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"commercial banks create that money despite each individual bank only lending out money that has been deposited in that bank"

This defines "deposit" too narrowly. A commercial bank can issue 100 checking account dollars in exchange for nothing but a "deposit" of the borrower's $100 IOU, or a "deposit" of a $100 government bond (just like central banks do).

Nick,

Even a quasi-knuckle-dragger like me can see that this is a brilliant post.

Comments:

“But what the textbook also reminds us is that an individual commercial bank that creates a deposit by making a loan will very likely lose that same deposit to another bank when the borrower spends the loan and the cheque gets deposited in a different bank. It is exactly as if the individual bank had made the loan by giving the borrower central bank currency, which then gets spent and deposited in a different bank.”

That is true and it is the type of thing that the cultist chanters either conveniently or ignorantly ignore. The overarching issue is really the effective differentiation of banking system behavior versus individual bank behavior – overcoming a sort of fallacy of composition in thinking things through. System loan and deposit creation is an expansion without a necessary net system reserve cause or effect. But individual bank loan creation typically results in a funding requirement including a requirement for reserves at the margin – because of your type of scenario.

I did a post on this sort of qualification. I differentiate between system loan and deposit creation versus the turbulence of competition for an existing deposit base, following that creation:

https://monetaryrealism.com/loans-create-deposits-in-context/

That said, I would still differentiate between the interpretation of the supply of currency and that of the supply of bank reserve balances. I think your overall theory works better for the supply of currency than the supply of reserve balances.

I think you move into very unconventional territory:

“And please don't be a knuckle-dragger and assume the money multiplier refers to the multiplier effect of an initial decision by the central bank only. Yes, the textbook usually illustrates the money multiplier with an example where the initial shock comes from the central bank, just as it usually illustrates the keynesian multiplier with an example where the initial shock comes from fiscal policy. But the money multiplier, just like the keynesian multiplier, multiplies anything that gets the ball rolling.”

Can you elaborate? You’re talking here about an extension of or maybe something quite different than the “required reserve multiplier” aren’t you? It almost sounds like you’re talking about something that would be unimpeded by the conventional textbook mathematics of the required reserve multiplier. I.e. more consistent with endogenous money liberation. It also sounds like something that could be quite consistent with the view that bank animal spirits in lending correspond to improving capital positions in the process – or at least not inconsistent with that. It might help to be much more specific about this framework if it is a real departure from the “required reserve multiplier” thinking – or maybe you already have in a previous post. Or maybe I just don't understand your point.

Side question:

The Keynesian multiplier doesn’t assume anything specifically or explicitly about credit and money creation, does it? It could work in (stretched) theory through velocity alone couldn't it?

Great post !

Of course both multipliers work together and are at the heart of the story of how money affects the economy.


Someone gives me $1000 of newly printed money. I spend some, I keep some in my wallet, and I put some in my bank account. The two multipliers then explain the series of flows within thew banking system and the rest of thee economy that continue until all the new money is either in someone's wallet or kept as bank reserves. They also help explain how prices and output have adjusted.

I am not certain of much in economics but I'm pretty sure this multiplier story is not too far away from what actually happens in the real world.

The "endogenous money" crowd like to focus on one bit of the story - the bit where banks create new loans and thereby increase the supply of broad money. They claim this undermines the whole multiplier story. Technically banks really do increase broad money when they issue loans but to focus on this above everything else in the story is to fail to see the woods for the trees.

The one danger with the multiplier story is possibly that you may forget (or simplify in your model) that as well as changes in the money supply there can be changes in other things (such as the ratios of money in people's wallet to spending and to the money they keep in the bank, banks reserve policies etc) that will change the values of the multipliers. If these other things are too volatile then the multiplier story may stop making so much sense.

Mike: let me rephrase it like this: "*Even if* each individual bank only lends out money that has been deposited in that bank, commercial banks create money."

JKH: thanks!

You are very far from a knuckle-dragger.

(I feel a little guilty using that term in this post. My visor was down, and I was swinging my sword alone, defending the truth beauty and usefulness of my fair multiplier maidens, against the hordes attacking from all directions....)

