A Monetary Policy Primer, Part 6: The Reserve-Deposit Multiplier

excess reserves, liquidity coverage ratio, required reserves, reserve ratio, reserve-deposit ratio
Money multiplier, Wikipedia. https://en.wikipedia.org/wiki/Money_multiplier#/media/File:Fractional_reserve_lending_varyingrates_100base.jpg

Multiplier2In my last post in this series, I observed that an economy's "base" money serves as the "raw material" that commercial banks and other private-market financial intermediaries employ in "producing" deposits of various kinds that can themselves serve as means of exchange.

If they could do so profitably, these private intermediaries would,  by making their substitutes more attractive than base money itself, collectively gain possession of every dollar of base money in existence. In some past monetary arrangements, most notably that of Scotland before 1845, banks came very close to achieving this ideal, thanks to the their freedom to supply their customers with circulating paper banknotes as well as with deposits, and to the fact that between them these two substitutes could serve every purpose coins might serve, and do so more conveniently than coins themselves.

All save a handful of commercial banks today are, in contrast, able to supply deposits only, so that only base money itself can serve as currency, that is, circulating money. The extent to which national money stocks have been "privatized," in the sense of being made up mainly of private IOUs of various kinds rather than officially-supplied base money, has been correspondingly limited, as has the extent to which private money holdings have served as a source of funding for bank loans.

When banks and other private-market intermediaries acquire base money, they do so, not for the sake of holding on to it, as they might were they mere warehouses, but in order to lend or otherwise invest it. More precisely, they do so in order to lend or invest most of the base money that comes their way, while keeping some on hand for the sake of either meeting their customers' requests for currency, or for settling accounts with other banks, as they must do at the end of each business day, if not more frequently. While banks' own substitutes for base money may serve in place of base money for all sorts of transactions among non-banks, those substitutes won't suffice for settling banks' dues to one another, for every bank is anxious to grab for itself as large a share of the market for money balances as possible, while contributing as little as possible to the shares possessed by rival banks.

Bankers have also learned, through hard experience, that by accumulating the IOUs of other banks, and thereby allowing other banks to accumulate their own IOUs in turn, they expose themselves to grave risks, which risks are best avoided by taking part in regular interbank settlements. Because even the most carefully-managed banks cannot perfectly control or predict the value of their net dues at the end of any particular settlement period, all would tend to equip themselves with a modest cushion of cash reserves even if they did not have to do so for the sake of stocking their ATM's or accommodating their customers' over-the-counter requests for cash.

Because banks typically receive fresh inflows of reserves every day, as a result of ordinary deposits, loan repayments, or maturing securities, a responsible banker, once having set-aside a reasonable cushion of reserves, has only to see to it that the lending and investment that his or her bank engages in just suffices to employ those inflows, in order to succeed in keeping it sufficiently liquid. Greater reserve inflows, if judged likely to be persistent, will inspire increased lending or investment, while reduced ones will have the opposite effect.* The bankers' general goal is to keep funds that come the bank's way profitably employed, while holding on to just so many reserves as are needed to accommodate fluctuations of net reserve drains around, and therefore often above, their long-run (zero) mean. More precisely, bankers' strive to keep reserves on hand sufficient to reduce the probability of losses exceeding available reserves to a (usually modest) level,  reflecting both the opportunity of holding reserves, which is to say the interest that might be earned on other assets, and the costs involved in making-up for reserve shortages, by borrowing from other banks or otherwise.

Throughout the history of banking, and despite laws that have suppressed commercial banknotes while often imposing minimum (but never maximum) reserve ratios on banks, bank reserves have generally constituted a very modest part of banks' total assets, and therefore a modest amount compared to their their total liabilities. Indeed, bank reserves have generally been but a small fraction of banks' readily redeemable or "demandable" liabilities. England's early"goldsmith" banks are supposed to have held reserves equal to only a third of their demandable liabilities — a remarkably low figure, given the circumstances; at the other extreme, Scottish banks at the height of that nation's pre-1845 "free banking" episode often managed quite well with gold or silver reserves equal to between one and two percent of their outstanding notes and demand deposits. Modern banks, even prior to the recent crisis, have generally had to keep somewhat higher reserve ratios than their pre-1845 Scottish counterparts, mainly owing to the fact, mentioned above, that they must stock their cash machines and tills with base money, instead of being able to do so using their own circulating banknotes.

