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A bit off topic, but I seem to remember Wynne Godley claiming some time ago that the elasticity of demand and supply for British exports and imports was such that devaluing the pound was a totally ineffective remedy for a balance of payments deficit in the case of Britain. I.e. the only remedy was mass emigration.

I suspect he was wrong, but I’m not 100% sure.

Do you regard a trading band as a fixed exchange rate? In a sense I guess it is because it's like the range that is used in inflation targeting -- plus didn't Bretton Woods work that way? However my impression is that when people say "managed exchange rates" that may be what they mean. Apparently people have also stopped referring to "dirty floats" to describe a nominally floating currency that is subject to frequent central bank intervention.

Ralph: he was probably talking about the "Marshall-Lerner condition". It's a bit like assuming the country produces a Giffen good. Cantabridgian "elasticity pessimism".

Vladimir: Hmmm. Good point. A trading band is like the weights switching from 100-0 to 0-100 when you cross the edge of the band.


Could a central bank conceivably hit two separate targets using two separate policy tools:

Policy tool #1 (Lender of last resort) - Central bank sets interest rate it will lend money at
Policy tool #2 (Open market operations) - Central bank sets price it will pay for existing government debt

Normally, these tools are aligned with each other - market price (interest rate) for government debt is very close to interest rate central bank will lend at. But this need not be the case.

Frank, I've seen that argument made. In that case the two tools are similar to what you stated: IOR and FFR. The targets were MB and inflation rate I think:
DOB (the author) used to leave comments here... but I haven't seen him for a while.

Nick R: Glasner got back to you.


Interesting article. One thing though:

"If the zero bound bothers you, just shatter it. In order to do that, the central banks will have to plug the physical currency loophole. That would involve clarifying that all contracts and financial instruments denominated in the currency it issues are really denominated in electronic currency. (This may require quite a bit of legal legwork)."

Greg Mankiw had an article about this type of thing a while back. He mentioned having the Fed zap out physical currency by the serial number printed on it - for instance one dollar bills whose serial number ends in "13" are now worthless.

My opinion, it would be better if currency was relegated to status as simply a medium of exchange rather than a storage of value / risk asset. Fiscal policy (government debt / equity) can handle risk appetite / storage of value needs with a lot less legal legwork.

Central banks tend to hold assets they consider safe, so if a CB is holding foreign-currency assets, that implies that the CB is managing the exchange rate. Because if the exchange rate is completely unmanaged, all foreign-currency assets would be risky.

Inflation targeting and exchange rate short/medium term targeting are compatible, just as very short run interest rate targeting is compatible with inflation targeting.

'Managing' the NEER upwards tends to tighten, while 'managing' it downwards tends to loosen. Interestingly this tends to correlate high rates with loosening, since a downwards sloping exchange rate trajectory, through interest-rate parity, results in interest rates higher than the foreign rate. Operationally it also means that loosening is unconstrained (can always print more money and sell it off, cutting the rate), unlike interest rates which have a ZLB problem. On the other hand tightening is limited by available foreign reserves (hence the riskiness in the Vox post).

Finally the band is more like a 0-0 fx rate-interest rate mix suddenly going to 100-0 at the band edge. The CB does nothing as long as the NEER is within the band, then leans hard near the band edges.

Squeeky: Hmmm. Good point. Changes in high frequency variation in interest rates or exchange rates, holding their average expected paths the same, could be compatible with inflation staying on target in a lower frequency. So central banks could either smooth interest rates or smooth exchange rates at that higher frequency.

Sort of off Topic.

In the recent brouhaha following the BOE's release of its paper on money creation, I made the following claim:

"Every textbook that presents the simple model of multiple deposit creation follows this with a critique clearly stating its “serious deficiencies”. In Mishkin’s intermediate level textbook (I have the 7th edition), not only is there such a section, the chapter in which it is taught is followed by a whole other chapter that makes it abundantly clear that the currency and reserve ratios are variables."