One example of an initial money multiplier shock would come from the central bank. Or it could be someone who decides to hold less currency and more deposits. Or it could be an individual bank that decides to make more loans and hold fewer reserves. Or other shocks I have forgotten. Just different ways of getting the same ball to start rolling. And the same ball can also roll in reverse, of course, like in a recession.

"The Keynesian multiplier doesn’t assume anything specifically or explicitly about credit and money creation, does it?"

It doesn't. It is silent on the question. But I think it can only be understood in tandem with some sort of money multiplier, as TMF says. Two sides of the same coin.

TMF: thanks!

"The one danger with the multiplier story is possibly that you may forget (or simplify in your model) that as well as changes in the money supply there can be changes in other things (such as the ratios of money in people's wallet to spending and to the money they keep in the bank, banks reserve policies etc) that will change the values of the multipliers."

Those things definitely need to be remembered. But above all else, we need to remember how the central bank responds, because that is our policy lever on the whole multiplier process.

Nick, you are one tough reactionary contrarian/curmudgeon, defiantly shaking your fist at googly-eyed "cultists" and the upstart sneering and "trendy sophisticates" alike! Hahaha :D

I followed about half that... the money multiplier half. My goal is to one day understand the other half too.

Question: you mention Keynes' "fundamental question" and a different way to state it, but I don't see that you mentioned the common/original way to state it, did you?

Also, one comment about this:
"And commercial banks create that money despite each individual bank only lending out money that has been deposited in that bank, as long as they have less than 100% desired reserve-deposit ratios."

This ignores the idea that a depositor can be induced to purchase a time deposit (or even bank equity) with his checkable deposit, thus eliminating the constraint in part or in whole.

Assuming again that there are only demand deposits: you are only covering a central bank "shock" in which a deposit starts at an initial bank. It could instead start from central bank money capital (and zero deposits): say a bunch of investors pooled their cash to start a new bank starting off with $0 in deposits. Then the 100% reserve requirement is not an upper bound: the requirement could be > 100% and the bank could still create deposits through lending. Say the initial capital was $100 and the reserve requirements was 200%, then the bank could create $50 in checkable deposits.

I realize you didn't use the term "reserve requirement" but I'm imagining that's one way to interpret "desired reserve-deposit ratios."

Also thanks for your response at Glasner's (to my question), and in case you didn't see it, he responded to your latest there.

The money "multiplier" simply tells us the limit of money creation by the commercial banks, given their reserves. In itself it is not sufficient to tell us how much money will actually be created.

Tom: here is Keynes' original way to state his question: "But one person's spending is another person's income, and it is not unreasonable to ask, as Keynes asked, what, if anything, ensures that our (permanent) desired aggregate spending is sufficient to equal our (permanent) desired aggregate income? What, if anything, might adjust to ensure that Say's Law holds?"

(I just stuck the words "permanent" in there.)

"This ignores the idea that a depositor can be induced to purchase a time deposit (or even bank equity) with his checkable deposit, thus eliminating the constraint in part or in whole."

Yep, and I was right to ignore that. Because that is just banks acting like non-bank financial intermediaries. Anyone can borrow money and lend it again, without creating money. I can do that myself.

A 100% reserve bank cannot create money. It can only transform money from one form (currency) into another form (demand deposits).

"I realize you didn't use the term "reserve requirement" but I'm imagining that's one way to interpret "desired reserve-deposit ratios.""

No, you must not interpret it like that. It is the desired reserve ratio that matters. Required reserve ratios only matter because they influence desired reserve ratios.

Min: no it doesn't. You are giving it that "American" interpretation, as the reciprocal of the *required* reserve ratio. And even then, it does not tell us an upper bound, unless initially the desired reserve ratio was equal to the required reserve ratio (it won't be), and there is no currency drain, and the central bank holds the base constant.

Nick,

What's your definition/concept of "desired reserves" - including reference to the relationship of desired reserves to statutorily required reserves and existing excess reserves?