Between 1997 and 2005, for instance, U.S. depository institutions' reserves ranged, with rare exceptions,  between 11 and 14 percent of their demand deposits (see figure below). Put another way, for every dollar of base money "raw material" they acquired, U.S. commercial banks were able to "manufacture" (that is, to create and administer) just under 10 dollars of demand deposits.  That figure, the inverse of the banking system reserve ratio, is what's known as the reserve-deposit "multiplier."

Depository Institutions' (Demand Deposit) Reserve Ratio, 1997-2005

The multiplier's significance to monetary policy is, or used to be, straightforward: it indicated the quantity of additional bank deposits that monetary authorities could expect to see banks produce in response to any increment of new bank reserves supplied them by means of either open-market operations or direct central bank loans. If, around 2000 (when the reserve-demand deposit multiplier was about 14), the Fed wanted to see bank's demand deposits increase by, say, $10 billion, it had only to see to it that they acquired $(10/14) billion in fresh reserves, which meant creating a somewhat larger quantity of new base dollars — the difference serving to make up for the tendency of some of any newly created bank reserves to be converted into currency. The ratio of the total amount of new money, including both currency and bank deposits, generated in response to any new increment of base money, to that increment of base money itself, is known as the "base money multiplier."

Since the recent crisis, all sorts of nonsense has been written about the "death" of the reserve-deposit and base-money multipliers, and even (in some cases) about how we ought to be glad to say "good riddance" to them. I say "nonsense" because, first of all, the multipliers in question, being mere quotients arrived at using values that are themselves certainly very much alive, cannot themselves have "died," and because the working of these multipliers does not, as some authorities suppose, depend on the particular operating procedures central banks employ. Finally, although it's true that, until the recent crisis, economists were inclined, with good reason, to take the stability of the reserve-deposit and base-money multipliers for granted, it doesn't follow that they (or good ones, at least) ever regarded these values as constants, as opposed to variables the values of which depended on various determinants that are themselves capable of changing.

What certainly has happened since the crisis is, not that the reserve-deposit and base-money multipliers have died, but that their determinants have changed enough to cause them to plummet. U.S. bank reserves, for example, have (as seen in the next picture) gone from being equal to a bit more than a tenth of demand deposits to being about twice the value of such deposits!  The base-money (M2) multiplier, shown further below, has, at the same time, fallen to below half its pre-crisis level, from about 8 to 3.5 or so (not long ago it was less than 3).

The Reserves-to-Demand-Deposits Ratio Since 2005


The Base-Money M2 Multiplier since 2005

These are remarkable changes, to be sure.  But they are hardly inexplicable. Banks' willingness to accumulate reserves depends, as I've already noted, on the cost of holding reserves, which itself depends on the interest yield of reserves compared to that of other assets banks might hold instead. Before the crisis, bank reserves earned no interest at all. On the other hand, banks had all sorts of ways in which to employ funds profitably, especially by lending to businesses both big and small. Consequently, banks held only modest reserves, and bank reserve and base-money multipliers were correspondingly large.

The crisis brought with it several changes that are more than capable of accounting for the multipliers' collapse.  The recession itself has, first of all, resulted in a general reduction in both nominal and real interest rates on loans and securities, to the point where some Treasury securities are now earning negative inflation-adjusted returns. Regulators have in turn responded to the crisis by cracking-down on all sorts of bank lending, making it costly, if not impossible, for banks, and smaller banks especially, to make many of the higher-return loans, including  small business loans, they would have been able to make, and to make profitably, before the crisis. (More here.) U.S. bank regulators have also begun to enforce Basel III's new "Liquidity Coverage Ratio" rules, compelling banks to increase the ratio of liquid assets, meaning reserves and Treasury securities, to less-liquid ones on their balance sheets. Finally, since October 2008, the Fed has been paying interest on bank reserves, at rates generally exceeding the yield on Treasury securities, thereby giving them reason to favor cash reserves over government securities for all their liquidity needs.

Whatever their cause, today's very low money multiplier values mean that commercial banks have ceased to contribute as they once did to the productive employment of scarce savings. Instead, those savings have been shunted to the Fed, and to other central banks, which use them to purchase government securities, and also for other purposes, but never, with rare exceptions (and with good reason), to fund potentially productive enterprises. Although discussions of monetary policy since the crisis have mainly had to do with the quantity of money, and central banks' efforts to expand that quantity so as to stimulate spending, the effects of the crisis, and of governments' response to it, on the quality of money, and especially on the investments its holders have been funding, deserve at least as much attention.

