The taxi multiplier

Suppose that you’re living in a city that requires a medallion to operate a taxi. Unlike New York, however, your city doesn’t sell permanent medallions. Instead, it distributes temporary medallions that last only a year, and those medallions trade at some price. How does the number of medallions influence the number of taxis?

If you were a budding macroeconomist, you might conjecture the existence of a “taxi multiplier” of one: as the city increases the supply of medallions, the number of taxis on the street increases by precisely the same amount. And in fact, this would be an extraordinarily accurate way of describing the data. As long as they’re constrained by the supply of medallions, the city’s taxi operators will put exactly enough taxis on the street to use up all the medallions. There will be no excess medallions floating around.

Now suppose that the city dramatically increases the supply of medallions, flooding the market. Will the “taxi multiplier” still hold?

At first, yes. As long as taxi operators are still constrained by the scarcity of medallions—or, equivalently, as long as medallions trade at a price above zero—the number of taxis will be exactly equal to the number of medallions. At some point, however, the number of medallions will exceed the number of taxis that it’s economical to put on the streets, no matter how little the medallions cost. (After all, cities without medallions don’t have an infinite number of taxis.) At this point, there will be no scarcity, the price of medallions will plummet to zero, and the “taxi multiplier” will cease to be operational. In fact, any further decisions to increase the supply of medallions will have zero impact on the city’s taxi fleet. The number of taxis is pinned down by the supply and demand for their services.

It’s instructive to think about the “money multiplier” in the same way. Up to a point, bank reserves are precisely tied to the amount held in checking accounts: since the required ratio is 10%, any increase in bank reserves will be mirrored by a 10-fold increase in checking account balances. There are no excess reserves. At some point, however, the Fed will increase the supply of bank reserves to such an extent that they’re no longer a binding constraint on the ability to put money in checking accounts. The cost of holding reserves will plummet to zero (as the fed funds rate falls to the rate paid on reserves), and checking account balances will be determined entirely by other factors: consumers’ desire for liquidity, consumers’ assets, the cost of financial intermediation, and so on. At the margin, there is no longer any money multiplier, at least in the textbook sense.

This isn’t to say, of course, that the Fed is powerless to affect the economy. But the “bank lending channel”, where an increase in the supply of reserves leads banks to accept more deposits and lend them out, cannot possibly have any impact.

As long ago as 1995, Bernanke and Gertler described a model of this channel as a “poorer description of reality than it used to be”. After the US eliminated every reserve requirement except the 10% on checking accounts, the direct impact of reserve supply on the amount of financial intermediation in the economy became questionable at best. But now that the interest rate on reserves is (more or less) the same as the federal funds rate, holding reserves to back deposits has become costless—and just as the taxi multiplier disappears when the price hits zero, the money multiplier ceases to be relevant.

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24 Comments

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24 responses to “The taxi multiplier

  1. Three points:

    1. “Supply” is not the same as “quantity supplied”, and not the same as “quantity”. The “supply” of medallions should mean the “supply *curve*” (or supply *function*). In which case, we can think of an increase in the supply of medallions as either a rightward shift in the supply curve, or a downward shift in that same curve. Is there any difference between the two? An “increase in supply” can be thought of as increasing the quantity you are willing to sell or reducing the price at which you are willing to sell them.

    2. Canada, for example, has no required reserves at all. Not even zero. (And the interest paid on reserves is set at 25 basis points below the target for the overnight rate). This is like saying you don’t need a medallion to operate a taxi. And yet the Bank of Canada can still control monetary policy and keep inflation on target. This is like saying the city can affect the price of taxis by controlling the supply of medallions even though you don’t need a medallion to run a taxi. There must be some problem with the medallion analogy.

    3. You are describing an equilibrium in which medallions are no longer scarce. If the city dropped medallions out of a helicopter, people would leave them lying on the sidewalk. Again, the analogy has a problem.

  2. JKH

    “Suppose that you’re living in a city that requires a medallion to operate a taxi”

    A variation/modification:

    Suppose the city requires a “taxi-worthy” statement of personal operating capability, prior to supplying the marginal medallion that a successful applicant would need in order to start business.

