlying the “money multiplier” (if there is any mechanism) is supposed to be the deposit multiplier, so in this instance the deposit multiplier is a good approximation for the money multiplier in general.

      To the extent that there are other influences on the “money multiplier” (when it’s interpreted as the ratio of some monetary aggregate, like M1, to base money), interpreting the apparent consistency of the money multiplier as a causal relationship is even worse. If historically, M1 has been 2*X whenever base money has been X, I think it would be silly to interpret that as a direct causal relationship, whereby “X” in base money leads to the creation of another “X” in inside money. It would be better to say that both demand for currency and demand for deposits move in tandem with nominal income, which is the ultimate driving force—so that correlation here definitely does not mean causation.

      Perhaps in the long run the supply of base money determines nominal income, so that there’s some roundabout causation—but this is not a short or even medium-term relationship, and there is absolutely no reason why we should expect a sudden increase in lending following an injection of reserves. More specifically, to the extent that base money affects nominal income in the short run, it does so by changing the stance of monetary policy as measured by nominal interest rates—so that when there is a change in the supply of base money that is not matched by a change in nominal interest rates (because they are pinned down by IOR), or expectations of future rates, we shouldn’t expect any kind of multiplier.

  3. With the primary point of the post, I can’t disagree. However, I again have to take issue with the implicit assumption that banks are determining the level of credit creation entirely on their own.

    This was one of Krugman’s main points in the original brookings paper on Japan, if you accept at all the idea that, on the full employment path, consumption in the future is far enough below current consumption that a negative real rate is needed to satisfy the euler equation then the fact is NOBODY WILL WANT TO BORROW! Especially the most credit worthy.

    If you’re thinking debt financed investment the same result applies, if the labour force is going to fall then keeping the capital labour ratio at it’s desired level requires contracting the capital stock.

    In a liquidity trap there is a lack of demand for credit, not a lack of supply.

    • Adam, I think we agree. I wasn’t very clear about it, but part of my critique above of the money multiplier is that you need borrowers to extend more credit—and particularly when the economy is at the zero lower bound, that isn’t easy.

      On a side note, though I think Krugman’s original BPEA paper on Japan was terrific, my guess is that financial frictions are responsible for the current ZLB situation, not an Euler equation where the equilibrium real rate is negative. The problem is that the “real rate” that’s relevant to the Euler equation and the riskless “real rate” in the fed funds market are not the same—the latter has a sizable liquidity premium built in that the former doesn’t. If the liquidity premium expands enough, it’s possible that the fed funds rate will hit the ZLB even when the real rate that you’d plug into the Euler equation is still well above zero.

  4. Dan

    Is monetary economics one of your fields of specialisation? You seem to be devoting quite a few posts to the topic. Being partial to microeconomics I must admit that most of this is flying over my head (I’m just in undergrad).

    • Good question! I suppose it depends on what “field of specialization” means—if it’s self-declared, and “specialization” means going to related seminars, reading papers, etc., then probably yes.

      If it’s a more formal designation, then it’s not really possible for me to have monetary economics as a field of specialization, since monetary econ is not a “major” field for an MIT econ PhD—only macro is. (At the end of the second year, you take field examinations in two major fields, which are intended to be more-or-less your fields of specialization.) My tentative major fields are (1) macro and (2) either international, micro theory, or public finance.

      The macro faculty at MIT is great (in my slightly biased opinion, the best of any department), but no one really specializes in monetary economics, except Olivier Blanchard if he decides to come back after his stint at the IMF.

      By the way, I was also partial to micro/applied micro for a very long time—macro seemed far too messy and ad-hoc. I took the grad macro core at Duke as a sophomore and although it was generally well-taught, it didn’t really live up to what I imagined “macro” would be, which led me to ignore macro for a long time. Eventually, though, I decided that the messiness of macro wasn’t a good reason to ignore it as a field—after all, it’s important, and we can’t ignore such a critical field simply because it’s less analytically and empirically tractable.

      Monetary economics, in particular, is an area where I believe that working hard to get the right intuition goes a long way. A lot of the popular discussion on monetary policy still seems to involve some fairly archaic ideas (glorified residuals like “velocity” or the “money multiplier”, etc.), and I think there is some value in blogging about them to clear things up—and to make sure that I have the intuition straight myself.

      • David Beckworth


        I take the “fairly archaic ideas” of velocity and the money multiplier more seriously than you for one reason: they provide an indicator of money demand. The money multiplier provides an indication of the demand for the monetary base and velocity for broader measures of money. Both have fallen and remain depressed (i.e. narrow and broad money demand remain elevated). Elevated money demand, in my view, is a key reason the recovery remains sluggish this far out.

      • Kitty

        Is it true that you received a B+ in a measure theory course in high school?

      • Doggy

        Hi, slightlyconfused1! I hope that you’re no longer so confused and would be willing to play with my rooster now.

  5. DKB @ NYU

    Sounds right to me. The comparison to Japan is wonderful, you might want to look at other countries, too — surely some have paid interest on reserves for years.

