Home > Macro/Monetary Theory > Banks Can Lend Out Excess Reserves

Banks Can Lend Out Excess Reserves

In the comment section of a post by Scott Sumner on EconLog, a commenter made the claim that banks cannot lend out excess reserves and cited this paper.   While most of the details discussed in the paper are correct, the conclusion that banks can’t lend excess reserves is not.  I will try to explain the confusion.

First, the author makes the important point that “A key distinction to bear in mind (hinted at in the last previous paragraph) is between individual banks and banks in aggregate.”  But then he goes on to “prove” his claim that banks can’t lend out excess reserves by showing that they can’t change the quantity of aggregate reserves.  This is true but an individual bank can lend out excess reserves.

Consider the bank’s balance sheet as represented in the paper.

Reserves (R) + Loans (L) + Bond holdings (B) = Deposits (D) + Equity (E)

When a bank makes a loan, they create additional deposits and additional loans (initially keeping their reserves unchanged).  However, people don’t just take out loans to keep the money in a deposit account at the bank who gave them the loan.  Usually they spend these deposits.  When they do this, they become deposits in someone else’s account, possibly at another bank (some may become cash held by the public).  When this happens the other bank settles with the first bank and reserves are transferred.  This decreases reserves and deposits at the first bank, keeping the above equation intact.  It’s true that this doesn’t change the total quantity of reserves in the economy but it does change the quantity of reserves held by that individual bank.  They have been traded for loans (notice that this still keeps the above equation intact, it has just changed the composition of the left-hand side.

If a bank does this, it will increase the money multiplier because while the total reserves in the economy remain unchanged (they have just changed banks) the total amount of loans and deposits has increased (those deposits ending up on the balance sheet of the other bank which got the reserves which left the first bank).

Note that even if you assume that when a bank makes loans, it increases its own deposits only and does not decrease its reserves at all, the minimum reserve requirement will still be a constraint on lending because as it increases lending, L and D will increase but R will remain the same.  Obviously, at some point, this will cause the ratio L/R to hit the minimum.

Now the claim that banks are not constrained by reserve requirements in normal times is mystifying.  Again, this is a case of making an argument about aggregates and extrapolating (erroneously) to the behavior of individual banks.  Here is the claim.

The money multiplier view of the world envisages the central bank creating reserves and the reserves multiplying into new lending. That is, reserves constrain bank lending. That would seem compelling. If banks are subject to minimum reserve requirements (requiring them to hold reserves in a certain proportion to their deposits, and deposits are the balance-sheet counterpart to loans at the point of credit creation), then, by restricting the amount of reserves that the central bank supplies, it should be able to control the amount of credit.

But modern central banking doesn’t work this way. Central banks don’t constrain the amount of bank reserves they supply. Rather they supply whatever amount of reserves that the banking system demands given the reserve requirements and the amount of deposits that have been created.

This seems to indicate a deep confusion about what it means to be “constrained.”  It’s true (or at least I will accept the premise) that the central bank sets an interest rate target and provides whatever amount of reserves are necessary to hit that target.  This does not mean that banks are not constrained by reserves! 

This fact I think is indisputable: a legal minimum requirement for reserves exists.  This means that if a bank has a ratio of loans to reserves which is equal to that minimum level, they cannot make more loans.  When banks make loans in the way described above (which is the same way described in the paper), they increase aggregate loans and deposits without changing the aggregate quantity of reserves.  This means that for a given quantity of reserves, there is a maximum amount of loans and deposits that the banking system is capable of creating and this maximum is determined by the minimum reserve requirement.

The author seems to claim that this technical constraint is meaningless because if a bank runs into it, the Fed just creates more reserves.  This is not true for an individual bank.  A bank cannot hit the minimum level of reserves, want to keep making loans, and just call up the Fed and say “give me more reserves, I want to keep making loans.”  They have to trade some other asset for more reserves (this may include attracting deposits) or else they cannot make more loans.   This means that the reserve requirement is a binding constraint if the bank is in that situation.

