Some Simple Basic Money, for Finance People

Finance people are good people. Economics needs finance people. Some of my best friends are finance people. But (you heard that "but" coming), finance people (though there are of course honourable exceptions) just don't seem to get money.

I can hear the reply now: "Yeah, and money people don't get finance either!". And I think you are right, but only half right, about that. I think that money people do get simple basic finance; it's the more complicated stuff we don't get. But finance people, it seems to me, often don't get the simple basic stuff about money.

And that's not because money people are smarter than finance people (though we are better-looking). It's because money is weird. Money is not like other assets. So when you take simple basic finance theory, that works OK for other assets, and apply it to money, you can get in a mess.

I watched a finance person on Twitter ask the question: what determines the market value of a zero-coupon perpetuity, like currency? That's a very good question to ask, but you won't get a sensible answer if you do a standard Present Value calculation of a perpetual stream of zeros. Why isn't it zero??

Let's do this Present Value calculation very slowly. (And please excuse my cruddy math, which I always get wrong.) Start with a perpetuity that has a fixed annual coupon C, a market price P(t) at time t, where people are willing to own it at a discount rate r(t). We know that:

P(0) = C + P(1)/(1+r(0))

and since P(1) = C + P(2)/(1+r(1), we get

P(0) = C + C/(1+r(0) + P(2)/[(1+r(0))(1+r(1)]

Wash, rinse, and repeat, for a horizon of T periods, and we get:

P(0) = PV[C] + PV[P(T)] where "PV[.]" stands for Present Value of, and you know the formula better than I do.

Now we want to take the limit of that equation as T approaches infinity. And it is very tempting to say that the second term PV[P(T)] approaches zero in the limit as T goes to infinity, unless there's some sort of bubble, so we can re-write that equation as

P(0) = PV[C]

Or, in the simple case where r(t) is a constant over time:

P(0) = C/r + lim[P(T)/(1+r)^T] as T goes to infinity

and the denominator in the second term goes to infinity if r > 0, so the second term must go to zero if the price is always finite.

So if currency is a zero-coupon perpetuity, it is very tempting to say it must have a fundamental value of zero. But since (obviously) currency does not have zero value, there's gotta be something funny going on.

Here's a different way to think about it, that you might find useful:

You know that liquidity matters. Other things equal, people prefer holding a more liquid asset than a less liquid asset. They will own a more liquid asset even when it has a lower rate of return than competing less liquid assets. The discount rate we should be using in the Present Value calculation should reflect the liquidity of that particular asset, and should be the rate at which people will just be willing to own that particular asset.

Now suppose there were some very liquid asset that people would just be willing to own at a zero rate of return?

If we stick r(t) = 0% for all t in the Present Value calculation above, we can't get rid of the second term PV[P(T)]=P(T)/(1+r)^T. Because the denominator stays at one, and does not approach infinity in the limit as T goes to infinity.

That really messes up the Present Value calculation. We can no longer say that the fundamental value of a zero-coupon perpetuity is zero, if it's very liquid so people are just willing to own it at a 0% rate of return. But what the hell is it? What is 0 divided by 0?

Here's the standard way that money people have answered that question:

Suppose the demand curve for liquidity slopes down, but is also an increasing function of Nominal GDP. So the rate of return at which people would be just willing to own a particular very liquid asset, at the margin, for a given set of rates of return on other less liquid assets, is an increasing function of the Market Capitalisation of that particular asset as a ratio of NGDP. So the r(t) we use in our Present Value calculation for this particular asset is an increasing function of M(t).P(t)/NGDP(t), where M(t) is the number of "shares". And the r(t) will go negative if the market capitalisation is small enough.

So, in the simple case where everything is constant over time, it's easy to reconcile the formula P(0) = C/r with a zero-coupon perpetuity like currency. Just use the liquidity demand function (we call it a "money demand function") to figure out the P(0) at which the ratio of market capitalisation to NGDP gives us an r=0%. Done.

Come to think of it though, shouldn't all finance be done a bit like this? Is it really plausible that the rate of return at which people are just willing to hold a particular asset, at the margin, is always strictly exogenous with respect to the price and hence market capitalisation of that asset? Sure, that might be an OK simplification for some partial equilibrium work in very competitive markets, but it won't be generally true.