    This requirement corresponds (simplified) to a (pre-existing) bank capital condition that allows for bank risk taking through lending. Such capital conditions are supervised (or are supposed to be) by the regulator.

    It is capital, not reserves, that is the binding constraint on bank lending and corresponding deposit creation (binding in the sense of the economic requirement – not necessarily the immediate availability).

    As far as reserves are concerned, the Fed supplies them readily in response to new lending and deposit creation that has already taken place – in order to control the Fed funds rate. In this sense, reserves are a binding constraint – not on lending and deposit creation – but on the Fed funds rate – because of their critical marginal pricing role in interbank settlement transactions, over and above any static, statutory ongoing stock requirement for reserves. The latter type of statutory requirement is effectively a tax on bank interest margins. Canada has a zero reserve requirement. Modulo a non-zero statutory parameter, the core settlement purpose of reserves requires only a small amount of excess reserves (in normal financial conditions) in order to ease potential friction in the target fed funds rate trading level.

    Even with US statutory reserve requirements, the current situation of “the great excess” means that the Fed has supplied reserves fantastically beyond the demand for reserves from the banking system, based on any reality-based assessment of expected bank lending and deposit creation, even over the very long term.

    Those reserves are there, not for settlement function purposes and not for statutory reserve requirement purposes, but because the Fed has temporarily taken over a substantial financial intermediation function that it normally does not assume. The issuance of reserves as a result of Fed asset expansion is the mechanical way in which private sector financial risk has been transferred to the Fed. Excess reserves are simply the Fed liability/commercial bank asset channel through which this risk transfer has been effected.

    This too shall pass.

    But while it is there, it has nothing to do with reserves in their core function of settlement medium or even statutory requirement positioning.

    On the other side of town, the binding constraint on the taxi driver in the modified architecture is not the medallion – but the statement of personal operating capability that is needed to get the medallion. The medallion is only a form of publicly accepted evidence of taxi capital and operating approval, and what prevents him from being hauled into jail after he starts driving (somewhat like capital adequacy normally allows banks to function in the interbank reserve settlement market without backing into the Fed).

    The medallion is public evidence that allows the taxi to “clear” passengers in and out (somewhat like supervisory approved capital positioning allows banks to clear reserves in and out through interbank settlement).

    If extraordinary levels of excess reserves are made available at the macro level, that does nothing in itself to increase the supply of capital required to back risk taking via bank lending and corresponding deposit creation. If extraordinary levels of medallions are supplied at the macro level, that does nothing in itself to increase the number of approved “taxi-worthy” applicants, since medallions are only awarded at the micro level on the basis of “taxi-worthy” capital.

    Perhaps the city is supplying excess medallions for another reason. Perhaps it has bought a fleet of used taxis, driven by city employees already signed up, and the medallions are only a bureaucratic by product in evidence of such a transaction.

    • David Beckworth

      JKH:

      As far as reserves are concerned, the Fed supplies them readily in response to new lending and deposit creation that has already taken place – in order to control the Fed funds rate. In this sense, reserves are a binding constraint – not on lending and deposit creation – but on the Fed funds rate
      This is only true for a given target federal funds rate (ffr). That is, the Fed responds to shifts in the demand for reserves in order to maintain its ffr target. In that narrow sense the monetary base is endogenously determined.

      Over time, however, the Fed is adjusting its target ffr in response to something like a Taylor Rule. From this perspective, the monetary base is being exogenously determined and is not be driven by new deposit and loan creation already taken place. For example, when the Fed suddenly changes its ffr target–a “shock”–it is pushing reserves into the banking system unrelated to any changes in bank reserve demand. Now this action may change expectations of future economic activity and that in turn may affect the demand for bank reserves, but the point is the exogenous change started with the Fed not the banking system.

      If extraordinary levels of excess reserves are made available at the macro level, that does nothing in itself to increase the supply of capital required to back risk taking via bank lending and corresponding deposit creation
      Bernanke and the Fed don’t see it that way. They have said numerous times that they can raise the interest paid on excess reserves if needed once the economy really starts recovering. They clearly see excess reserves being an important factor–not the only one though–for deposit creation down the road. Yes, capital concerns and the demand for credit are determinants too, but they apparently they see these becoming less of a constraint on deposit creation as the economy recovers.