Furthermore, and more importantly, this claim that Fed just supplies whatever reserves the banking sector “demands” given the reserve requirements and deposits being created is complete nonsense.  He is just saying that, instead of the Fed determining the amount of reserves (money base) and this leading to some amount of deposits which is determined by the reserve requirement (which is a constraint on the creation of deposits), there is some exogenously given quantity of deposits and the Fed just mindlessly fills in the reserves which this amount of deposits requires.  That’s completely upside down.  The amount of deposits depends on the amount of loans.  The amount of loans and interest rates are determined in the market.  Yes the Fed tries to target an interest rate but how do they do this?

A bank has the ability to trade assets of one kind for assets of another kind at certain prices which are determined in the market.  Different assets have different rates of return.  Barring any other constraints on their behavior, they will choose the quantities of these assets (and the market prices will adjust) in such a way that the rate of return (net of risk premiums and other such considerations) is equal.  Reserves usually have a low or zero rate of return.  This is fixed by the rate of interest on reserves.

The rate of return on loans is determined by the supply and demand.  The demand is beyond the control of the banks.  The aggregate supply of loans is essentially flat (maybe not perfectly flat but at least pretty flat) at (or near) the rate of IOR (abstracting from risk premiums) for quantities up to the maximum quantity of loans which is possible for the given quantity of total reserves and the minimum reserve requirement.  At that point, it becomes perfectly inelastic (vertical) because there is no way that the banking system can make more loans without the Fed either increasing the total reserves or lowering the reserve requirement. (In other words it is constrained by these two things!)

In normal times, interest rates on loans are high enough that the return on them dominates the return on holding reserves so banks try to make more loans and they do this until they hit the reserve requirement constraint and the market interest rate is determined by where this quantity of loans hits the demand for loans.

Market For Loans

loans market normal

Here i* is the market interest rate R is total reserves and r is the minimum reserve requirement and I am assuming there is no currency held by the public just for simplicity. (I don’t know why it’s blurry I’m not very good at blogging…)  Now if the Fed were to increase the total amount of reserves in the economy, this supply curve would shift to the right which would lower interest rates (of course there could be some effect on demand from changing expectations about the stance of monetary policy but that isn’t important for our purposes).  The Fed can increase or decrease the quantity of total reserves to try to hit its interest rate target but this doesn’t mean that banks aren’t constrained by reserves.  On the contrary, it is because banks are constrained that this works.  By increasing the total quantity of reserves (money base) they are relaxing the constraint and this allows banks to make more loans until the constraint becomes binding again.

The quantity of reserves (money base) is a tool the Fed uses to manipulate interest rates to the supposed target.  The reason this works is that the expansion of credit is constrained by this quantity.  This means that the quantity of base money determines the quantity of credit created and the interest rate.  You can say that the quantity of reserves the Fed has to create is determined by the interest rate target and the demand for loans and the reserve requirement but this is not saying something different from the “fractional-reserve banking theory of credit creation,” it is just saying it in a different order.  It is still a fact that the Fed controls the size of the monetary base and that this puts a constraint on the total amount of loans and deposits banks can create.

“Zero” Lower Bound and Interest On Reserves

If for some reason the quantity of base money becomes high enough relative to the demand for loans that the demand hits the supply to the left of the maximum quantity of loans which can be created, then this constraint will cease to be binding and instead bank behavior (on an individual level) will be equating the marginal return on loans to the marginal return on reserves (recall that while banks as a whole cannot reduce their reserves, individual banks can).  The reserve-requirement constraint still exists but it is not binding.  When this happens banks could make additional loans but they are choosing not to because the rates at which they would have to make those loans are not worth it.  This is not a criticism of banks.  So while the imagery of reserves being parked at the Federal Reserve instead of being loaned out may seem misleading, this is only because if banks made more loans, the reserves in the aggregate would still be parked there.  This does not mean that the presence of those reserves, however they are described, does mean that banks have the ability to make more loans.

In this environment, increasing the money base does not relax the constraint on lending because it is not binding and therefore, it does not have the usual effect on interest rates and borrowing/lending.  (This is not to say it has no effect since it still affects inflation expectations which affect the demand).  On the other hand, lowering the IOR would lower the rate of return on reserves (obviously) which would make loans relatively more attractive.  In other words, it would shift supply downward, which would increase the quantity of loans and further reduce interest rates.

