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Agree with Steve Roth. In a world of credit transactions, we have to throw out the concept of a quantity of money. There is nothing in modern economies that corresponds to M. (Unused borrowing capacity might be conceptually equivalent in some ways, but I don't think there's any way of operationalizing that. Can't measure red money.) We also have to throw out the idea of a demand function for output as a whole. On this point Keynes takes some of the blame. If he had written "aggregate expenditure" instead of "aggregate demand" a lot of confusion could have been avoided. We also have to throw out the idea of an intertemporal budget constraint. But that was nonsense anyway.

Where I perhaps disagree with Steve is, I think that the quantity-theoretic framework was valid/useful during much of the 20th century. It's not inherently wrong, just obsolete.

JW: how is "aggregate *desired* expenditure" different from "aggregate demand"?



I don't understand that argument.

When did banks not make loans?

Credit cards are just a type of loan.

Debit cards are just an electronic extension of a check.

Changes in velocity maybe.

But where was the tipping point in terms of M suddenly not being useful?

(It was always complicated and subject to oversimplification.)

I see credit cards and debit cards having nothing to do with it, conceptually.

M rocks.

"M rocks" Lol

Nick does M rock? If so, what is it exactly? Is it quantity of MOA as measured by UOA? As in the quantity of known gold in existence measured in dollars (under the gold standard)? The dollar amount of "base money" right now? I'm thinking here specifically with regard to long term neutrality.

Sorry. I'm reading it on Kindle, so I'm not paying enough attention to the headings. I mean The Preface.

"We are thus led to a more general theory, which includes the classical theory with which we are familiar, as a special case."

Why? How so? How does this follow? Give me the implicit assumptions leading us into this path. You don't need to answer me. I'm simply trying to throw some philosophy at you, where philosophy means making assumptions of a theory explicit, as Hubert Dryfus taught me to.


I’ll butt back in and say my answer is that it’s dangerous to be overly dogmatic about classification. The definition of M should always be context specific - and the context should always be specific. It shouldn’t be categorically rigid. The definition should be flexible in adapting to context, but rigid once context is established. So base, bank reserves, bank notes, bank deposits, CB, no CB, banks, no banks, whatever. But M in some sense is always involved.

Oh - and not unused credit card limits. That's contingent M, not M.

And I see no conflict between this approach and emphasizing the role of interest rates in monetary policy.

They’re both relevant.

JKH, you bring up some messy complications!... which could well have some merit. I'm guessing Nick and Scott have a simpler view though, especially in regards to what M is for the purposes of calculating the effects on the long term price level (long term neutrality). Nick and Scott might even agree w/ each other on what M is in that regard. I'd like to clarify their view, starting with Nick. :D

Just to continue the more or less beside the point nit picking, Kevin, I think that equation should have a beta in place of one those 1-beta's.

I'm still not sure it works if you collapse it to a one period model. Then it becomes a standard Edgeworth Box with one good just being called "money" (as opposed to "exotic fruit" or "dshkjfdfhj") and maybe a fixed price at which exchange has to take place (that's what "excess demand for money" means in that context). In that case there's no role for money as a store of wealth, interest rates, or any of that. You can't squeeze out time out of the point that you're trying to make.


I think I'm with JW here.

In the traditional model, M has two key characteristics. It represents a form in which wealth can be held. And it represents the extent to which the holder can transfer net wealth to someone else. (Like store of value and medium of exchange - although those terms aren't exactly what I mean here.) Although wealth may be held in other forms, there is usually nothing else in the model which has the latter characteristic.

In modern finance, credit lines, both committed and uncommitted, play an important role in providing the latter function. So much so that any model that includes M but not credit lines, is not going to tell you very much.

Debit cards aren't relevant to this - I agree they're just a way of giving a payment instruction, like a cheque. But credit cards are because you can't tell anything about the behaviour of M without knowing something about the size of credit card facilities. Or looking at interbank, you need to understand what is happening with interbank credit lines to interpret changes in liquid asset demand.

It may be possible to hold on to M and try to explain all this stuff as things that change V, but my own sense is that then V just becomes less an less meaningful and more and more just the balancing item.

And I'm not sure I could identify a tipping point when M ceased to be useful.