(institutional thickets moment)

"The money multiplier, and the keynesian multiplier, are rare examples of positive feedback processes. The equilibrium increase in money supplied is bigger than the original increase in money supplied. The equilibrium increase in output demanded is bigger than the original increase in output demanded."

I don't think so. Gain is not a sufficient criterion for feedback. The money multiplier is an example of gain (with negative feedback, if you like, in the textbook picture).

The formula for negative feedback is closedLoopGain = openLoopGain / (1 + feedback * openLoopGain). With no feedback, obviously, openLoopGain = closedLoopGain

With positive feedback, The + in the denominator would be a - and closedLoopGain would go to infinity until it hit some other constraint. Positive feedback is almost always unstable (exceptions are unusual, complicated and generally to be avoided).

Of course in real systems, things get more complicated, but rarely more stable. Under certain conditions, even negative feedback systems can be unstable (c.f. phase margin and gain margin).

"Anyone can borrow money and lend it again, without creating money. I can do that myself."

Cute. An amusing riff on:

"everyone can create money; the problem is to get it accepted". (Hyman Minsky, Stabilizing an Unstable Economy. Yale University Press, New Haven and London.)

Mike Sproul: well put! That sentence bothered me too, but I let it go because I couldn't state my objection as clearly as you did. Nick's fix is acceptable to me.

Peter N: Also well put!... that sentence of Nick's also bothered me a bit (but I was too lazy/not-clever-enough to think through a coherent objection)! Did you study feedback control systems in school too? (that was my major).

Peter N: closedLoopGain = forwardLoopGain/(1 + forwardLoopGain) with negative feedback. If we're just talking scaler gain blocks here (no integrators or differentiators or delays) then if forwardLoopGain > 0, then 0 < closedLoopGain < forwardLoopGain. If we have positive feeback then closedLoopGain = forwardLoopGain/(1 - forwardLoopGain) and if forwardLoopGain is on (0,1), then 0 < forwardLoopGain < closedLoopGain, with closedLoopGain going to infinity as forwardLoopGain goes to 1. However forwardLoopGain can be > 1. So actually with simple gain blocks, positive feedback is OK here, and can produce a stable gain > 1. But if we have a characteristic polynomial in forwardLoopGain, then you'll be unstable if the roots of 1-forwardLoopGain are not in the open left half plane. (assuming this system is well described by a LTI approximation, which it probably isn't).

... when you wrote "feedback" in the denominator did you mean "unit delay" (i.e. Z^-1)? as in a discrete time system? If we assume we're talking about a discrete time system and there's a unit delay in the feedback path, then the characteristic polynomial of the closed loop system is 1-forwardLoopGain*(Z^-1) with positive feedback which is equivalent to Z-forwardLoopGain (regarding roots). And thus if forwardLoopGain is a real scaler with magnitude >= 1, then we have a root outside the unit circle, and the system is unstable, but with smaller magnitude forwardLoopGains it's stable. I think I did that all correct! Let me know if I got it wrong there.

... the upshot is nick, you're not necessarily unstable with positive feedback and in fact that could give you a stable steady state gain higher than the forward loop.

... as if you cared. Lol.

Nick Rowe:

"You are giving [the money multiplier] that "American" interpretation, as the reciprocal of the *required* reserve ratio."

Thanks, Nick. Definition, please?

JKH and Min: "desired reserves" is that level of reserves (or ratio of reserves to deposits) that commercial banks *choose* to keep, taking into account legally required reserves, liquidity risk, etc.

E.g. in the 1930's, banks chose to keep much higher levels of reserves than were legally required, to provide a buffer zone before they would be forced to call in loans in the event of a run to keep above the legal minimum.

Quantity of reserves demanded.

Tom Brown,

So much for trying to keep it simple. For time stepped systems, z transforms are the natural approach. Though the standard model isn't a filter, the treatment of stability is similar, once you do some tricks to reduce the number of dimensions.

This paper is rather interesting about the limitations of the model -

https://www.econ2.jhu.edu/people/ccarroll/death.pdf


Nick, you write:

"And that excess supply of money causes P and/or Y to increase until the quantity of money demanded adjusts to equal the quantity supplied. Say's Law, paradoxically, only applies to money itself. The supply of money creates its own demand."