Market for Loans

loans market zlb2

Now if demand suddenly increased in this environment, banks would start making more loans and this could cause inflation if the Fed did nothing to restrain it.  However, I agree with the author that the Fed would have no difficulty reigning this in by reducing the base if such a thing occurred.  Indeed, I believe the Fed would love to have that problem instead of the current one.  However, just because the Fed can change the constraint by changing the total quantity of reserves does mean that it isn’t a constraint.

The claim that “banks can’t lend out reserves” seems to be purely a semantic argument.  He doesn’t want to call it “lending out reserves” but his reasoning for this–that an individual bank’s reserves don’t decrease when they lend more–is not correct since, even though they may trade deposits for loans, those deposits are usually quickly transferred, along with reserves, to other banks.  This means that individual banks can’t change the total quantity of reserves but they most certainly can change the quantity of their own reserves.

  1. Dustin
    January 4, 2014 at 4:35 pm

    Excellent response! I would point out that the argument isn’t semantic… When a loan is made, in keeping with the accounting identity, the reserves account isn’t reduced.

    -> Loans (A) up and Deposit (L) up

    While this may predictably result in the reduction of reserves when the newly created deposits on account are spent to an external party, to state this is semantically lending out reserves is equivalent to stating that a bank loans itself net income strictly because earned interest is a predictable consequence of making a loan.

    Within the reserves account, however, there is an immediate impact: Excess reserves are reduced and required reserves are increased, both at an amount equal to (reserve requirement * loan)

  2. talldave2
    January 4, 2014 at 6:20 pm

    Interesting, thanks for sharing.

  3. Free Radical
    January 5, 2014 at 9:37 pm

    Thanks guys. Dustin, yes, there are two ways in which lending reduces excess reserves. By increasing loans/deposits which lowers reserves relative to them (on a aggregate level) and on an individual level by actually reducing reserves.

    There are two main arguments in that paper, one is that banks are not constrained by reserve requirements. That is simply wrong. The second is that banks don’t “lend out” reserves and that is semantic but misleading. When you teach the money multiplier in an introductory econ class most people (in my experience) treat the reserves as cash and when banks make loans they actually hand the cash to the borrower, the borrower spends it and then the person who they give it to deposits it in their bank. This decreases reserves but only momentarily until the money is deposited again.

    You can say that they don’t really “lend out” the reserves, they actually create new credit in the form of bank deposits and give that to the borrower and so reserves (at least in the aggregate) are not affected. However, this does not change the analysis in any way, the total amount of credit which can be created from a given amount of reserves is the same, the incentives and constraints of the banks are still the same. It’s a meaningless distinction.

  4. Spencer Hall
    January 7, 2014 at 10:20 pm

    Commercial banks need excess reserves for clearing balances. They do lend them & they are either redeposited internally (within the individual bank), or redistributed externally (within the system).

    The remuneration rate is a credit control device. It induces dis-intermediation within the non-banks. Since non-bank lending/investing is restricted, the Fed must increase the rate of expansion in Reserve Bank credit to try and compensate.

  5. Free Radical
    January 8, 2014 at 12:45 am


    I think the first thing you said is basically what I’m trying to say. I’m not sure what you mean by the second.

  6. Spencer Hall
    January 8, 2014 at 6:56 pm

    Commercial banks -CBs (as a system) pay for what they already own (interest on their deposit liabilities). Providing the CBs with a preferential, interest rate differential (the remuneration rate), sucks savings (& loan insurance), out of the non-banks (i.e., it induces dis-intermediation, or an outflow of funds, or creates a negative cash flow). And the Fed cannot offset the damage to the economy (loss of jobs, production, etc.), without unnecessarily increasing inflation beyond what it would have otherwise have been (the 1966 S&L credit crisis is the paradigm).

    I.e., the non-banks (NBs) are not in competition with the CBs. And lending/investing by the NBs is non-inflationary, ceteris paribus (matching savings with investment). Whereas lending/investing by the CBs is inflationary (results in newly created money). Unspent savings (savings impounded within the CB system) are lost to investment, indeed to any type of expenditure.