    • Excellent. I think that this is a great adaptation of the analogy to make it a better depiction of reality.

    • Jeff Hallman

      @wh10

      If capital constraints are preventing a bank from making a profitable loan, why doesn’t it just sell some stock? Most corporations have registered a lot of stock that they haven’t issued, so legalities are not the issue. And asymmetric information isn’t the answer either, because the bank should be able to find a big investor that it can share the info with, even if it can’t convey the info to the wider market.

      The only story I’ve ever heard that explains why a bank can’t sell stock is the debt-overhang story. In that story, additional capital makes the bank’s debt less risky, so the market value of the debt increases. This value had to come from somewhere, so it must be that the existing stockholders lost it. But the debt-overhang story doesn’t work if the bank is sound to begin with, because then there’s not much risk to affect the value of the bank’s debt. And I’m not sure I believe it even in the case of a bad bank.

  3. That came off as too negative. It’s a good post, and I think it’s very instructive to probe into that analogy deeper. In learning why the analogy might break down, we will learn more about money, and why the monetary base might be different from taxi medallions.

  4. wh10

    To echo JKH’s point regarding the role of reserves and the money multiplier, the money multiplier is a misrepresentation of how bank loans and money supply change in the real world.

    A bank’s ability to expand its balance sheet is not constrained by the quantity of reserves it holds or any fractional reserve requirements. The bank expands its balance sheet by lending. Loans create deposits which are then backed by reserves after the fact. So as long as the margin between the return on the loan and the rate they would have to borrow in the interbank market or from the central bank through the discount window is sufficient, the bank will lend. Certainly the “price of reserves” will play some role in the credit department’s decision to loan funds. But the reserve position per se will not matter. At the end of the day, the Fed must supply the reserves to defend its FFR target. Else the FFR would sky rocket.

    And empirical evidence from the Fed: http://www.federalreserve.gov/pubs/feds/2010/201041/201041pap.pdf

  5. who10: “At the end of the day, the Fed must supply the reserves to defend its FFR target. Else the FFR would sky rocket.”

    But if bank lending increases, and that increases aggregate demand and inflationary pressure, the Fed will not want to defend its previous FFR target. It will want the FFR to “skyrocket”. (More precisely, it will want the FFR to rise to whatever level it takes to prevent those inflationary pressures, which means preventing AD rising, which means preventing bank loans increasing.)

    This is the exact opposite to saying that the Fed “must” supply the reserves demanded. On the contrary, it must “not”. The Fed’s target is not the FFR. It is the rate of inflation. (Um, OK, I expect I’m really talking about an inflation-targeting central bank here. God only knows what the Fed is really targeting.)

    • wh10

      “The Fed’s target is not the FFR.”

      Hm, I think that is a bit stretching it. At each of 8 annual FOMC meetings, the committee votes on the FFR they wish to target for the time being. Once decided, the FOMC instructs the Fed’s open market desk to carry out the policy decision through the use of OMO.

      So, the FFR is most certainly defended, for an extended period of time, until the FOMC decides to change it, for the precise reasons you have listed.

      So much more often than not it is subtracting/supplying reserves at rates consist with its target FFR.

      For this reason, and the many listed in the paper I linked to, the money multiplier is simply a terrible representation of what happens in reality.

      • wh10

        Additionally, stigma not withstanding, the discount window is always there.

      • wh10: if you are looking at what happens in the very short run, within that 6.5 week period, it might be correct to take the FFR as the Fed’s target. (But it even then it might take longer than 6.5 weeks for commercial banks’ deposit creation and lending to get to equilibrium, so it still wouldn’t be correct to say that the money stock is demand-determined). Any longer than that and it would be more correct to say the Fed targets the output gap, so the LM curve is vertical (because the Fed makes it vertical to fully offset perceived shifts in the IS curve). Go longer still, and the target is inflation (?). And if you go to the ultra short run, like in hourly data, the way the Fed hits its FFR target is by adding or subtracting reserves from the system.