  6. So if that is true and the real rate of return has been falling since the start of the industrial revolution what happens when the real rate of return gets so low that it is overwhelmed by the expense of making and collecting loans? So the demand for bank loans falls. Say the real rate of return is below 1% but it costs the bank 3% so fewer bank loans are made. Do you get to a point were the post-Keynesian ideas make sense? I think that the same thing can be produced by free banking were the banks spend more at the rate to keep their currency from rising or falling in value. So if the value of their currency is rising (deflation) they make spend more. If the value of their currency is falling (inflation) they destroy some currency and spend less.

    • anon

      “what happens when the real rate of return gets so low that it is overwhelmed by the expense of making and collecting loans?”

      Since the ROR is set at the margin, the easiest answer here is that fewer loans are made, so the ROR on bank loans doesn’t really fall that much. Negative real interest rates are feasible, but I doubt they will persist in the long run; instead, most savings would simply shift to other assets with low administrative costs. I’m not sure about the impact on short-run expenditure: perhaps bank loans are better than other asset classes, in which case a targeted subsidy might make sense.

  7. Jeff Hallman

    I’ve said this several times, but you seem to be ignoring it. When the Fed pays interest on excess reserves that is equal to or higher than the riskless rate, the money multiplier is one. Not one over the reserve requirement, and not zero, but one.

    Think of Milton Friedman’s proposal for a 100 percent reserve requirement. The money supply is exactly equal to the monetary base, because everything you can use as medium of exchange is either part of the monetary base (currency) or a bank deposit that has a 100 percent reserve requirement against it. The only way the money supply changes is if the Fed buys or sells something. If the Fed buys a T-bill on the open market, it pays with a check. The seller deposits the check and his bank, in turn, redeposits the funds with the Fed. Both the monetary base and the money supply increase by the amount of the purchase.

    When the Fed pays interest on excess reserves, exactly the same thing happens.

    The money multiplier could only be zero if the guy who sold the T-bill to the Fed deposited the funds in some kind of long-term account that doesn’t count as money. If the bank redeposits the funds with the Fed, you’d still have an increase in the monetary base, but with no increase in transactions deposits. But if there is a positive term premium, and there usually is, the bank will sit on the excess reserves only if the interest paid on excess reserves is higher than the term premium. Otherwise it would pay to make loans with maturities matching the term of the long-term account the T-bill seller deposited the funds in.

    The money multiplier as an empirical regularity has been around for a very long time. As such, it does not owe its existence to any particular macroeconomic theory or fashion. If you have a model in your head in which the multiplier is just an illusion, perhaps you should consider whether or not your model is missing something important.

    • As far as I know, excess reserves are not themselves counted in any monetary aggregate—this is how the M1 “money multiplier” is now below one. (By the way, the same chart shows that the M1 multiplier declined from over 3 in the late 80s to a little over 1.5 pre-crisis… I think it’s stretching to call that an “empirical regularity”. The M2 multiplier hasn’t changed as much, but it also declined dramatically from about 12 in 1985 to about 8 by 1995.)

      The money multiplier could only be zero if the guy who sold the T-bill to the Fed deposited the funds in some kind of long-term account that doesn’t count as money. If the bank redeposits the funds with the Fed, you’d still have an increase in the monetary base, but with no increase in transactions deposits. But if there is a positive term premium, and there usually is, the bank will sit on the excess reserves only if the interest paid on excess reserves is higher than the term premium. Otherwise it would pay to make loans with maturities matching the term of the long-term account the T-bill seller deposited the funds in.

      I don’t understand. Why will the bank be more willing to lend when it has base money than when it has the T-bill? Surely it’s not the minor maturity difference between T-bills (less than a year) and money (zero), right? I agree that when there is a positive term premium, a bank will (all else being equal) be more willing to dispose of short-maturity assets and make longer-maturity loans… but this applies equally to T-bills and base money. After all, once base money is no longer useful at the margin to satisfy reserve requirements, it has pretty much the same properties as a T-bill on a bank’s balance sheet.

      • Jeff Hallman

        The bank never had the T-bill, one of its depositors did. He sold the T-bill to the Fed and put the proceeds in, say, a CD.

        I looked at the chart showing the M1 Money Multiplier declining from 3 to 1.5 over the 25 years prior to the crisis. That multiplier is defined as M1 divided by the monetary base, and the reason it declined was because currency grew a lot more than did DDA (demand deposits) and OCD (Other Checkable Deposits), the other major components of M1.

        Most US currency is overseas, making the monetary base a poor indicator of anything but the size of the Fed’s balance sheet. What’s more important to the discussion here is that, until the Fed started paying interest on them, excess reserves were pretty low, and had been for a long time. The multiplier that matters applies to reserves, not the base.

        We’re not really in violent disagreement. I’d like to see the Fed either stop paying interest on excess reserves, or go all in with a 100 percent reserves requirement. What’s killing us is this slow transition from a 10 percent reserve requirement to a 100 percent regime brought about by the payment of interest on excess reserves. And, of course, by the Fed’s failure to “target the forecast” as Scott Sumner keeps pointing out.