    The elimination of Reg Q ceilings increased the costs (lowering CB’s profits), and decreased the volume of loan-funds (raising long-term rates). In essence, introducing the payment of interest on excess reserves (even though reserve balances aren’t included in the money stock), does the same thing.

  7. Spencer Hall
    January 8, 2014 at 7:20 pm

    The CB’s reserves today are largely driven by bank payments (debits). 90-95 percent of all demand drafts clear thru transaction based accounts (reservable liabilities). Legal (required) reserves are then based on transaction liabilities 30 days prior, etc.

    In c. 1995 legal (fractional) reserves ceased to be binding: because increasing levels of vault cash (larger ATM networks), retail deposit sweep programs, fewer applicable deposit classifications, & lower reserve ratios, combined to remove most reserve, & reserve ratio, restrictions.

    I.e., 85% of all required reserves are now satisfied using applied vault cash (so the CBs aren’t necessarily reserve bound from any statutory requirement). But CBs still need central bank deposits for clearing checks and making other interbank payments, which potentially gives the central bank leverage over money and bond markets. The problem is the FOMC members don’t (in fact, never have), watch reserves. Their transmission mechanism is interest rates [sic].

  8. Spencer Hall
    January 8, 2014 at 7:30 pm

    See: http://bit.ly/yUdRIZ

    Quantitative Easing and Money Growth:
    Potential for Higher Inflation?
    Daniel L. Thornton

  9. Free Radical
    January 8, 2014 at 8:12 pm

    I’m still not sure what you are arguing here but a couple things at least jump out at me.

    1. You say reserves ceased to be binding in 1995 but the graph in the paper you link to clearly shows excess reserves at zero until 2008.

    2. You say the FOMC members don’t watch reserves, they watch interest rates. Fine but that doesn’t change the fact that they change interest rates by changing the supply of base money which affects reserves and the presence of (large) excess reserves changes the way that their policy affects interest rates.

    3. You say that banks need excess reserves for clearing balances etc. and I agree, they never have literally zero excess reserves but in “normal” times they keep only a small amount which is required for these purposes. A more accurate supply curve would be a monotonically increasing curve above and to the left of the one I drew which is very flat and close to the level of IOR for low quantities and approaches infinity as the quantity approaches the maximum possible quantity but gets pretty close to that quantity for moderately high interest rates. It doesn’t change the essential point I am trying to make.

  10. Spencer Hall
    January 9, 2014 at 5:24 pm

    I wasn’t arguing. Rather enjoyed your uncommonly literate explaination.

    Re (1): the multiplier is commercial bank credit divided by required reserves. The expansion coefficient exploded as legal reserves ceased to be binding in 1995 (after the 1/3 reduction in reserve requirements from the 1990-1991 regulatory changes). I.e., contrary to all pundits, the MB has never been a base for the expansion of new money & credit.

    Re (2): the Fed’s research staff is political. And they (citing Friedman), naively believe that reserves are a tax [sic]. See – ” the Board–as authorized by the act (FSRRA of 2006)–could consider reducing or even eliminating reserve requirements, thereby reducing a regulatory burden for all depository institutions”

    Re (3): Here, your analysis is actually non-sensical. Keynes’ liquidity preference curve (demand for money), is a false doctrine. Interest rates are determined by the supply of and demand for loan-funds, not the supply of and demand for money. That’s been the Fed’s operational error since William McChesney Martin switched from using a net free or net borrowed reserve aggregate approach, to the Federal Funds “Bracket Racket” in c. 1965.

  11. Spencer Hall
    January 9, 2014 at 5:52 pm

    POMOs between the Reserve Bank (FRB-NY – our Central Bank) & the non-bank public (the only way new money could be created by QE operations:
    ……………………. Reserve Banks
    [+] U.S. Obligations…… [+] Demand deposits (banks)
    …………………… Commercial Banks
    [+] Reserves…………….. [+] Demand deposits

    It is assumed that the seller of the security received a deposit credit.

    The excess reserves of the CB typically increase less than total reserves, since the expansion of Reserve Bank credit causes an equal increase in the CB’s deposit liabilities (i.e., depending upon the deposit classification, this may or may not increase the CB’s required reserves – if it is “e-bound”).