        Plus, what matters (for commercial banks, and the whole economy) is not just what the Fed does now, but what the Fed is expected to do in the future, and what the Fed *would* do if circumstances changed. Banks won’t create deposits and extend loans if the FFR is low today but is expected to be higher in future. What matters is the whole monetary policy reaction function, not just today’s FFR.

        The story that works well with one data frequency, holding some things constant, won’t work well at another data frequency, holding different things constant.

        “The Fed sets the FFR” is just one social construction of reality.

      • wh10

        Nick, thanks for the reply.

        First, I misspoke: “So much more often than not it is subtracting/supplying reserves at rates consistent with its target FFR.” What I meant to say is the Fed is always defending some FFR, because there always is a prevailing target. The FFR may change, but then it is that FFR which is defended, which means reserves must always be supplied on demand at a rate consistent with that target.

        I am not sure how any of this affects the argument that it is the price of reserves that matters (whether current and/or anticipated), not the amount.

        David commented on JKH’s post with your same viewpoint, so I’ll let the discussion continue there. JKH is much more knowledgeable, articulate, and intelligent than I am.

  6. Scott Sumner

    Interesting post, but the analogy doesn’t hold. Increases in the supply of taxi medallions don’t increase the nominal demand for taxi services. Hence a glut develops at some point. In contrast, increasing the supply of base money does increase the nominal demand for base money, via a higher price level. So the (nominal) demand for demand deposits is never satiated when M increases. (Here I assume a premanent increase in M, which increases P. For temporary increases you are completely right.)

    Your post predicts that increasing the supply of money reduces the nominal interest rate. But if you compare money growth rates cross-sectionally, you find that the fastest money growth is associated with the highest nominal interest rate. That empirical finding refutes your basic monetary model, which assumes that more money reduces interest rates.

    BTW, it’s GREAT to have another thoughtful, provocative, innovative blog like Nick’s.

  7. Dear all,

    Thanks for the comments. I agree that the analogy is limited. I was trying to use it to depict one particular channel: the impact of reserves on money creation through the “money multiplier”. It certainly doesn’t extend to all the other impacts of monetary policy. (After all, as Scott says, prices in the economy aren’t quoted in terms of taxi medallions.) In fact, I don’t think that changes in the cost of holding reserves are a remotely important channel of monetary policy. But not everyone agrees with this: after all, back in 1994 Kashyap and Stein wrote at length about the “bank lending channel” of monetary policy. Maybe by now they’ve decided that this has become relatively unimportant, but I’m not so sure.

    The core intuition is that there is a certain level of taxi services determined by supply and demand in the market—just like there is a certain level of lending and financial intermediation pinned down by variables other than the cost of holding reserves. (I don’t want to say “real variables”, since of course the Fed’s influence over the real interest rate makes a big difference here.)

    As either the cost of medallions or the nominal interest rate hits zero, the constraint posed by medallions or reserves ceases to bind, and the textbook “multiplier” relationship breaks down. This post is just an intuition-building exercise to clarify that fact. (An extremely smart and accomplished professor of mine once confessed to me that he never completely understood the idea of a money multiplier, so I think there is some value to the exercise.)

    “Taxis” could, of course, be replaced by virtually any good or service where there is some input like “medallions” that can be supplied only by the government.

    I agree with wh10 that given how the government implements monetary policy in practice, a better analogy would be that the government buys and sells medallions in order to hit a target price. Effectively, then, the government is charging a tax on the operation of a taxi—just like the fed funds rate minus IOR is a “tax” on taking checking deposits.

    • wh10

      “As either the cost of medallions or the nominal interest rate hits zero, the constraint posed by medallions or reserves ceases to bind, and the textbook “multiplier” relationship breaks down. This post is just an intuition-building exercise to clarify that fact. (An extremely smart and accomplished professor of mine once confessed to me that he never completely understood the idea of a money multiplier, so I think there is some value to the exercise.)”

      I think your professor did not understand it precisely because there is no such thing as the money multiplier, regardless of the nominal interest rate :P!

      “It’s instructive to think about the “money multiplier” in the same way. Up to a point, bank reserves are precisely tied to the amount held in checking accounts: since the required ratio is 10%, any increase in bank reserves will be mirrored by a 10-fold increase in checking account balances. There are no excess reserves.”