If you read the comments section you'll find Philip Pilkington making the following claim:

"Paul Samuelson & William Nordhaus 'Economics': "We can see that there is a new kind of multiplier operating on reserves. FOR EVERY ADDITIONAL DOLLAR IN RESERVES PROVIDED TO THE BANKING SYSTEM, BANKS EVENTUALLY CREATE $10 OF ADDITIONAL DEPOSITS OR BANK MONEY." (p493 - My Emphasis)"

To which I responded:

"I have the 16th edition (1998) of Samuelson and Nordhaus and that sentence can be found on page 480 of my copy. On the very following page it states: "THE ACTUAL FINANCIAL SYSTEM IS MORE COMPLICATED THAN OUR SIMPLE EXAMPLE."(My Emphasis.) It then goes on to state that in actuality depositors may choose to hold currency and that banks may choose to hold reserves above the reserve requirement."

Well, the reason why I bring this up is this is routine behavior among that portion of the econblogosphere population which manifests a bizarre pathological rage against a simple accounting identity. Sometimes, however, they quote from a textbook I'm not familiar with so there's no way for me to show that if they turn the page and read the subsequent text all is right with the world.

One such example is Unlearning Economics, who for several years now has been reflexively quoting the following passage:

"Models of the money supply multiplier link the money supply to the monetary base in a relationship of the following form:

M = mB


M = the money supply;
m = the money supply multiplier;
B = the monetary base.

In models such as this, m tells us how many times the money supply will rise following an increase in the monetary base."

Most recently Unlearning Economics posted a snapshot of this passage in a Twitter in response to Noah Smith, which stopped Noah dead in his tracks, seemingly because Noah, like me, didn't know where this passage came from.

Well, now, I have the answer.

It's from "Applied Economics" by Alan Griffiths and Stuart Wall:


This appears to be a textbook that's common only to the UK, so you'll excuse Noah and myself if we haven't heard of this textbook until now.

But the point is, I can finally turn the page to find the following written:

"But what determines the value of m? In fact, there are two factors: the decisions of depositors about their holdings of currency and deposits, and the level of reserves the banks hold to meet customer demands for currency...Whether the money supply multiplier is an adequate explanation of the money supply process depends partly on the stability of the ratios c and r [currency and reserve ratios]...Certainly for the UK the general view is that the money supply multiplier is unstable in the short run."

So just remember, anytime the "rage against a simple accounting identity" crowd starts quoting what any economics textbook says about the money multiplier, be sure and ask them to turn the page.

Mark, how did you figure that out? Well it's nice to know the student gets a fuller picture on the next page, but to be fair, the excerpt you quote there, however out of context it might be, doesn't sound all that different than David Glasner's latest post on this subject:


"The point of the money multiplier is to provide a rationale for saying: “sure, we know that banks create a lot of money, and we don’t really understand what governs the amount of money banks create, but whatever amount of money banks create, that amount is ultimately under the control of the monetary authority, the amount being some multiple of the monetary base. So it’s still as if the central bank decides what M is, so that it really is OK to say that the central bank can control the price level even though M in the quantity equation is not really produced by the central bank. M is exogenously determined, because there is a money multiplier that relates M to B."



Like you perhaps, I am somewhat puzzled when I read some of the things people write about the money multiplier these days.

When I learned this stuff, some years ago, we were taught the money multiplier simply in the context of understanding the relationship between a small monetary base and a larger stock of broad money. As far as I recall, it was never suggested as being the way in which the broad money supply was determined. Coming back to this more recently, I wonder where and when this interpretation crept in.

I found this out by some artful googling and ultimately by tracking down the information in the following comment section:


And, evidently, an unhealthy rage against a simple accounting identity is something which cuts across economic schools. I disagree with Glasner's characterization of how the money multiplier has been used, and agree with the Nick E.'s comment above for example.