Oh, and money is special because it's the unit of account, so its price is normally written as 1/P(t), where P(t) is the price of everything else in terms of money, and so its market capitalisation is M(t)/P(t). And the ratio of market cap to NGDP becomes M(t)/P(t).RGDP(t) where RGDP is real GDP.

And the reason money is so very liquid (in fact the most liquid) asset is because everything else is bought and sold for money (it's the medium of exchange), but getting properly into that issue is beyond the scope of this post.

Comments

[jreality]

The present value is whatever people agree the money will buy, or whatever other amounts of currencies people agree could exchanged for the currency in question.

[Avon Barksdale]

Nick,

"...finance people (though there are of course honourable exceptions) just don't seem to get money." Hmmmm. Perhaps they understand it better than you might think:

http://faculty.chicagobooth.edu/john.cochrane/research/papers/cochrane_stock_as_money.pdf

[Nick Edmonds]

As someone who considers themselves a finance person, I see it like this:

A typical financial asset entitles me to a series of payments, where a payment means a credit to an account of my direction, such payment either creating an asset or extinguishing a liability. In discounting the payments to value the asset, I take account of possible choices about when the payments are made - if I can choose the date on which I receive a particular amount of payment, I would generally discount it from the earliest possible date.

Currency enables me to receive a payment. If I take a $100 bill to the bank, I can have $100 credited to an account of my direction, creating an asset or extinguishing a liability. The earliest date I can do so is today. So its discounted value is just its face value.

[Ramanan]

I think Brian Romanchuk has written a wonderful article here in reply to this:

http://www.bondeconomics.com/2016/07/seriously-money-is-not-zero-coupon.html?spref=tw

Nick R, as Brian says, you ignored the optionality in valuation of the bond and ended up with a wrong conclusion. Brian - like a good finance person - considered it and reached the right conclusion.

[Eric Tymoigne]

Monetary instruments are not perpetual, they have an instantaneous maturity (zero term to maturity) i.e. due on demand. While some of them are not convertible, they are all redeemable at face value to the issuer on demand (payments can be made to the issuer with its monetary instruments at face value: tax payments or debt service to banks). As such, given that they are zero-coupon securities, their fair value is face value.

[Jacques René Giguère]

Eric: monetary instruments are also immediately redeemable in goods and services, the ultimate definition of liquidity.

[Nick Rowe]

Avon: that's why I put in the bit about honourable exceptions. You might like my similar http://worthwhile.typepad.com/worthwhile_canadian_initi/2015/02/money-as-closed-end-mutual-fund.html

Damn! I've forgotten how to do links!

Nick E: The face value (and market value) of one apple is one apple. But that says nothing about the price of apples in terms of other goods.

Ramanan: I will return to it later, but on a very quick skim, it sounds like "100 apples are worth 100 apples".

[Majromax]

> Damn! I've forgotten how to do links!

<a href="http:/url-goes-here">link text</a>

[reason]

Aha - I should point now to the excellent Cameron Murray http://www.fresheconomicthinking.com/ .
Money is an OPTION not a bond.

[Dave Welsh]

Brian Romanchuk's "put option" and the author's "liquidity demand" seem like the same thing to me.

[Eric Tymoigne]

Nick R about Nick E: issues of bond valuations are about determining the nominal value not real value. The fact that fair price is face value is central for the payment system.
In addition, nominalism prevails in the law so bearers of financial instrument do not have to be compensated for loss of purchasing power. As such, the purchasing power of any financial instrument is zero if one gives it enough time or if inflation is high enough.
More here
http://neweconomicperspectives.org/2016/05/money-banking-part-15-monetary-systems.html

Main point though is that one must make a difference between what determines nominal value (structure of financial instrument and creditworthiness of issuer) and real value (theory of inflation)

[Market Fiscalist]

It strikes me that all goods derive their present value from the discounted value of the future stream of services they provide, and these services can be more than just financial and/or liquidity services.