  8. Scott Sumner

    Matt, I partly agree:

    1. Yes, the demand for M1 and M2 are a function of NGDP, among other variables. So I’m happy to accept causation from NGDP to M1.

    2. Yes, changes in the base rarely have an immediate effect on NGDP.

    3. But causation most certainly runs from the base to NGDP. That’s something Keynesians often overlook. They quickly dispose of naive versions of monetarism, and then lose sight of the fact that Woodfordian views of causation rescue monetarism. Current changes in NGDP are caused by changes in the expected future path of the base (plus IOR of course, if you assume that is a factor. Most of monetary theory was developed in a world with non-interest bearing base money.)

    You are right that textbooks assume the deposit multiplier is the key, but the textbooks are wrong. They completely misunderstand the multiplier process. You are correct that to a great extent the demand for the aggregates responds to NGDP. Textbooks assume the new money goes into reserves, but in fact most new money goes into cash in circulation.

  9. axiom

    Right. There’s never been one, but not for reasons presented here.

    Start with the FACT that banks don’t “lend reserves” (other than to each other) and work through the bookkeeping. There can’t be a multiplier.

  10. Matt: The money multiplier describes the relationship between the monetary base (which the central bank can control) and “the” money supply (however defined). You are saying this relationship is unstable.

    New Keynesians rely on a relationship between the overnight rate (which the central bank can control) and “the” interest rate (however defined). Are you saying that this relationship is stable? Because obviously it isn’t. Look at yield spreads recently.

    It might be more useful to ask: which relationship is more stable/unstable (in some usefully defined sense)?

  11. Gary

    After all, money market funds share many of the characteristics of checking accounts, and yet they have a reserve requirement of zero. Shouldn’t that make the money multiplier infinity?

    Can you think of no other reason to hold reserves save regulation? How about prudence?

    • David Beckworth


      Yes, that reminds of the successful free banking episodes in Scottland and Canada where bank reserves dropped to low levels, but still were positive because of precautionary demand for bank reserves. Here there was no reserve requirement.

    • Can you think of no other reason to hold reserves save regulation? How about prudence?

      But why should they hold reserves in the form of base money, rather than T-bills or some other perfectly liquid investment? Those have the same value as electronic reserves for a fund concerned about “prudence”. If a fund has a sudden need for liquidity, it can just take their money out of overnight repo or sell T-bills; there’s no need to hold precautionary balances of base money.

      Indeed, I don’t think it’s even technically possible for money market funds to hold electronic bank reserves—that’s only for depository institutions that are part of the Fed system. Now, often the funds will be offered by a division of a bank, which will have its own electronic reserves—but the funds themselves are not “banks”, and do not have any technical capacity to hold electronic reserves. They can hold checkable deposits or currency, but as table L.121 from the Fed Flow of Funds report tells us, these amount to only $14 billion out of $2.7 trillion in money market fund assets. Assuming that $14 billion consists of checkable deposits (I have no idea why a money market fund would hold paper money), then the amount of reserve balances supporting it is $1.4 billion, or less than one-thousandth the value of the funds.

      So… to the extent that in practice there are some base money reserves held by money market funds (through their checkable deposits), the ratio is incredibly, incredibly tiny, less than 0.1%. If you subscribe to a pure “deposit multiplier” view of money creation, this still cries out for some explanation—why haven’t money market funds spiraled into the zillions of dollars?

      As I mentioned in the post, the amount of reserves held by banks in the US has been almost exactly equal to the reserve requirement. No doubt the banks would hold some reserves for payment purposes if this requirement didn’t exist—but potentially it would be a very small amount (except for vault cash), since banks can be very clever about how they arrange their transactions, and lifting the reserve requirement would encourage banks to find new ways to economize on precautionary reserves.

  12. flow5

    The so called “money multiplier” never existed because the “monetary base” [sic] has never been a base for the expansion of new money & credit.

  13. John

    the foregoing is an excellent example of what is wrong with economics (and this blog). Wasted meaningless word after wasted meaningless word.

    The first sentence in the first economics class and text should be “There is no rule of economics that the amount of money available to be lent is equal to the amount of good loans.”

    In fact, one hell or an argument exists that what we have tipped over the horizon and that we have reached the inside of the black hole, were underlying economic forces mean there are no good loans.

    For some time we in the United States have been destroying jobs faster than we create good new ones. No facts show the future is going to change. 20 to 40 years from now, machines will build and replace themselves. There will then be: (a) no good jobs; and (b) no good loans.

  14. Becky Hargrove

    Thanks so much for this post – while my understanding may not be spot on, I can at least surmise that the supposed money multiplier is really an ideal set of circumstances for the loan itself; the confidence on the part of both lender and customer that they will benefit from the transaction itself. You said, “when an input is scarce, output will move with it” and this reminds me of the greater returns to human skill (monetarily) in the early years of the Industrial Revolution.

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