This makes it sound like it takes some time for P and/or Y to increase. At least in terms of P, that seems consistent with the idea of sticky prices. So does that mean it's fair to re-write that final sentence to read:

"The supply of money eventually creates its own demand?"

Does that mean that at any one point in time, Say's Law is not necessarily true for money since P and/or Y may not yet have adjusted, and thus the quantity supplied does not yet match the quantity demanded? Is it helpful to introduce distinct concepts for the nominal demand for money (Mdn) vs the real demand for money (Mdr = Mdn/P) here? Thanks.

Peter N, "So much for trying to keep it simple." Lol, ... sorry, you got my rapid endorsement for introducing the concept... followed by me actually thinking about it a bit. OK, so then it sounds like my 2nd hunch was correct: that by "feedback" in your denominator here:

"closedLoopGain = openLoopGain / (1 + feedback * openLoopGain)"

We could substitute Z^-1 (a unit delay block), true? Then there is a set of openLoopGains > 0 which would produce a stable system, with the steady state gain > openLoopGain over a range of openLoopGains with positive feedback (positive feedback meaning replace your "+" in the denominator with a "-").

Thanks for the link BTW, I'll take a look.

Peter N, was that the correct paper? I searched for "Z-transform," "transform," "discrete time," "stability," "gain," "open loop," "closed loop"... and I didn't find those inside. Was there a particular section I should look at?

Nick: I think the usual complaint is that many people assume multiplier must equals 1/reserve-requirement. In that case any increase in reserves results in a much larger increase in bank deposits. But as you say, an increase in CB money could be coincident with an increase in desired reserves.

Related to your previous posts on velocity - I want to thank you for enabling me to resolve a quandary I've had for years. When I travel, I recognize that I boost (very slightly) the economy of the locality I go to. I used to think of that as taking money from one place and spending it in another, but since deposits never really leave the jurisdiction of their CB (even Eurodollars have corresponding deposits in US banks), that didn't work. I realized yesterday that my spending increases the velocity of money in the locality I travel to. That should be sufficient to explain the small boost I provide.

Nick says “And commercial banks, neither individually nor collectively, can create loans, unless they can persuade people to hold their deposits and not hold central bank money instead.”

That’s true at full employment, but not necessarily true if the economy is below capacity. If commercial banks loaned money into existence when the economy was below capacity, and no one wanted to hold the resulting deposits, the extra money would be treated like a hot potato – people would try to spend it away – and the result would be increased demand.

Nick Rowe:

"desired reserves" is that level of reserves (or ratio of reserves to deposits) that commercial banks *choose* to keep"

So the money multiplier is the ratio of total deposits to total reserves, system wide?

Nick, I am not exactly sure what the difference is between you and the "cultists" with regard to the money multiplier. Does it have to do with whether there actually is an iterative process of depositing and lending? On the one hand, the picture is that banks wait until they have deposits before deciding how much to lend, and on the other hand, banks do not base lending decisions on their deposits. Is that it?

If so, isn't that an empirical question, one that would not be difficult to answer?

Min, there's another parameter; the "currency ratio" = c = (currency in circulation (not in bank vaults)) / (checkable deposits)

If the "reserve ratio" = r = (total reserves, i.e. vault cash + electronic) / (checkable deposits)

Then the money multiplier = (1+c)/(r+c) = M1/MB.

Since

M1 = (currency in circulation) + (checkable deposits)
MB = (currency in circulation) + (total reserves)

You can easily check and see the formula is true.

Of course that may not be the "first year" money multiplier Nick is talking about in this post. That one may just be 1/r like you point out.

"What matters is that those magnitudes are bigger than one."

What is so magical about one, in the sense that a multiplier of 1.1 would lead you to radically different conclusions than 0.9? If you want to explain the cycle with "shocks too small to see" don't you need a multiplier of 10, or 100?