      There are no excess reserves not because an influx of reserves somehow instantly floods the private sector with new deposits until the point at which the reserve requirement is met (while ignoring capital requirements, credit demand, credit worthiness, and so on). There are no excess reserves because if there were, the Fed would not be hitting its FFR, as it plummets towards 0%. Studies that purport to show the money multiplier exists are just showing Fed accommodation. Again, see http://www.federalreserve.gov/pubs/feds/2010/201041/201041pap.pdf

      I am glad and honored we agree, but I am not sure on what we exactly agree upon!

  8. In contrast, increasing the supply of base money does increase the nominal demand for base money, via a higher price level. So the (nominal) demand for demand deposits is never satiated when M increases. (Here I assume a premanent increase in M, which increases P. For temporary increases you are completely right.)

    I think it depends on how the increase in base money is viewed. If it’s viewed as part of a long-term shift to a lower inflation target, then it can also increase real demand for base money by lowering the expected nominal interest rate—not just in the short term, but permanently. In practice I don’t think this is too relevant, since the Fed’s decisions are almost always interpreted as short-term moves, not long-term changes in its target away from the current 1-2% inflation. But it’s conceivable.

    Your post predicts that increasing the supply of money reduces the nominal interest rate. But if you compare money growth rates cross-sectionally, you find that the fastest money growth is associated with the highest nominal interest rate. That empirical finding refutes your basic monetary model, which assumes that more money reduces interest rates.

    This is definitely a problem with the taxi analogy—there are only “medallions”, not “real medallion balances”. In the short run where the price level is fixed, this isn’t so much of an issue, but I agree that this is another way in which its depiction of the long-term impact of monetary policy is seriously flawed, and limited to the very narrow “bank lending channel”.

  9. JKH

    David,

    First, it should go without saying that when the Fed is controlling the Fed funds rate, it is controlling the rate in the context of its behaviour compared to the prevailing target rate.

    Second, and similarly, the Fed can change the target rate any time it chooses to.

    Third, it can use a Taylor rule or whatever criteria it chooses to change the target rate.

    Fourth, it is NOT the case that the Fed needs to do much of anything material with the level of excess reserves in order to execute a change in the target rate. The announcement itself induces market pricing arbitrage that is immediately effective in this regard.

    Fifth, NONE of these issues changes in anyway the statement that the Fed supplies required reserves in response to new deposit creation.

    Finally, on a separate aspect, the fact that the Fed will want to pay interest on reserves has nothing to do with the “danger” that reserves pose for excess lending and deposit creation. Rather, it is a necessity in order to control the Fed funds rate in a tightening cycle, when such excess reserves are present. IOR must be paid to set a floor for the funds rate, which otherwise will head toward zero, which is an obvious contradiction of the operational objective. And these things are unrelated to the aspect of capital, which is the required driver of new lending and deposit creation, not reserves. The constraint is capital, not necessarily in the sense that it won’t be available, but in the sense that it must be allocated in order to acquire new risk assets. And the target fed funds rate is an input, directly or indirectly, into any economic capital allocation – not the availability of reserves.

    • JKH:

      “Fourth, it is NOT the case that the Fed needs to do much of anything material with the level of excess reserves in order to execute a change in the target rate. The announcement itself induces market pricing arbitrage that is immediately effective in this regard.”

      True, and a point that can be generalised. Monetary policy (for a credible central bank) is 99% communications policy. That is how (credible) inflation targeting central banks keep inflation on target. They announce their target inflation rate, expectations match that target, and arbitrage ensures the target is more or less hit. They don’t actually have to do anything — just makes sure they don’t contradict those expectations they have created. There is no mechanical transmissions policy for monetary policy.

      “Fifth, NONE of these issues changes in anyway the statement that the Fed supplies required reserves in response to new deposit creation.”

      Yes they do. If the deposit creation starts to lead to the Bank of Canada…I mean the Fed….fearing that inflation will rise above target, it will tighten up on the supply of reserves.

      • JKH

        No, Nick.

        They will increase the Bank of Canada rate, probably following a lead up period where they do some jawboning about their general intentions.