I checked my old textbook and there is no question but that the message was definitely causality from bank reserves to deposit expansion via the reciprocal of the required reserve ratio

The causality is expressed as a time series of propagated t-accounts, as excess reserves are "used up" in an iterative process, which is still a not uncommon interpretation as far as I can tell

'Economic Analysis and Canadian Policy' by David Stager 1979 - maybe Nick R. knows it

I remember it well because I was working in a bank at the time, and I knew then that the causality was wrong - through direct observation (not theory)- the Canadian reserve system operated similarly to the pre-2008 Fed system at that time - reserves played no role in core lending and deposit creation

As I've before with Nick, the causality story amounted to an academic confusion between how bank money market liquidity management works, and how main lending operations work

Causality was the core theme as it was explained in the book - adjustments such as changes in the reserve ratio or people taking out currency etc. are at the margin to that

There was no "next page" correction to that basic causality

And that's the way I see it appearing mostly in the blogosphere today

The age of texts must have something to do with this - I haven't looked at a modern text to see how its treated or modified

If it's simply a "ratio", then there's no reason to imply or confuse causality by using the term "multiplier"

That said, it is perhaps easier to argue that causality under conditions of QE, but its still the wrong way to explain the motivation for bank lending

Fair enough on "rage against the identity" - for a few reasons

But the fact remains that it's a sloppy piece of economics "theory" (and what really should be documented as fact), however it is expressed, and needs comprehensive overhaul

Meanwhile, there seem to be a variety of versions of this in the recent debates - very non-standardized interpretations for something that should be far more fact than theory


1. Suppose, just suppose, the Boc had a perfectly inelastic supply curve of base money, and shifted that curve to the right.

2. Now suppose the BoC had an upward-sloping supply curve (interest rate on the vertical axis), and shifted it to the right/shifted it down.

3. Now suppose the BoC had a horizontal supply curve of base money, and shifted it down.

In all 3 cases, causality would run from the BoC to the banks.

You think in terms of the third case. But that is just one way of thinking about it. The rate of interest the BoC targets for 6.5 week periods is no more exogenous than the base, under inflation targeting.

BTW: I spoke to Paul Jenkins last night. Paul was deputy governor Bank of Canada until recently (he's now at Carleton). He agreed with the statement that the only thing the BoC ultimately controls is its own balance sheet (though he added it has an input in regulation), and said I could post this. He said that was the common view at the BoC.

Nick: you hob-knob with some interesting folks. What's on schedule for tomorrow? Tea with the queen?



Is your case 2 consistent with inflation targeting? And furthermore targeting a higher rate of inflation (by shifting the curve either rightwards or downwards)?


“Now suppose the BoC had a horizontal supply curve of base money, and shifted it down.”

etc. - OK

It’s just that one relevant technical issue for the pre-2008 Fed (and the old Bank of Canada) is that the creation of deposits resulted in a lagged demand from the commercial banks for the central bank to inject the needed amount of required reserves – precisely when that lagged incremental requirement became effective. That precision was required for the CB's short term interest rate control. The CB literally had to inject more reserves on the day when the addition to the requirement became effective. That’s a fact, and I’m surprised that no academic study seems to have documented that (apparently). So I would interpret that sort of periodic jerky adjustment as the CB moving horizontally to the right along its horizontal supply curve to meet an equal short term rightward shift of the banks' vertical demand curve for JUST THE REQUIRED reserve portion. The excess reserve position is then managed independently from that – in fact, that portion is nearly vertical in the short run for both supply and demand (pre-2008 Fed; old BoC). I think you probably need two different supply demand diagrams to distinguish between these two effects for statutory required and excess reserves respectively.

(That all gets screwed with QE and/or a zero reserve requirement system)

As far as the longer term is concerned, I understand that’s different. I don’t think I completely ignore that – just that I’m looking for a smoother interface between short and long before I can make full sense of the long – maybe even in a way (with a miracle) that’s not just “one damn interest rate after the other”.

I agree that the central bank controls its balance sheet. I don’t think that’s incompatible with saying that in controlling it, the CB responds to the demand for the monetary base in the context of consistency with short term interest rate control. One of those consistencies is providing the lagged supply of the quantity of newly required reserves as the deposit base expands (as above). And that is a response to a background process that in fact the CB does not control directly in the short term – i.e. the “endogenous” creation of deposits from new loans. So, yes the CB is in control of its balance sheet. But it needs to exercise that control consistent with its short term interesting rate targeting and with related processes that determine in part what it must do in exercising such “control”. In this sense, the CB is in control of whether or not it screws up its interest rate targeting, depending on background processes that it doesn’t necessarily control in the short term.