The price I would pay for a backscratcher depends upon the future stream of services it provides. This may just be a stream of backscratching services. But if I could rent it out to others for money its value increases. If there is thriving market in used backscratchers then I may pay more for it if I know I can resell it for a good price in the future if I need to. If (for some reason) backscratchers become the commonly used medium of exchange then their value will increase further and they would maintain value even if everyone lost interest in backscratching and the value they provide was purely a liquidity service and the discounted value of all other future services was 0. In all cases the value of all other goods measured in backscratchers would adjust so that people would hold the existing stock of backscratchers at that price level.

If however backscratchers did become money, while also acting as a provider of backscratching service - is it possible that (if prices measured in backscratchers were sticky) that we could get a recession driven by increased demand for backscratching services ?

[Roger Sparks]

You begin with "P(0) = C + P(1)/(1+r(0))".

I don't think that is a good place to start. I would begin this way:

At the end of year one, you have a coupon payment C and a future value which you are deciding right now . The future value that you presently assign will ultimately determine the value you pay today.

Therefore, I would write

(1+r(0))P(0) = C + P(1)

or

P(0) + r(0)*P(0) = C + P(1)

Now we notice that we have three unknowns and only one known quantity, C.

The equation has no rational valuation. Therefore, the decision of what to pay for the coupon is purely an emotional decision.

Hmmm. I don't know how much I would sacrifice to purchase an infinite stream of future payments. If I was hungry, food would come first. Probably this years vacation would come first. I might make a choice between farm land and a perpetual bond under some conditions. I presently do not own any perpetual bonds.

[Adam P]

Hi Nick,

FWIW it seems to me quite clear that Brian is wrong and you are correct.

Brian thinks the value derives from the ability to put money to the government to extinguish a tax liability, this is a bit of bait and switch as this is not the put option the rest of his post is talking about. In his discussion of the puttable bond it's quite different as the holder can put it to the government whether or not he has a tax liability, and in the full amount, not limited to the amount of his tax liability.

Seems clear people value money even if they don't need it for tax payments, it gives a convenience yield that derives from its liquidity.

The use of money to extinguish tax liabilities does give it some fundamental value (FTPL) but most value comes from the liquidity aspect which has nothing at all to do with any embedded put option.

Brian's characterization gets us nowhere to understanding either aspect of money's value or how they may be related.

[Eric Tymoigne]

To Adam P: the fact that gov accepts its monetary instruments at any time at face value value in payment of gov dues is what makes its monetary instrument perfectly liquid (i.e. constant nominal value). Again, mon instruments are securities, we all agree on that, but their term to maturity is not infinite, it is zero so promise of issuer to take back its instrument at face value is central. In the past, some gov changed the price at which they took back their monetary instrument by crying down the (effective default) and fair price would converge to that new face value. Other government refused to take back at any time, maturity was infinite, and fair price converged to zero.
Point is creditworthiness is central like for any other securities to determine the nominal value at which an instrument circulate.
Now issues of what determine the purchasing power of that nominal value is a different issue.

[csissoko]

I have a model of 19th c. banking school's answer to this question: As a practical matter as long as what is used as money is debt (think bank credit lines offered to businesses), then the marginal benefit of holding fiat money is not the zero return that it pays, but the interest it can save a business that uses fiat money instead of drawing on its credit line. Thus, depending on how you model money, the marginal return of fiat money may not be zero.

BTW, the paper also argues that the fact that banks accept deposits or fiat money in payment of debt owed to the banks is enough to get them to circulate -- you don't need the government/tax system to make this work.

See: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2775493

[Nick Rowe]

Adam P: "Brian thinks the value derives from the ability to put money to the government to extinguish a tax liability, this is a bit of bait and switch as this is not the put option the rest of his post is talking about. In his discussion of the puttable bond it's quite different as the holder can put it to the government whether or not he has a tax liability, and in the full amount, not limited to the amount of his tax liability."

That is a very good point (though I need to re-check what Brian actually said). To re-state it:
1. the *right* to *sell* an *unlimited* amount of asset C (at a fixed price 1/P in terms of some real goods), is very different from
2.the *obligation* to *deliver* a *limited* amount of C (in exchange for nothing for you personally, except staying out of prison).

1. is a true "put option" (right?). Is there a technical finance term for 2?