This seems like a nit pick but it reminded me of another comment I heard on a podcast recently (Econtalk or LSE) talking about multiplier estimates either side of one (IIRC a range of 0.6-1.5, from Ramey) as a big problem when considering stimulus policy.

I couldn't understand why. 1 means extra government spending is completely "free" as far as crowding out the private sector goes (leaving aside the DWL of raising tax revenue), 0.6-1.5 means there might be a bit of crowding out or crowding in. But insofar as there is a minimum value for stimulus spending to be desirable, isn't 0 (+ a bit for the DWL of tax collection) rather than 1 the natural starting point?

Nick,

You may find this interesting and relevant to your post:

https://www.thomaspalley.com/docs/research/ad_and_debt.pdf

(HT Ramanan)

Tom Brown,

That was the right paper. I thought the math was more accessible than most such. A standard treatment would be

https://www.pitt.edu/~jduffy/courses/talk4.pdf
https://www.pitt.edu/~jduffy/courses/talk5.pdf

This is probably more than you want to know while still not being entirely clear, so I think, having gone through my bookmarks and downloads, that

https://www.econ.ku.dk/personal/henrikj/makok3_2012/Dynamics.pdf

and

https://ns.fujimori.cache.waseda.ac.jp/PKR/2013/asada.pdf

are probably more on point. The math is much clearer than Duffy.

Nick, interesting post. You need to put all these post together and produce a monograph. It would be great for a money and banking class.

Along these same lines, I also tried my hand at reconciling my views with endogenous money. Not sure how clear it is, but here it is: https://macromarketmusings.blogspot.com/2014/03/market-monetarism-and-endogenous-money.html

Ralph: An excess supply of money will force up either Y and/or P. The slope of the Phillips Curve/AS curve determines which of those two will get forced up.

Declan: fair point. What matters is that those multipliers might be very big. Infinity is more of a magic number than one. But even when people think they can identify the original shock (e.g. the US housing market etc.) they often wonder why the recession was much bigger than the obvious direct effect, which suggests they are comparing it to one.

Thanks JKH. I had a quick read of it. I think he's too hung up on Steve Keen's assumption that V=1, which was just for simplicity.

David: thanks!

From reading your post, I think we are very much on the same page.

Mike Sproul says 'This defines "deposit" too narrowly. A commercial bank can issue 100 checking account dollars in exchange for nothing but a "deposit" of the borrower's $100 IOU, or a "deposit" of a $100 government bond (just like central banks do). '

They can do indeed do this but but when the 100 checking account dollars is used to buy something and the seller deposits the check in his bank account , won't the original bank need real reserves (not just the collateral) to settle ? It may have these reserves already, or need to get them after the initial loan, but at some point its going to need them, right ?

(Note: I think I can image a different banking system where banks could indeed issue money directly against collateral, and money would be truly endogenous - but that's just not how the current system works).

Peter N, Thanks for taking the time to dig those out. I haven't gone through all that yet, but the last two certainly used a lot more of the language I'm used to (I have yet to look at the 1st two).

Clarification on "It may have these reserves already, or need to get them after the initial loan" from my earlier comment.....of course it will likely have available reserves already, but the new loan (when spent) may lead to it dropping below the optimal level of reserves and it may as a result need to take action to address that.

"And the medium of exchange is not like refrigerators, because we buy money in order to sell it again, not just to hold it. Suppliers of money, unlike suppliers of refrigerators, can "force" us to buy more money than we want to hold, because each buys it planning to sell it again to someone else. And that excess supply of money causes P and/or Y to increase until the quantity of money demanded adjusts to equal the quantity supplied."

Or alternatively, an excess supply of money causes money supply to be unprofitable, while P and Y remain constant. (Why would a bank issue money unprofitably? Wouldn't that be crazy? Yes, unless maybe the bank read in a textbook that an increase in the money supply would cause an increase in P or Y).