    So QE was a farce. The total increase in the volume of securities held outright on the Fed’s balance sheet: H.4.1 since Oct 6, 2008 = $3,270,714 trillion dollars. Note this increase in SOMA securities is related to quantitative easing or the purchase of Treasury & MBS securities (or the reinvestment of maturing securities), by the FRB_NY’s “trading desk” (our Central Bank).

    Total increase in bank accounts included in M1 & M2 (less currency) since Oct 6, 2008 = $2,334,700 trillion dollars.

    So at this point, bank money, relative to POMOs, grew by only .71 percent of all open market operations of the buying type. Whereas prior to Oct 3, 2008, any one dollar increase in excess reserve balances (due to POMOs) resulted in the multiplier (required reserves) expanding CB credit by 208 times.

    Commercial bank credit (all loans + investments), increased by $1,074 trillion dollars during roughly the same period (from 7/30/2008 until 12/18/13). I.e., lending/investing by the CBs involves the creation of new money somewhere in the commercial banking system.

    The cash-drain factor during this period = $381.7b

    The other principal drain on bank deposits during this period was from the increase in bank capital accounts (roughly $312b?).

    Then when you subtract the money created by the CBs you get 39 percent on the dollar. I.e., out of every dollar of assets purchased by the FRB_NY’s “trading desk”, only 39 cents on the dollar could possibly have ended up as new money.

    Finally, you need to subtract the loans & investments from the NBs (CUs, MSBs, & S&Ls). So you see, the POMOs were conducted with the CBs & not the NBs. Ergo, remunerated excess reserves induce dis-intermediation among the NBs (as the CBs outbid them for “specials”).

  12. Spencer Hall
    January 9, 2014 at 5:57 pm


    Finally, you need to subtract the loans + investments from the former NBs

  13. Free Radical
    January 9, 2014 at 10:24 pm

    Yeah, I want sure if you were arguing with me or not, thanks for the compliment. You are speaking a language I’m not used to so I’m still working on it. I will point out though that I never mentioned the demand for money, that’s about currency held by the public which I abstracted from. The market I portrayed was in fact the market for loanable funds.

    I disagree with this statement: ” the MB has never been a base for the expansion of new money & credit.”

    I suspect that at the heart of it there is a semantic argument but I still don’t fully comprehend how you are arriving at this conclusion so I cant really do anything to try and sort it out. I sense you may have some experience in banking and bankers and economists tend to see things in different terms without one necessarily being wrong and the other right.

  14. flow5
    January 10, 2014 at 7:53 pm

    Currency has no expansion coefficient (fractional reserve banking doesn’t work without warehouse money). And you can prove this several ways, one, by dividing the money stock by the MB and then compare your findings to dividing the money stock by required reserves. This gave traders an edge when there were reporting errors, e.g., back in 79 & 80, when T-bond future’s traders followed m1.

    But the debate as to whether CBs lend their reserves or not (their own assets), should be obvious (e.g., there’s a federal funds market), although the Fed’s actual target was the daily repo rate prior to the intro of the payment of interest on reserves (the one-day cost-of-carry on all government bonds), which meant that the Fed’s transmission mechanism actually worked through buying & selling gov’ts. The Fed’s new reverse repo facility didn’t change the game (see: Paul Meek – “Open Market Operations”).

    Keep up the good work.

  15. Spencer Hall
    January 13, 2014 at 11:12 pm

    The assumption (mechanical accounting process) is that when commercial banks (CBs) make loans or invest, reserve balances:

    [both (1) the CB’s interbank demand deposits (IBDDs), or as of Oct 6, 2008, the newly transformed earning assets held in their respective District Reserve bank (and any respondent’s “pass thru” reserve-deposit accounts), and/or (2) the individual CB’s vault cash applied within its ATM network – i.e., “warehouse money” which isn’t counted in M1 or M2],

    …are either re-deposited within the same CB, or reapportioned as they are redistributed (either re-concentrated in A: money center/TBTF clearing banks and/or B: disproportionately re-concentrated within the FBOs lacking FDIC insurance fees), within the commercial banking system.