BTW, one of the things that’s puzzled me about this broad based multiplier discussion is that I only recall the multiplier idea from the old textbook as the lagged response of deposit creation to an assumed supply of incremental excess reserves. I don’t recall seeing the full monetary base used in the denominator. But maybe that's been around for a long time. And I also don’t see anybody remarking on that distinction, which I find equally puzzling.

Nick: One reason that central banks were established was to improve the elasticity of the banking system in its ability to supply credit. From that point of view, although all cases are possible, in analysing the system only cases 2 and 3 are consistent with the purpose and activities of a central bank. There is no reason for the central to exist in case 1 (unless you are referring to an intra-day horizon).

Due to the central bank's LOLR and stability obligations they must supply the base money required by the system (at a price of their choosing), otherwise banks could not offer the products that they do. But in case 2, bank loan and deposit pricing will be informed by their expectations of the cost of base money in the future, i.e. the central bank reaction function. Perhaps the 'multiplier' should be revised to be in terms of the expected base money supply?


I doubt it has anything to do with the age of the textbook. I've seen a copy of the 1948 edition of Paul Samuelson's "Economics" and it also states that the currency ratio and the desired reserve ratio are variables. After all, both soared during the Great Depression.

Maybe it's a Canadian thing.

"Maybe it's a Canadian thing." ... that's it! The money multiplier "works" in Canada. That explains it!


Just so I know I'm not losing it on at least one issue, one of the well known Fed papers in this "debate" defines the money multiplier the same way as I remember it:

"The most simple money multiplier described in textbooks links reservable deposits to
bank reserves:

∆D = 1/r ∆R

where ∆R refers to changes in total reserves

∆D refers to changes in reservable deposits

r is the required reserves ratio,

1/r is the simple multiplier."

i.e. no full monetary base, no restriction to demand deposits - just bank reserves and reservable deposits


JKH, you might want to double check your old textbook... Sadowski has a put out a call to see if anybody has one:



But Sadowski needs to read the comments he's criticizing a lot more closely

And maybe not misrepresent what they say

JKH, just thought I'd give you a heads up. Not owning anything remotely resembling an econ text book myself, I'm at the mercy off all you econ-text owners to sort this out.

JKH: first year textbooks usually have it as dM=(1/r)dR. They only discuss currency verbally, and hold it constant when the central bank changes the base, but say currency affects the results.
Second year texts usually do M=[(1+c)/(c+r)]B. But you need algebra for that, and it would be much harder working through a numerical example.

Hmm. When I Canadianised Mankiw's first year text, I did a box on zero reserve ratios. (Not to be confused with zero required reserve ratios).

"With a zero reserve ratio, all currency would be in people's wallets, rather than in banks' reserves. For a given amount of currency, the size of the money supply depends on the currency ratio - the fraction of the total money supply that people want to hold in the form of currency...........In an economy where banks hold zero reserves against deposits, the money supply will be the reciprocal of the currency ratio times the quantity of currency.....In Canada's monetary system today, where banks' reserve ratios are very small, the reserve ratio is much less important than the currency ratio."

Hmmm. My little box seems to have disappeared from later editions. Oh well. All is ephemeral.

JKH, BTW, do you have a side you favor int he Rowe/Glasner debate in Glasner's latest post? I can't figure out if everybody is now in complete agreement and has moved on, or if they are pretty much where they started off.


That seems like a sensible update, especially when expressed as a ratio rather than a multiplier.

I can't believe anybody would deny the relevance of examining the proportionality of currency to forms of bank money. That's an interesting data point.

But surely you must recall the kind of T-account progression I described for reserves and deposits - in older textbooks?


Just pulled out my 1975 Canadian edition of Samuelson.

Goes through exactly the same process with respect to reserve to deposit causality.

Same accounting progression.

Makes a point that the reserve ratio isn't necessarily fixed or that banks can hold excess reserves as a choice.

The alleged causality process is a constraint - not a mandate.

Which should be obvious (and nothing I've denied).