Did I re-state that right? Any way to re-state it even more clearly? Think I'm gonna use it.

[Nick Rowe]

Roger:

The value of the bond the second *before* the annual coupon is delivered is:

P(0) = C + P(1)/(1+r)

The value of the bond the second *after* the annual coupon has been delivered is:

P(0) = C/(1+r) + P(1)/(1+r)

But it doesn't make any material difference to my post.

[Nick Rowe]

csissoko: Interesting. I'm seeing one firm holding a sawtooth pattern of (0% interest) M. And a second firm, otherwise identical, paying interest r% on the same sawtooth pattern of overdraft at the bank. But if the first firm switches to act like the second firm, it can also sell its peak stock of M and earn interest on it.

And this makes me think about my old posts about two sorts of money: positively-valued green notes and negatively valued red notes. And the green interest rate (paid to holders of green notes) may exceed the red interest rate (paid by holders of red notes).

[Brian Romanchuk]

Since modern bank money is pegged at a 1:1 ratio to government money, you can put "money" back to either the government to pay tax, or you can put it to a bank for a bank deposit, or to pay down a bank debt. That is, the put option is not solely to the government. If that 1:1 ratio was not legally enforced, then we could see different "monetary" instruments trading at different prices, and then we have to be much more worried about what entity that I can redeem that money to.

In the Canadian context, the private sector rolls over debts that are a multiple of the monetary base every week (working from memory). In other words, we cannot conclude anything about the amount of "redemptions" by looking at the time series of the monetary base.

Even if I do not have a tax liability to extinguish, or my money holdings are larger than my immediate tax payment needs, I am not going to give a free lunch to someone who does. Since I know how they value the monetary instrument, I will sell it to them only at that price. This has nothing to with a "convenience yield", it has everything to do with not being a sucker being arbitraged. If I inherited an equity portfolio which contained shares in a speculative company that I think are inherently worthless, I am not going to give those shares away - I will sell them at the market price.

The people who are obligated to raise money to meet debt/tax obligations that day are the ones setting the price of money that day.

[csissoko]

Nick: I'm not sure where your sawtooth patter of M is coming from. I'm used to working with new monetarist models where the distribution of M is degenerate so every firm chooses to hold the same quantity of M (holdings diverge in a sub-period and at the end of the period every firm chooses to hold the same quantity of M again). So I'm not sure in what environment it would make sense for "otherwise identical firms" to pay with M and to pay with debt. To me it makes more sense for a firm to hold enough M to pay in full when stochastic needs turn out to be low and to use up holdings of M and borrow when stochastic needs turn out to be high. Thus, I can't imagine an environment where "otherwise identical firms" would choose to pay with M and with debt as alternatives. Their identicalness inherently implies that they must hold the same quantity of M.

I'm probably completely missing the model that you have in mind, so please do let me know how I'm confused.

BTW I think that your discussions of negatively valued notes get much closer to a practical theory of money than just about anything else I've read.

[JKH]

Just use the liquidity demand function (we call it a "money demand function") to figure out the P(0) at which the ratio of market capitalisation to NGDP gives us an r=0%. Done.”

Does this determine the nominal money supply function?

[Nick Rowe]

Brian: commercial banks promise to convert their money to central bank money at a fixed exchange rate (of one). That explains why the Bank of Montreal dollar is worth exactly one Bank of Canada dollar. (I call that "asymmetric redeemability", because it is the Bank of Montreal, not the Bank of Canada, that makes the promise to fix the exchange rate). But it does not explain why the Bank of Canada dollar (and the Bank of Montreal dollar along with it) has positive real value in terms of real goods.

I'm afraid you lost me on the rest of your comment.

Did you see Adam P.'s comment above (and my re-statement of it @4.54pm)?

csissoko: Thanks! (I confess I find it hard to keep my head straight in the red/green world, and keep reverting back to the pure green world, even though I know the red/green world is more accurate.)

I had in mind some sort of old-fashioned inventory-theoretic model of money demand, like Baumol-Tobin or similar, where an individual's stock of money, plotted over time, goes up and down when he sells or buys something. It's a sawtooth in Baumol-Tobin, because it jumps up when he sells a bond (or gets his paycheque) then declines slowly as he steadily spends it.