    Reserve balances are either “transferred” (re-circulate), directly via FED-wire or indirectly via the currency route, from one commercial bank to another (i.e., have reserve velocity/exchange hands). For example, items “due from other banks” are credited or settled, or as (1) the newly generated money is initially deposited and clears, and/or existing (surplus) vault cash is applied (re-classified), or as any new individual CB requirements are satisfied: (2) bought outright: in the interbank market (indeed lent!), money market, borrowed from the discount window, or obtained via daylight credit (depending on net debit caps on Fedwire, NSS, & ACH credit transactions), etc.

    Under Reserve Simplification Procedures effective July 2013, required clearing balances (excess IBDDs), have been comingled with required reserves: thus further confusing liquidity with legal reserves (vault cash was permitted to be counted in 1959), & thereby further eroding the FOMC’s power to closely monitor & absolutely control the creation of new money & credit (& thereby the price level).

  16. J Thomas
    March 5, 2014 at 11:12 am

    I’m not sure when the last time I used cash was. Maybe a week or two ago, I had a $5 bill in my pocket and I bought something with it.

    Vault cash has become far less important in recent years. I read somewhere that banks now keep something less than .5% cash, because they never need more. Especially when any large cash withdrawal encourages them to tip off the police to a possible drug bust….

    Money transfers between banks now happen in seconds — or at least the knowledge of them does. The actual change in ownership can legally take days, right? So bank reserves are on computer. A bank owns what the clearinghouse says it does.

    If a bank has reserve problems, can it sell loans to handle them? Sometimes. Remember the tranche stuff, where banks were able to convert real estate loans into commodities that could be sold to any trader? And when they started potentially going bad nobody know which bank had which loans? If AAA rated loans turn into commodities, then a bank can sell them at any time for electronic cash. A bank gets in trouble if it becomes insolvent, or if the Fed thinks it has too many bad loans to handle its liabilities. As long as there’s sufficient liquidity the bank’s reserve requirements are only an accounting issue.

    The way I read it a long time ago, if a bank has a loan they really want to make but they don’t have the resources to handle it, they can borrow money from the Fed to do it. They borrow at the rate they get from the Fed, tack on their own rate, and lend it out. Of course if the loan goes bad they owe the Fed for it, so they need to be pretty sure it’s good. The Fed controls interest rates partly by setting the rate it will lend to banks, right? So banks aren’t completely limited in their lending by their reserve requirements. And they can borrow from each other if they can agree on a deal. Usually a bank should be an excellent credit risk….

    Banks can keep part of their reserves as government bonds and get interest. Why not? It’s a completely safe investment. Not like they need the reserves on hand to deal with bank runs or fluctuations in withdrawals.

    Federal Reserve member banks are required to keep some of their reserves in the Fed. So the Fed has a fraction of all the money in the country, that it can lend. In seconds. It pays some interest for some of the money that banks deposit with it. Not like they need to hold those reserves themselves when they can get the money back in seconds.

    Individual bank reserves are a sort of legal fiction, one that reflects a historical reality or maybe a historical accident. The reality they bow to is that a bank must be ready to handle some risk — it owns a collection of loans and it owes money to various people, and it must be able to handle a reasonable chance that some of the loans might go bad.

    The details describing how the system has evolved to maintain responsibility for tracking that risk while evading the onerous reserve requirements of yesteryear are surely very complicated. Some of them were surely designed to hide the fact that the old requirements are being evaded. And the details matter, because every tiny detail which has a flaw is an invitation for somebody to figure out a new kind of fraud.

  17. June 30, 2014 at 8:04 pm

    Oh, finally someone that thinks straight and understands the issue correctly.

    I was just goggling for information regarding banks excess reserves and came across a bunch of economists that claimed that there is no such thing as a money multiplier, and that bank lending is not restrained by their reserves.

    Thanks for restoring sanity…

    • Free Radical
      June 30, 2014 at 10:04 pm

      My pleasure.

  18. Spencer Hall
    August 3, 2014 at 2:16 am

    I disagree with this statement: ” the MB has never been a base for the expansion of new money & credit.”

    NO, an expansion of currency held by the non-bank public is quite literally – contractionary.

  1. March 13, 2014 at 3:24 am
  2. March 25, 2014 at 12:40 am

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