By "price" you presumably mean "interest rate". But the "base money required by the system" is proportional to the price level. If central banks did what you say they do, they would not be targeting inflation. The price level would be indeterminate if central banks "supply the base money required by the system". A doubling of the price level would double the base required by the system, and if the central bank accommodated that doubling of demand, the price level could double again. The whole point of central banking is to ensure that this does *not* happen. If they did what you say they should do, that would be a recipe for disaster.

It is a very very different thing for central banks *under the gold standard* to adjust the base in response to "the needs of trade" (as this doctrine used to be called a century or so back), because the gold standard put a constraint on their ability to do that, and kept the price level determinate.

And it is precisely this point that lies at the root of all the arguments about whether the stock of money is "demand determined". Any central bank that lets the stock of money be "demand-determined" has lost control of inflation. We learned that lesson the hard way in the 1970's.

Yes, central banks do not keep the base constant. They act as lenders of last resort, and do allow the stock of money to respond to *some* changes in demand. BUT, first you start with a model where the price level is determinate. Like with a fixed base. Only then do you relax the assumptions in that model, to handle seasonal fluctuations in money demand, bank runs, etc.


I'm still circling around that debate.

I very much liked the Tobin paper that Glasner likes, and commented on it there.

I know Nick has some concerns about that paper.

My guess is that I'll end up thinking that the best answer is a combination of views from both sides, because I have a hard time thinking they need to be or should be mutually exclusive interpretations - even though they seem to be on the surface.

JKH: "But surely you must recall the kind of T-account progression I described for reserves and deposits - in older textbooks?"

Definitely. That's still there. As it should be IMO. It would still be there with 0% desired reserves, except it would never end (except for the currency drain), until the central bank ended it!


Carpenter and Demiralp say "[t]he most simple money multiplier described in textbooks".

They don't say that there are textbooks that stop at that point and go no further.

And on the bottom of page 4, Footnote #3 reads:

"The simple multiplier abstracts from excess reserves and currency. A more general but perhaps less rigorously derived multiplier links the monetary base to broader monetary aggregates (such as M2) to the monetary base according to:

ΔM = [(1+c)/(c+e+r)]ΔMB

where c is the ratio of currency in circulation to reservable deposits, e is the ratio of
excess reserves to reservable deposits, and r is the required reserves ratio. In the special case where c=e=0, this version of the money multiplier, reduces to the simple multiplier. The lower panel in Figure 1 shows that the discrepancy between this theoretical money multiplier (black bars) and the implied empirical money multiplier (gray bars) is even greater."

But even this is misleading, as I don't recall any textbook using deltas in this fashion, which would imply that M and MB are variables but that c, e and r are relatively stable. (Deltas would be needlessly confusing for first or second years students anyway.)


I don't think these older textbooks used the term "desired reserves" so much, if at all.

They typically start the process with some sort of appearance of excess reserves - where it comes from is downplayed. The banks then have that chunk of reserves to play with. Moreover, the clear emphasis on the causality flow means implicitly that it is really a concept of required reserves that they are talking about - the provision of reserves at the beginning unbinds an otherwise binding constraint on loan and deposit creation.

My impression: your "desired reserves" interpretation is post first year or generally more advanced than the old style of presentation - i.e. has evolved with the times?

JKH: Dunno. I can always remember being taught that banks needed to keep reserves in case customers came in and wanted to withdraw cash. And that if they were required to keep 10% reserves, all that meant was that they would keep (say) 12% reserves instead of 2%, because if 2% of your customers wanted to withdraw all their money, you would be in trouble either way. There's an old joke about requiring there to be always 10 taxis waiting at the airport at all times to make sure there's a taxi available.


Interesting and basic point.

That idea certainly makes sense in terms of currency held in the branch.

But once everything is consolidated (currency plus central bank deposit balances), I don't think it works so well at the residual level of central bank deposit balances - i.e. when it comes to the differentiation between required reserve balances and excess reserve balances.