The otherwise identical firms making different choices was really just a way of looking at the two choices open to one firm. It could use money, or credit, and imagines both, to decide which is best.

[Tel]

If your purpose is to calculate the value of a fiat currency as measured in the same fiat currency, then it seems to be that a hundred bucks is a hundred bucks and you don't need any conversion factor to answer that (nor any marketplace for that matter).

[Tel]

But it does not explain why the Bank of Canada dollar (and the Bank of Montreal dollar along with it) has positive real value in terms of real goods.

If you want to relate to real goods, then it seems the following formula is quite peculiar:

P(0) = PV[C]

Or, in the simple case where r(t) is a constant over time:

P(0) = C/r + lim[P(T)/(1+r)T] as T goes to infinity

For starters, both sides of the equation are measured in currency (none of it is measured in real goods), but secondly you presume this currency is held for infinite time (i.e. never gets spent) and if your intention is to hold currency in your hand forever then the value (in real goods) would indeed be zero. In order to spend it, you have to get rid of it.

Ultimately, all fiat currency ends up going back to the government as a tax payments. Since the IOU note is in the hands of the IOU issuer at that stage, the value is automatically nullified. The real-world value of fiat currency is based on the ability of government to force people to pay tax (i.e. backed by threat of violence). Since your life is valuable (to you at least) you will also value the tickets that allow you to keep yourself safe. The subjective value thus would depend on the individual holding that currency and when this individual is predicting they will spend it (and that's a probability wave because no one knows exactly when they will need to spend) but if you don't like individual subjective valuations I guess you can work out the "r(t)" in terms of the typical trajectory of the fiat currency after leaving the hands of government and then cycling through the economy and getting back to government... certainly not an infinite time period, but I don't know any easy way to determine the actual period.

[Brian Romanchuk]

Nick,

Versus real goods - who knows? (Will comment further below.) NPV calculations live in a world where one unit of dollars has a NPV of $1 by definition; I was just demonstrating a fixed income instrument that converges to that NPV behaviour. We can imagine a world where instruments that are labelled "money" as having a NPV different than one, using another unit of account, but it is very painful to write about. (Although it happens in practice; one argues with counterparties about the NPV of positions all of the time.) After a hyperinflation, those NPV dollars may be worthless to anyone other than a collector. (I had an initial comment to that effect; it got mangled, and so this point was not emphasised enough.)

For the redeemability, the government requires cheques to clear at par, similarly for bank transfers; this was not the case (e.g.in the U.S. In the 19th century). Tax payments made by cheque/transfer clear at par. Banks have to accept government money and cheques at par. We have deposit insurance, and there is a "too big to fail" assumption that depositors will be made whole (outside of the euro area, which is a basket case). I see the obligations as being symmetric in practice; the government imposes them on everyone, including itself.

I saw Adam P.'s comment. I guess that I am assuming the "law of one price," which is a pretty standard assumption in pricing theory. If I have 200 money units, and a tax obligation of $100 (using some "true" pricing measure), and the government accepts my units at a price of $1, the first 100 units certainly have a value of $100 to me. The remaining 100 units has a price of $1 as well, following the "law of one price". The fact that I do not always have a right to redeem all of my money does not matter. We can extend this to relying on me knowing that other entities will value at least some money units at $1; I value money based on their valuation. Otherwise, I am going to be the sucker in an arbitrage.

What is the alternative? Saying "money is worth par to *some people*, and worthless to *other people*, so who knows what the price is?" Although that might be realistic, it is not in character for a field that has collapsed all the decisions in an economy to a single optimising household.

Returning to real value, my argument is that you either end up at the Fiscal Theory of the Price Level, or Chartalism. The Chartalists (MMTers) would scream bloody murder about the assumptions behind the FTPL, and I am in that camp. I would argue that the key factors are institutional, such as pre-existing contracts - which create demand for money to meet them. You can then add in all of the psychological factors (inertia, etc.), which a mathematical model is going to have fits dealing with.

[Nick Rowe]

Brian: or you can end up with the (standard) money demand-money supply theory of the price level I have stated here (the only non-standard thing about it is I have re-stated it in finance-speak) which is neither FTPL nor Chartalist..