The Market Fiscalist,

You are correct, in the case where the recipient of the funds banks at a different bank. And re: your second point: I've often imagined the same thing I think. I draw out the balance sheets here:
https://brown-blog-5.blogspot.com/2013/03/banking-example-12-loand-deposit.html
This one with a purchase:
https://brown-blog-5.blogspot.com/2013/03/banking-example-11.html
But in some sense, why did the CB need to temporarily create any liabilities at all there? I think that's what you're asking, right? Why couldn't Bank A go straight to owing Bank B the $100 in reserves and leave the CB out of it.

The Market Fiscalist, you are correct. I draw out the balance sheets here: rather than a link, just Google
Banking Example #1.1
1st hit. I wondered the same thing: why can't Bank A just going straight to owing Bank B the reserves w/o the CB ever getting involved.

Max: an individual bank will create more money when it is profitable for the individual bank to do so. That's not at issue. But what adjusts in response to that increased money creation?

Nick,

Saw your comment at Glasner's about how excess supply of money can still dominate shifts in the mix between base and bank money when the interest rate on bank money changes.

This may be a basic question that you've answer a thousand times before - but how do you relate excess supply or demand to velocity? Does excess supply or demand correlate with volatility of velocity?

Tom,

on "why can't Bank A just going straight to owing Bank B the reserves w/o the CB ever getting involved."

I can image a world where banks create their own currency unit (for example equal in value to a set bundle of goods). They then issue loans against collateral in this currency unit. If people deposit the money created by these loans in a different bank then they will need to transfer reserves just like in today's system but rather then being CB base money these reserves would consist of collateral equal in value to the reserves needed (there would need to be some efficient way of measuring the value of collateral in the chosen currency unit). Of course a bank that simply issues loans again collateral and then transfers the collateral would be a useless bank, so they would also need to make their money attractive to hold (that is attract customers willing to keep their balances with them). Making their money redeemable against the bundle of goods that defines the currency unit would be a good way of doing this.

In this system they probably should call the currency unit the "sproul".

JKH: good question. Rough answer (don't hold me precisely to this): excess supply of money = actual velocity is less than desired velocity. People want to spend money more quickly than they are actually spending it.


"... I think he's too hung up on Steve Keen's assumption that V=1, which was just for simplicity."

Yes there should be a multiplier of V(t)/2 on the ΔD terms. You might be able to calculate v(t) from Y(t) and D1(t) to get something like:

C1(t)= zY(t)- S(t)+ ((Y(t)/ D1(t)) / 2) * (ΔD1(t) + ΔD2(t))

I think his treatment of W is also a problem. Can you really hide the difference between his W and net worth in a2 (the propensity to consume from wealth). It's not a2(t) after all.

I expect a some of Keen's problems come from his requirement that the theory be stock-flow correct (by Godley standards). OTOH this makes it very easy to generate the necessary values to run simulations, which he has done.

I think this paper on credit is worth a look. It looks at where consumer debt came from, and the extent to which future primary consumer surpluses can reduce debt. It may at least partly explain why the recovery has been so weak and protracted, and why the Fed has had to work so hard.

It's relevant to any discussion of the value of austerity. I learned a lot from it. The lead author is a regular here - J W Mason.

https://repec.umb.edu/RePEc/files/FisherDynamics.pdf

Tom Brown: "Of course that may not be the "first year" money multiplier Nick is talking about in this post."

Thanks, Tom. For this and your previous note. :)

It helps to know what definition is being used. ;)

Nick,

You asked "But what adjusts in response to that increased money creation?"

That may be 2 questions - what should normally adjust and what actually did.

It certainly didn't lead to an increase in the stock of broad money. A bit of a mystery and a bit scary -

Peter N: "That may be 2 questions - what should normally adjust and what actually did."

Yep. What do we want to adjust, if the central bank is doing what we want it to do; and what actually adjusts if the central bank does what it actually does.

The failure of broad measures of money suppy to expand in the US (and the UK)following QE was predictable in a liquidity-trap recession. As far as I remember, Krugman did predict it on the basis of his analysis in his Japanese liquidity-trap paper. It was also predictable given US experience in the 1930s.

Palley on Keen:

https://monetaryrealism.com/thomas-palley-on-steve-keens-model-of-aggregate-demand/

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