No, the coefficient on current disposable income, Y(0), has to be the same as the coefficient on the PV of E[Y(future)]. To the NK household a $1.00 increase in the PV of expected future income is just as good as a $1.00 increase in current income. Either way $(1-B), i.e. about $0.01 will be added to planned spending by the household in period 0. The marginal propensity to consume is tiny.

The model I have in mind is Gali, Ch 3. There's no wealth in it at all, the RHS of the budget constraint is the PV of disposable income for t=0 to infinity. Of course you could call that wealth if you wanted to. Bonds are not wealth even if government is included; the representative agent is Polonius, neither a borrower nor a lender. There's no stock of money and if there was it wouldn't be held, since it's not in the utility function.

To be clear, the representative agent is neither a borrower nor a lender unless there is government debt, but even if there is, it's not net wealth. Ricardian equivalence rules.

Nick E,

You guys are the experts in the theory and how it is applied/relevant to the world. But this is a fairly significant factor even at the highest conceptual level.

If you apply it to credit cards, you have to apply it to everything, including corporate lines of credit. I can’t imagine an argument against not doing both if doing one. As a tangential aspect regarding credit cards, the study of limit utilization by banks is an important aspect of pricing and profitability – mostly as it relates to those to tend to carry over balances and pay interest on them versus those who don’t, which in turn is a likely function of income distribution. But more broadly, unutilized credit lines make a very significant difference to the quantum of M when compared to actual demand deposits in existence for example. I think the quantum differential is very meaningful and therefore the identification of what is being demanded in terms of money is very different.

The demand for stock balances of money then becomes demand for a stock of credit limits. This is interesting to me from a credit risk standpoint because actual M is homogenous whereas credit limits are not.

Anyway, it would be interesting to see Nick R. do a post on this. Why would the selection of credit limits versus actual M be important to the theory and if so how is it important and why is the decision credit limits rather than actual M?

meant the study by banks of their customers' limit utilizations

Kevin: I am not sure if we are disagreeing.

This is what I have in mind:

Let income be Yp per period from time 0 to time p, then Yf thereafter. Yp is "present" (or "current") income, and Yf is "future" income.

Consumption will be a function of Yp, Yf, and r.

In one limit, as p approaches 0, the marginal propensity to consume out of current income (dCp/dYp) approaches zero.

In the other limit, as p approaches infinity, the marginal propensity to consume out of current income approaches one, and the function collapses to Cp=Yp.

If we redefine Cp and Yp as the annuitised value of consumption and income from time 0 to time p, we could relax the assumption that they are constant from time 0 to time p. And in the limit, as p approaches infinity, Cp is permanent consumption and Yp is permanent income. And the budget constraint says that the PV of C must equal the PV of Y, so permanent consumption must equal permanent income.


Good questions / points. By "corporate lines of credit", I'm not sure whether you meant facilities provided by banks to corporates or simply corporate willingness to sell products on credit, but in any event I'd agree that both do matter.

I'm not sure it's right to say that M is strictly homogenous. A $1 at Bank A is not identical to a $1 at Bank B, because the credit risk is different. It's actually quite an interesting story how these different balances can be treated as an apparently homogenous medium - how the credit exposures change when a payment is made - but it's a story that's quite difficult to tell without looking at the role of credit lines.

The ability to make payments on credit means that M can be arbitrarily small. In theory, it could be zero with all payments simply varying the extent to which agents were overdrawn. A decent theory of money should work equally well in that scenario as it does in the more usual case.

Nick E.,

I was thinking of straightforward bank credit lines for corporates.

True about homogenous – perhaps a question of degree in that money is not strictly homogeneous but arguably “more homogenous” than credit due to the nature of banking as risk transformation

“The ability to make payments on credit means that M can be arbitrarily small.”

That’s a function of the accounting time period, which is generally not less than one day – but it could be. E.g. the balance sheet of a central bank is larger during the day than overnight due to daylight overdrafts of loans of reserves to commercial banks.

Indeed, balance sheet accounting can be an indicator as to whether money exists.

This all reminds me (although I’m probably not recalling this correctly) that I don’t think Nick or I looked at commercial banking in the discussion of red and green money. I think you may have bypassed that question in your post.