(Required balances are the residual of the total requirement less the branch credit in terms of currency).

i.e. excess balances were typically very small relative to requirements - too small to be considered as hoarding for future deposit creation

these authors could have seen that data as well as the jumps in required reserves that I referred to earlier

JKH, Nick, Mark, anybody, what are "reservable deposits?" They are mentioned in the Fed paper JKH provided a link to. Also, I thought the reserve requirement applied to checkable deposits, and that M2 includes non-checkable (i.e. non-demand) deposits. So is the Fed paper calculating an empirical money multiplier (gray bars) based on M2/MB? or deltaM2/deltaMB? Why?

Reservable deposits are deposits that are subject to reserve requirements. Technically speaking, net transaction accounts (checkable deposits), nonpersonal time deposits and eurocurrency liabilities are all subject to reserve requirments, but since late December 1990 the reserve requirement on nonpersonal time deposits and eurocurrency liabilities has been zero:


The gray bars (Figure 1) are the ratio of the change in reservable deposits to the change in reserves. Nonpersonal time deposits and eurocurrency liabilities are components of small time deposits and hence are included in M2.

Mark, thanks!

Nick @09:06: By assuming the equation of exchange theory of the price level you are begging the question as to whether the central bank must control the stock of money to keep the price level determinate. I know you are not too keen on the wage mark-up theory (some might say that it explains the 70s better anyway) or the fiscal theory, but are there any other theories of price determination that you would consider? For example Metzler (1951) or Sargent & Wallace (1975, footnote 5) seem to suggest that there are other theories.
Otherwise what I was mostly trying to suggest was that the banks anticipate the fact that the central bank won't let them double the supply of money and factor this into their loan and deposit pricing. The idea is that the current amount of deposits is not so much based on the currency supply of base but the supply expected in the future.

HJC: "Otherwise what I was mostly trying to suggest was that the banks anticipate the fact that the central bank won't let them double the supply of money and factor this into their loan and deposit pricing. ***The idea is that the current amount of deposits is not so much based on the curren[t] supply of base but the supply expected in the future***." (My emphasis and fix of assumed typo).

Ah! I am totally on board with that idea. By far the biggest problem with the money multiplier theory as exposited in the textbooks is that it implicitly assumes a permanent change in base, and says nothing explicitly about the future. What would happen if the BoC announced that, due to technical screw-ups, it was doubling the current base, but would fix the problem next month? Approximately nothing. Banks would just roll their eyes, and sit on the extra reserves. Just like the US banks now.

That idea is worthy of a blog post, if I weren't too burned out.

It's not so much the "equation of exchange" but the *monetary* theory of the price level. MV=PT is just one way of talking about that theory. Yes, there are other theories of the price level, like FTPL for example (the "wage markup theory" is not a theory, unless you believe that wages are totally exogenous with respect to the price level). But if you believe that the Bank of Canada is responsible for keeping inflation at 2% (as I do, and as most people do) then you must believe some sort of monetary theory of the price level. And all the empirical evidence supports the idea that the BoC can control the price level, in much the same sense that can I control my car. Is the position of the steering wheel exogenous or endogenous? Yes. Once I have decided on the road, it is the road itself that (mostly) determines the position of the steering wheel.



I understand why you write that, but that's not a completely fair analogy is it? Isn't it more like if the BoC were to say they were doubling the size of the base, but they can't say precisely why they did it and they aren't sure how long they'll leave it doubled, but they can say they will be adding a set amount more to the base on a monthly basis, they just won't say for how long (although at one time they did mention something about unemployment)? I hope you're not too burned out. Maybe you need a vacation from all this. :D

Glasner got back to you BTW, in a long comment. I disagree w/ one of his main points... and JP Koning agrees w/ me.

Nick, regarding your car on the road analogy, in light of the need for the CB to be clear and credible to be affective, perhaps riding a horse is a better analogy? If the horse senses a lack of confidence and clear intention on the rider's part, it may not respond. I don't know much about horses... but that's how I imagine they are.

Tom, and all: let's switch all discussion of these points to my new post, which riffs off HJC's excellent comment.

Yes, horses are a better analogy, for the reasons you state. But I understand cars a lot better than horses.

Just testingblockquotesto see if they work.

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