Continue Reading A Monetary Policy Primer:


*Besides funding loans with retail deposits banks can and do fund them by borrowing on wholesale markets.  In that case, loans may be arranged in anticipation of a bank's acquisition of funds. Either way, banks must acquire base-money sufficient to finance their lending (that is, to cover their settlement dues) if they are to avoid having to rely too often on funding from last-minute interbank loans.

  • CavemanEconomist

    In part 5, you stated that the Fed influences the "quantity" of money substitutes created by the private sector. By "quantity" do you mean dollar value? Are mortgages and mortgage derivatives considered money substitutes? If so, does that necessarily imply that the Fed had a role in creating the housing boom?
    You state that you would like to see the Fed work to maintain stable, steadily rising, spending. Are you referring to private spending by entrepreneurs, investors, and consumers or do you include government spending? Doesn't a stated policy of maintaining spending give credence to Keynesian "pump primers" in times of recession?
    What happens in situations such as the one we are now in, when government regulations have stifled investment? Would the Fed continue to step on the accelerator in order to follow your rules even though government policy has placed the "car" up on blocks? What would keep it from doing that?

  • BigAppleSailor

    Hi George,
    Thanks for this primer material – I'm relatively new to the content here. I am an amateur "self-directed" reader (as your thesis adviser described you) of things monetary. However, I've repeatedly come up against a theoretical roadblock that I can't seem to overcome. After wading carefully through the seemingly endless "Fractional Reserve" banking debates here and elsewhere, I keep running headlong into a fundamental collision between two diametrically opposed positions with respect to commercial bank deposit "creation". On the one hand, there seems to be a position that holds a "intermediary of loanable funds" model – that banks cannot lend out more than they receive in deposits. You clearly (and articulately) include yourself in this camp – and you are certainly not alone by any means.

    "An individual bank can't get away with lending more than its excess reserves; …That is, it is limited to lending rather less than the savings brought to it, which means there's no "thin air" lending."

    On the other hand, there would appear to be an equally large (and well credentialed) group contending that ex-nihilo deposit creation does, in fact, take place without anything but a post-facto reference to reserves. Michael Kumhof (IMF and Bank of England); Richard Werner; Bernard Lietaer etc. Even Bernanke seemed to be agitating towards the elimination of reserve requirements entirely – suggesting that the order of precedence is ex-nihilo loan (deposit) creation first, then find/obtain the reserves (the Central Bank will always provide the necessary reserves).

    As far as I can tell, this issue has been spilling out onto econ 'blogs everywhere like so much thrown paint – including not too long ago with a long and unsettled worldwide exchange stemming from both comments and writings of Krugman – stretching from Naked Capitalism to Steve Keen in Australia. A recent study commissioned by the Government of Iceland also appears to also tread in this area. The rather crazed MMTers are actively mixing the brew, too. The Bank of England seems to have taken BOTH positions depending on when and whom you ask. The US Federal Reserve seems to consistently come down on the side of "thin-air"…


    Bizarrely, everybody seems to happily agree the textbooks (and associated undergraduate curricula) have it largely wrong, but no clear resolution as to the absolute truth of the matter seems to present. It's not my intention to inquire here out loud after the "fraud" aspect, or the relative merits of fractional reserve banking – both of which questions I will answer on my own. Rather, in order to do so, I must first establish precisely the facts of the "money" creation mechanism – especially the temporal order of events. It is repellent to me that the most senior names in the monetary Econosphere cannot seem to agree on the actual mechanics of this essential aspect. Loanable funds or "endogenous" money creation? To me, the fact that this discussion even exists at all (and the positions are so vehemently argued), would suggest that recent monetary "policy" in this world may have been based on one of the biggest theoretical fallacies in history. I cannot soundlessly accept Krugman's, "How do you do economics?" explanation. For the money question, can there not be a scientific, empirically indisputable answer? I don't see how urgently needed monetary reform can take place until this matter is resolved with a clear consensus.

    I would respectfully ask you to also comment on the existence (and substance) of this dispute – which seems to stretch well beyond semantics to a fundamental error in the actual theoretical underpinnings of the whole game! Then, of course, I would welcome reasoned argument for your position. If I have overlooked your specific answer elsewhere on this paradox already, perhaps you or an active reader could point me in the right direction with some links. (Apologies in advance).

    So, are commercial banks always and only intermediaries of loanable funds (bank credit "money" deposits precede the act of loan issuance)… or does the magical, mystical ex-nihilo endogenous "money" (bank credit) creation functionally and legally take place without so much as an afterthought to obtaining necessary reserves, which logically follow said deposit creation. Feel free to restate the question in such a way to facilitate your answer, if my question itself belies a logical problem.