A commercial bank that provides green money has credit on the asset side.

(Without thinking about the question) what does a commercial bank that provides red money have on the liability side?


A bank providing red money can have anything on the liability side providing it's not green money. So it depends what you want to call money. If you want to limit that to transaction account balances, then the liability side could include time deposits. If you want to include all deposits, then you need to imagine a bank wholly funded with capital instruments, or even entirely equity capitalised.


You say that, for Keynes, Yd was a negative function of r, but the New Keynesians change Keynes's model, so that

(a) it is not the *level* but the *growth rate* of Yd that depends on r, and

(b) that growth rate depends *positively* on r, for a given time path of Y.

I say (a) is false. In the log utility case for example, it's clear from the equation I posted that C(0) depends only on the PV of Y(t). For a given time path of Y, the level of C (& hence Yd) depends negatively on r, for Gali as for Keynes. In Gali's case that's simply because the PV is inversely related to r. (For Keynes of course it's investment that does it.)

As regards (b), if Keynes had concerned himself with the growth rate of Yd when he was discussing the consumption function, there's no reason to suppose he'd have been put out by the idea that it's increasing in r. (AFAICT he never really bothered himself with the future path of consumption; the only remark I can recall him making about that sort of model related to Ramsey's famous paper and all he said was that it's difficult.)

Nick E: “The ability to make payments on credit means that M can be arbitrarily small.”

Generalise that: if an individual can perfectly synchronise his buying and selling, the amount of M he holds (on average) can be arbitrarily small. (Non-monetary IOUs are just one of the many things we buy and sell).


1. It is costly for an individual to perfectly sychronise his buying and selling.

2. If one individual synchronises his buying and selling, that may desynchronise somebody else's buying and selling.

Imagine 7 people, all in a Wicksellian circle. M sells on Monday, and buys on Tuesday from T, who buys on Wednesday from Woden, who buys on Thursday from Thor, who buys on Friday from F, who buys on Saturday from S, who buys on Sunday from Sunny, who buys on Monday from M. If M switches her buying to Monday, she holds money for a shorter period, but T holds it for a longer period, unless all of them bring forward their buying by one day.

Nick E.,

Good point.


The budget constraint is that PV(C)=PV(Y). Equivalently, that a.PV(C)=a.PV(Y), where "a" is the annuity factor, which means "permanent consumption = permanent income".

Let the rate of time preference be p. If r=p, C(t) will be constant over time, and equal to permanent income. If r > p, C(t) will be rising over time, so C(0) will be less than permanent income. If r > p, C(t) will be falling over time, so C(0) will be greater than permanent income.

The equation you posted assumed that C was constant over time (steady state), so it implicitly assumed that r = p.


I meant something like this.

Take your circle of payments. Assume each payment is $10. M starts with $10 and everyone else has a zero balance. The $10 goes round and ends up with M again. On every day the money supply is always $10.

But if we allow for some of these people to be overdrawn, then the money supply is sometimes less than $10. If Woden starts off overdrawn by $3, then on Wednesday night the money supply is $7.

In the extreme case, where everyone starts off overdrawn by at least $10, then the money supply is permanently zero.

Nick E: I would describe that case as red money flowing around the circle in the same direction as the goods, as opposed to the green money which flows in the opposite direction from the goods.

Nick E.,


Doesn't that require an assumption about how the overdrawn state is initialized - and what else happens as a result?

"Drawing down" produces money.

What happened to that money?

Doesn't that require an assumption - maybe similar to the balance sheet state arrived at and described in your last response to me?


If we take M to mean the greater of conventional money, or the aggregate balance of overdrawn accounts or similar, then I'd agree that it cannot be arbitrarily small.


"What happened to the money?"

Yes that requires the assumption that it was used to buy bank equity or similar.

Nick E.,

That asset-liability structure you described is like a 'Chicago Plan' type of constraint on credit banking.

Nick R.'s pure red money system in that context would be like a Chicago Plan - but without green money produced by the state.

JKH: "(Without thinking about the question) what does a commercial bank that provides red money have on the liability side?"

Good question.

The simplest answer would be "Nothing". Assume that initially I have a stock of assets (my house) on the asset side, and no mortgage or other liabilities. So I have positive net worth. Then I decide to start issuing money.