        And you just contradicted my point 4 (as I intended it), after agreeing with it.

    • David Beckworth

      JKH:

      Fourth, it is NOT the case that the Fed needs to do much of anything material with the level of excess reserves in order to execute a change in the target rate. The announcement itself induces market pricing arbitrage that is immediately effective in this regard.

      What you see as immaterial I see as material. The market pricing arbitrage you mentioned occurs only because the market knows the Fed will make sure the announced ffr target change is realized. That is, the market anticipates the Fed will adjust reserves as needed to hit its target (on average) and based on that expectation does most of the heavy lifting.

      Thus, we see the Fed engaged in repo transactions day-to-day to make sure the target is being hit. And over the longer term the the total amount of reserves are being permanently changed by the Fed as it stance of monetary policy changes (e.g. going from say a prolonged phase of easing to tightening). This figure shows, for example, bank reserves generally growing as the ffr target goes down (i.e. the liquidity effect) and vice versa. From this longer-term perspective it is easier to see that the Fed is changing bank reserves independent of the demand for them.

      Finally, on a separate aspect, the fact that the Fed will want to pay interest on reserves has nothing to do with the “danger” that reserves pose for excess lending and deposit creation. Rather, it is a necessity in order to control the Fed funds rate…

      I agree that the IOR creates a floor for the ffr as part of a corridor for the ffr target. However, this corridor will have to be adjusted as the economy recovers otherwise there will be a “danger” that the reserves will leak out to higher yielding opportunities. Again, Bernanke and the Fed have been saying this for some time as part of their “exit strategy.” (i.e. the Fed can raise IOR to prevent these reserves from leaking out and becoming inflationary).

      Finally, here is a figure that we both can appreciate. It shows that the growth rate of bank reserves and demand deposits for the commercial banking system are highly correlated. Obviously we view causality differently between these two series differently, but what a neat picture.

  10. Jeff Hallman

    @Matt;
    When the interest rate paid on excess reserves is higher than the risk-free rate, as it is now, the money multiplier falls from 10 to 1, but not to 0. Think of it this way: The Fed buys $1 million in Treasury bonds from someone. It pays with a check. The seller deposits the check, and his account is credited by the bank for $1 million. So at this point deposits have increased by $1 million.

    Next, the bank takes the check to the local Federal Reserve Bank and deposits it. It’s reserve account at the Fed is credited for $ 1 million, of which $900 thousand are excess reserves. The other $100 thousand are newly required reserves, because the bank customer’s deposit increased by $1 million.

    If no interest was paid on excess reserves, the bank would loan out the $900 thousand, which would increase deposits by $900 thousand and result in $90 thousand of formerly excess reserves becoming required reserves. And so on and so on until all the excess reserves have become required reserves. It it this secondary process that gets cut short by interest on excess reserves, but the original $1 million in deposits is still there.

  11. JKH

    David,

    That graph appears to show the growth in required reserves decelerating as policy is being tightened, etc., where policy is indicated by the target fed funds rate.

    I’ve said nothing inconsistent with that. It shows that that economic growth and bank credit/deposit creation (as the independent variable for the required reserve calculation) decelerates as policy tightens. And I agree that this effect is important for the policy objective.

    But the Fed provides the reserves that the banks require based on their actual credit and deposit growth, whatever the prevailing policy level for the funds rate and economic environment. The Fed must do this to keep the funds rate in line with the prevailing target. It is the target rate that the Fed adjusts in accordance with policy objectives – not the nature of the function whereby it provides required reserves in accordance with emerging deposits and calculated reserve requirements. And it is only when the Fed wants to change that funds rate that it will start to tinker with the excess reserve position – and even that may be muted due to the announcement effect and the anticipation of the announcement.

    “From this longer-term perspective it is easier to see that the Fed is changing bank reserves independent of the demand for them.”

    I’m not sure of your meaning there. I’m saying that the Fed supplies required reserves according to the requirement as a non-zero percentage of deposits. It does so ex post in response to the actual creation of those deposits (and the credit side activity that resulted in that deposit creation). And then I’m saying in addition that the Fed supplies the level of excess reserves that the system requires in order for the actual funds rate to track to the target funds rate. That existing funds rate calibration is a continuous process of ex ante judgement and feedback, using excess reserves as the sensitivity mechanism.