    Thank you.

    • Gold-man

      This one may be relevant to the discussion too:

      S&P Economic Research:
      Paul Sheard, Chief Global Economist and Head of Global Economics and Research, New York

      Title: Repeat After Me: Banks Cannot And Do Not "Lend Out" Reserves


      • George Selgin

        "A key distinction to bear in mind (hinted at in the last previous paragraph) is between individual banks and banks in aggregate. Neither individual banks nor banks as a whole can "lend out" reserves, but individual banks can and do offload their reserves (particularly excess reserves) by lending them to other banks or by buying assets; but the banks in aggregate cannot do this–in such cases, the reserves that leave one bank's balance sheet just pop up on another, remaining on the central bank's balance sheet all the while."

        This is the same tiresome argument I have addressed in numerous places: the fact that banks cannot collectively rid themselves of reserves (no qualifier) does not mean that they can't rid themselves of ("lend away") _excess_ reserves! Growth in the multiplier denominator (to use the author's language) tends to lead to corresponding growth in the numerator (deposits) unless something has happened to cause banks' demand for excess reserves (note the qualifier again) to rise.

        The bottom line here is that many who deny that banks can lend away excess reserves, and who otherwise smugly dismiss the suggestion that there is such a thing as a reserve multiplier, exemplify the fact that "a little learning is a dangerous thing."

        • Sam Levey

          "This is the same tiresome argument I have addressed in numerous places: the fact that banks cannot collectively rid themselves of reserves (no qualifier) does not mean that they can't rid themselves of ("lend away") _excess_ reserves! Growth in the multiplier denominator (to use the author's language) tends to lead to corresponding growth in the numerator (deposits) unless something has happened to cause banks' demand for excess reserves (note the qualifier again) to rise."

          Would love to see the other places that you address this issue. It seems to me that there are actually two issues at stake here. One is, as you address, the banks mechanical capability of "lending out" reserves. On this I quite agree with you: banks cannot lend out reserves in total (as they only exist on the central bank balance sheet), but any individual bank can convert excess reserves into required reserves (by creating deposits), or can lend its own excess reserves off to another bank that is short.

          However, I don't agree that your final sentence follows from the previous point. The mechanical possibility of converting excess reserves into required reserves doesn't address the question of what the real-life constraint on bank lending is. It's conceivable that this constraint is excess reserves, in which case we might imagine that a bank that didn't have sufficient reserves wouldn't lend, in which case providing it with more reserves would enable it to lend, and therefore your concluding sentence would be true.

          However, following the BoE (and MMT more generally), we know that it isn't, because in an interest rate targeting regime, the central bank stands ready to provide any desired reserves to the banking system, ensuring that banks always have access to reserves. And if reserves are not actually the thing that's constraining bank lending (because banks can get ahold of reserves whenever they want, at some price, typically automatically through overdrafts), then there's no reason to think that providing additional excess reserves, above what the banks choose to obtain on their own (which the central bank must provide in order to maintain its interest rate target), should lead to any increase in bank lending.

          Therefore, in the deposit multiplier, the causation is better thought of going from deposits to reserves (the loan creates the deposit, then the bank obtains any reserves it needs), except in the case of substantial excess reserves provided by the central bank like after QE (where we'd expect the level of reserves to basically flatline, while deposit creation continues at more or less the same previous pace until it "catches up" with the level of reserves).

          • George Selgin

            "However, following the BoE (and MMT more generally), we know that it
            isn't, because in an interest rate targeting regime, the central bank
            stands ready to provide any desired reserves to the banking system,
            ensuring that banks always have access to reserves."

            Well, this is one of many reasons why I am not a fan of MMT. For it simply doesn't go deep enough. The Fed did indeed (before October 2008) target the effective FFR (that has changed since); but this "intermediate" policy target was predicated on the Fed's more fundamental inflation and employment objectives. That is, it was never a case that the banks could get whatever quantity of reserves they wanted at a given rate, for if the Fed found that the banks' willingness to expand credit, and to acquire reserves for the sake of so doing, was such as to might cause, say, the inflation rate to rise above the Fed's target, the Fed would raise its funds rate target–that is, it would cease to supply any desired R at the previously-established ffr rate.

            Indeed, as anyone familiar with Wicksellian monetary theory understands, the key to establishing a stable monetary policy lies precisely in having the central bank keep its policy rate in line with the corresponding "natural" rate, lest the result should be either an upward spiral of lending and prices or a downward spiral of deflation.