Red money: I then sell my house, and give the buyer of the house red money in exchange. That red money is now my asset. The buyer of the house has red money as a liability, and the house as an asset.

Green money: I then buy a second house, give the seller of the house green money, so I now have two houses on the asset side, and green money on the liability side.

But the simplest commercial bank would be one that issues both red and green money, in equal quantities, so net money is always zero, but gross money (the absolute sum of red and green) is positive. It has red money on the asset side, and green money on the liability side, plus a bit of capital. All bank lending is lending on overdraft, rather than fixed term loans. If you want to buy a $100 house, and you only have a $25 down payment, you borrow $75 from the bank by writing a cheque for the $75, so your chequing account is now overdrawn by $75 (with your house as security).

This makes my head hurt. But it's all very logical, really.


Isn't that a bit like New Keynesian money?

Nick R.,

So red money by definition becomes the most elementary form/unit of credit.

And the most elementary form of bank is:

Red money assets = green money liabilities plus equity.

Nick E: Yes. It is exactly the money in the New Keynesian model (if the bank is a combined central/commercial bank).

JKH: Yes. But it is credit that is universally (or, at least in Canada, or wherever) accepted as a medium of exchange. Unlike simple credit, where you need to know and trust the person who signed the IOU.

I read all that but I still don't know how Nick R. would count M in a simple case for the purpose of calculating the effect of a change in M on the long term price level P.

Cashless society, t=0, reserves=R0, deposits=D0

No red money, credit cards, lines of credit, or credit limits.

What is M?

Based on case 7 of this Sumner post:

I think it's clear Scott would say M = R0 = quantity of MOA as measured in UOA. I'm guessing Nick would agree.

Now should the CB take over the banks, I think Scott would say M=D0 based on my recent conversation with him. And thus deposits become the new MOA. I *think* Nick would agree.

But they'd also say this is a special case because demand shifts from one good to the other during the CB take over, so that P does not go to P*D0/R0, instead it just stays at P. (Under normal circumstances if P0 corresponds to M0, then P1 = P0*M1/M0 after prices reach equilibrium again).

Nick, here's what I get in the general case, i.e. where we're not in a steady state.

C(0) is the same fraction, 1-B, of PV(Y).





What is M?

I don't know what Nick R. would say, but I suggest that M is always the money that government pays for labor and services. My logic is simple:

1. The government is responsible for preventing counterfeit money. Therefore, we can safely assume that all money received from government is legitimate money.

2. Money received from government is often received as deposits in a bank. We can safely assume that these deposits are all accounting entries of legitimate money.

3. All money received from the government is carefully shepherded. This money may be loaned to others.

If you agree with this logic, we can calculate the amount of money available for loan by subtracting tax revenue from the total amount of government payments over the course of history.


I forgot the closing parenthesis behind "........ What is M?". Sorry about that.

Kevin: OK. I think I follow the math. But (if we assume r is constant over time, otherwise I can't do the math):

Permanent income = r.PV(Y)

(Intuitively, if r is constant over time, permanent income is the interest earned on wealth.)

So I can re-write your solution as:

C(0) = [(1-B)/r].(permanent income)

So consumption today depends positively on permanent income and negatively on the rate of interest.

I think that reconciles our intuitions.

Tom: are you talking about a barter economy? If so, M=0.

Nick, no barter: just no paper notes or coins: no cash. Same as Sumner addressed here in case 7:
"Now let’s assume a cashless economy where the MOA is 100% reserves. Still no change; reserves are still a hot potato."

My scenario: bank reserves are $R and commercial bank deposits are $D

Sumner describes the HPE acting on R, regardless of what D is. R is the only MOA in that scenario. D may be an MOE, but the HPE acts on R not D. Things change if the CB takes over the banks. Reserves become meaningless (According to Sadowski, ... and I think you, Sumner and Glasner agree). Now those D deposits are direct liabilities of the CB. They maybe can't be called "base money" but according to Sadowski and Sumner they're the closest thing to money, so they take on that role. Sumner's OK with calling them "base money" actually. Sadowski isn't, but I think both would agree they are the MOA in that scenario. So no barter: there are still bank deposits (now direct CB-deposit-liabilities) in the amount of $D to transact with.