    One type of data that is more provocatively consistent with the point I’m making is that of the long term time series on the level of excess reserves, pre-crisis. That will illustrate for example that the level of excess reserves supplied by the Fed has been fundamentally no different, longer term, regardless of the level of the funds rate – 8 per cent or 3 per cent, for example. In particular, there is no cycle in excess reserves that correlates with changes in economic or balance sheet activity as there is for required reserves as per your graph reference.

    The point I made about the market arbitrage around fed fund rate changes is a question of degree. Even if the market was “slow” to recognize what the Fed had done (which might have been more the case before the Fed started formally announcing its target rate changes), any temporary increase or decrease in excess reserves is reversed quickly once the intended interest rate delta effect is complete. And then it’s back to square one for the excess reserve level that works whatever the funds rate level. With the announcement effect, the arbitrage takes care of the heavy lifting fairly quickly. I think it’s also the case that the Fed often allows drifting of the funds rate toward the boundary of the existing range, when the next target rate change is fully anticipated by the market. This drift might be accommodated by some relatively small scale tapping on the excess reserve accelerator or brake as the case may be for a few days prior to the actual target rate change.

    Back when Volcker was tightening, he periodically exercised particularly vicious withdrawals of excess reserves – even to the point of negative excess reserves – in order to effect particularly vicious changes in the funds rate. The Bank of Canada was doing much the same thing, sometimes forcing at least one bank to the window, just to get the rate up right away. But the point about about relatively quick change, market recognition (in the days when there was no formal announcement), and then reversal, still holds. Volcker implemented spasmodic tightening throughout the longer upward trend, but always stopped to return excess reserves to norm in order to hold the new funds rate trading range. That required reversal of short term tactical tightening of excess reserves was why rates didn’t go to 1000 per cent. And it was the interest rate that he affected directly. The effect on bank balance sheets and economic growth and inflation was a function of that rate impact over time. The effect on bank balance sheets longer term was not due to reserve withdrawal, because the required tactical reversal of excess reserve withdrawal was required fairly quickly in order to contain the upward movement in the funds rate. He was always testing the effect of the funds rate on the economy and money supply, using changes in excess reserves to change the funds rate – notwithstanding the popular myth that he effected some operational change in the way policy was implemented. He didn’t really. He was just looking at the Thursday money supply numbers (broad money), like everybody else who knew he did, and reacting to them with funds rate responses, using excess reserve settings to achieve whatever interest rate effect he thought was appropriate. The excess reserve supply affected interest rates – it did not affect the mechanical capability for banks to create new loans and deposits at that particular interest rate level.

    Put another way, it is (at most) a short term tactical manipulation of excess reserve levels that steers the funds rate as the operating objective. Apart from that, required reserves are a function of emerging balance sheets – not vice versa.

    I agree to a point regarding Bernanke/Fed communication. But I’d qualify by saying they’ve been ambiguous about it. Both Bernanke and Dudley have also said recently they’ll have absolutely no problem tightening monetary policy with the funds rate and interest on reserves. And I think the ambiguity in communication has steadily skewed over time toward this latter emphasis.

    I would describe the noted “leakage” more as “suction”, in the sense that as the economy improves and the aggregates grow, there will be some migration of excess reserves (assuming they still exist) to required reserves, based on deposit growth as it develops. But the mathematics of that equation under any interpretation suggest we would be here for decades until the existing level of excess reserves would be used up (hypothetically) in such fashion, based on the starting point for required reserves, and assuming (hypothetically) no other action to drain excess reserves. In any event, I view that marginal “suction” activity as a passive side show to the important stuff, which is the development of the economy and bank balance sheets (apart from that reserve classification activity) and the Fed’s policy response over time in the form of the funds rate. And the additional idea of proactively draining existing excess reserves in my view is more like house cleaning and tidying up of the Fed’s credit risk profile and balance sheet management, rather than a critical monetary policy determinant.

    The demand deposit/required reserve correlation as per your referenced graph is to be expected, but as you say is not an illustration of causation.

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