            It follows that, so long as central banks don't persist in maintaining below-natural policy rates, reserves will tend to be a scarce banking input rather than one that banks can acquire willy-nilly. In other words, a "horizontal" reserve supply schedule that shifts in response to changing macro conditions, and especially in response to movements in the price level, is hardly the same thing as the rigidly horizontal schedule that informs so much of the MMT framework.

          • Sam Levey

            Hello George, thanks for your reply. Though I have to say that I see it as untenable on many fronts.

            For one, though you argue that banks are reserve-constrained, you conclude by asserting a horizontal supply schedule. I don't see how these things are compatible. If the supply schedule is horizontal at some price at some time, then banks are not reserve constrained at that time, because they can obtain as many as they want, at that price. The fact that this price changes at some time in the future to a different horizontal supply curve doesn't change this. It just means that at some later point, banks will still be able to obtain as many reserves as they want, but at a different price. This might translate into demand for fewer reserves in the future (if higher interest rates reduces demand for loans) but it doesn't imply that banks are constrained in making loans by the quantity of reserves. It seems to me this is a contradiction. And furthermore, that MMT endorses the 'shifting supply curve' model, not the 'rigid' model: we all know that the FFR changes occasionally.

            Though I'd certainly be willing to grant you a central bank reaction function as you're describing, again, I don't see how this causes banks to be reserve-constrained. Remember that I'm looking for an answer to the question of "if 100 creditworthy borrowers come into the bank on Tuesday, how many of them is the bank capable of lending to, even if it doesn't have enough reserves?" And my argument would be that it's capable of lending to all of them, and it will see to it that it has enough reserves to meet requirements and settlement needs before those needs arise, one way or another, probably within the next few days. Surely the fact that the Fed might raise rates in 9 months if inflation is too high can't play a serious factor in answering this question? Especially since the Fed routinely leaves rates static for years (or more recently, decades).

            Granting you for a moment that you've got the mechanics right, and the Wicksellian concept is correct, in order for the Fed's changes of target to affect the ability of the bank to obtain reserves on Wednesday that it needs for loans it made the prior Monday, we'd have to imagine that the Fed is changing the rate every single day, maybe even every hour, and that it does so according to extremely rigid rules to keep it at this "Wicksellian" rate. But we know it doesn't change the rates but every few months at minimum, and we know it doesn't stick to anything remotely like rigid rules.

            To illustrate this latter point, here some quotes from Fed minutes: "In a world where we do not have monetary aggregates to guide us as to the thrust of monetary policy actions, we are kind of groping around just trying to characterize where the stance is”, "policy formation has become
            more intuitive”, “You can tell whether you’re below
            or above, but until you’re there, you’re not quite sure you are there. And we
            know at this stage, at one and a quarter percent federal funds rate, that we
            are below neutral. When we arrive at neutral, we will know it."

            Clearly, the idea that the Fed is moving rates around in real-time with such precision as to keep banks reserve constrained from day-to-day is hard to swallow.

            But also, I do not grant you that those mechanics are correct. As I say, I see your argument that a shifting horizontal supply curve implies that banks are reserve constrained as contradictory. The fact that the curve is horizontal, even if it shifts occasionally, should mean that banks are never reserve constrained, as long as they're willing to pay the current price. And presumably, they do their best to pass any change in these prices to their customers, in order to preserve their NIM.

            And I also do not grant you that there's such thing as a Wicksellian natural rate. I think the concept fails for situations where profit expectations are so depressed (or previous debt burdens so high) that businesses won't borrow to invest no matter what the interest rate is. And it especially fails for the case of a large outstanding government debt. If government debt is very high, then raising interest rates will increase the government deficit, and this will be stimulatory, while lowering interest rates will reduce the government deficit, and be contractionary. At some level of government debt, this effect must grow equal to and then larger than any effect of changes in interest rates on borrowing, at which point interest rate changes have no effect, and then have the opposite effect as "normal." The best estimates I've seen for when this point is are around 60-80% of government debt-to-GDP.

            In other words, in our current climate, lowering interest rates might be deflationary, while raising interest rates might be inflationary, rendering the concept of a "natural rate" useless.

            Thanks again for the reply, nice chatting with you!

  • BigAppleSailor

    George: Thanks for the prompt note… and apologies for the lack of depth in my inquiry. Can you point me to your writings (or related links) that describe the specific mechanism by which the banking sector can lend away excess reserves. How does it work?