We talked about this before where I gave values for R and D: R=$1 and D=$10. You described how the CB taking over the banks would increase supply (of money) 10 fold, (i.e. M would go up 10 fold I think), but in this particular case demand for money would also increase 10 fold, thus leaving P unchanged. Sadowksi was "mystified" by your response because I'd written it as "nationalized" rather than the CB taking over. But the original way you read it: CB taking over, is great though! Let's leave it at the CB takes over, so your original explanation of 10-fold increases in both supply and demand still applies, and Sadowski will not be mystified.

All that gives me the impression that M should be counted as MOA in this simple case.
M = $1 = R prior to CB take over
M = $10 = D after CB takes over (D is the only game in town: no cash and no reserves... but NOT barter!)

If M were MOE instead, then you would have said M goes from $11 to $10, right? Because reserves are both MOA and MOE and bank deposits are just MOE: So add up all the MOE prior to CB take over and you have R+D = $11. Afterwards, only D left, so it's $10.

Why do I care? It doesn't affect P either way, right? Well the part I'm interested in is what I call this "demand transference" from non-MOA (bank deposits) to MOA (direct CB deposit-liabilities) that you've already described. I'd never seen that brought up before. It makes sense (you explained it with a house analogy), but I'd never seen it.

So what happens now if the CB takes over money market funds too? They take the assets and replace them with CB deposit liabilities. Can a "demand transference" happen here too between a different non-MOA (money market funds in this case rather than bank deposits) and direct CB-liabilities (MOA)? Will that cancel out the effect of the increase in M and leave P unchanged also?



Is M really always involved when we look at national income accounting? For example, a farmer paying part of the wages of his workers in produce would be considered providing "in-kind renumeration of labor" per BEA and that would be included in the national accounts. Actual transfer ("sale") of goods and labor took place but no "money" exchanged (as least as I can see). We have changes in the respective balance sheets but if that constitutes the most basic definition of M does that not mean M = GDP?

Just a problem with the way we do the national accounts or with our definition of M?

Tom: it does not matter what we call it. What matters is demand, and what it depends on, and supply, and what it depends on. Scott's key insight (some time back) is that private banks only care about real things, so that leaves only the central bank to care about nominal things. It does not matter what nominal thing the central bank cares about. If it doubles it, P doubles too. It could be the nominal price of gold.


NIPA excludes or looks through M, but is still coherent in itself.

A complete set of accounting statements includes income, balance sheet, and flow of funds.

3 of them.

That holds at micro and macro levels.

NIPA is the macro income statement.

You can see M stock somewhere in balance sheets, depending on how you want to define it.

You can see M flow somewhere in the flow of funds, depending on how you want to define it.

And its beneath the surface in NIPA.

The three of them together are coherent with respect to M and other stocks and flows.

Nick, I'm with you, I don't care at all about what we call "it" either, but I'd like to be able to do the math, Market Monetarist style. So the long term neutrality of money claims that if M changes from M0 to M1 then P changes from P0 to P1 = P0*M1/M0 (eventually), correct? M and P are scalers at any one point in time (unlike supply and demand). So this is what I'd like to know:

Cashless society (but definitely not barter!):
time = t0, reserves = $R, commercial bank deposits = $D, CB deposits = $0; What is M0 = M(t0)?
Now the CB takes over banking:
time = t1, reserves = $0, commercial bank deposits = $0, CB deposits = $D; What is M1 = M(t1)?

Once we know M0 and M1 we can calculate P1. OR not correct? I.e., the formula doesn't tell the whole story: we need to consider that demand may have transferred from non-M to M or vice versa? I.e. not all else is being held equal, so a simple application of the formula doesn't apply? Are either of those explanations true?

Sorry to be such a pest about this, but I want to really understand how this works from the MM viewpoint, and for that purpose hypotheticals are helpful to me. But why should I have to tell the man who invented the haircut economy and red money about the value of hypotheticals? :D

... what I think I hear you saying (in previous comments) is the formula doesn't apply in this case because of demand transfer. And furthermore that M0 = R, M1 = D and P0 = P1.

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