[Nick Rowe]

Brian: but sadly, my post seems to have failed miserably. Because I was trying to explain the standard theory of the price level in a way that would make it accessible to finance people, like you.

[csissoko]

Nick: Here's how I think the way I think about money relates to Baumol-Tobin (hope I don't make a mess out of this). I'm going to use FM for fiat money.

Take that sawtooth diagram and now think about it as being applied to a variety of different initial money-holding positions, so that instead of needing money before you spend it, you can just borrow it. One version of the diagram will lie completely below zero, so that your paycheck is just used to pay off your debt. Another version lies completely above zero, so you never borrow.
I think of agents as getting to decide where they want to be across this range of all debt and no debt -- with the understanding that accumulating money to bring to the start of a Baumol-Tobin period is not costless (because you have to give up the value of the money in order to be able to carry it into the period).

I also think of agents as having a stochastic demand for money, so that it's not optimal to always bring the maximum amount of FM you could possibly need (because when your demand for money is low, you've incurred costs to carry "too much" FM into the period). Then for a given interest rate there's going to be some optimal level of money/debt that you bring into a Baumol-Tobin period.

Hope this makes sense.

[Too Much Fed]

Brian,

Nick said: "Brian: commercial banks promise to convert their money to central bank money at a fixed exchange rate (of one). That explains why the Bank of Montreal dollar is worth exactly one Bank of Canada dollar. (I call that "asymmetric redeemability", because it is the Bank of Montreal, not the Bank of Canada, that makes the promise to fix the exchange rate)."

Brian, I think this is the question to ask.

Does the price inflation target apply to the lender of last resort function of the central bank to the commercial banks?

[JKH]

Nick,

Perhaps you could explain why the following reasoning is wrong:

At one point, you compare M to the number of “shares” of the liquid asset in question.

Assume the liquid asset in question is money
Assume money pays a nominal contractual interest rate of 0 per cent – e.g. banknotes
Assume each “share” of M has a nominal value of $ 1
E.g. M is equivalent to 1 billion $ 1 bills (in the US, or loonies in Canada)

Then:

M is the nominal “market capitalization” of money
M/P is the real “market capitalization” of money
M/NGDP = (M/P)/RGDP = the ratio of market capitalization to GDP
I.e. nominal and real ratios are the same

I think you are saying that the value of money is explained by the point on the money demand curve where the ratio of market capitalization to GDP corresponds to r = 0

You explain that in terms of M/P and RGDP
But it must hold in the same way for M and NDGP because the nominal and real ratios are the same

So the point where r = 0 on the money demand curve corresponds to a unique point on the money demand curve, which must correspond to the nominal quantity of money supplied M

This suggests that a nominal, contractual interest rate of zero is determined by a unique quantity of money demanded/supplied for a given level of GDP (nominal or real)

This seems to be a contradiction, because it suggests that any other quantity of money supplied will result in a different contractual interest rate on money. But that contractual interest rate of zero is fixed and set to zero under all circumstances, including the supply of money. That’s why I asked earlier if such a money demand function itself determines the supply function.

(In general, I obviously agree with the kinds of finance explanations provided by Eric, Nick E., and Brian)

[Adam P]

Brian,

It's generally incorrect to 'assume' the law of one price, one assumes the absence of arbitrage. In many cases the absence of arbitrage implies the law of one price but there are a plethora of real life examples where the law of one price appears to fail due to constraints on the ability to do the arbitrage.

This seems to me to be clearly such a case.

Furthermore, there are a multitude of real life examples of places (not like the US or Canada) where a foreign currency (usually USD or Euros) are more highly valued and more liquid than the local currency despite not being redeemable to the local government and these people not being able to put them to the US government (not being American).

The value of the US dollar in such situations derives from it's liquidity which in turn derives from the fact others will accept it (not limited to Americans or Europeans).

This liquidity is some sort of equilibrium in some sort of coordination game and we know from historical experience that such equilibria can appear stable for a very long time. However, we also know from historical experience that they can collapse very suddenly which itself is prima facie evidence that they are not maintained by arbitrage.

This also addresses Eric's response. I'm well aware that the acceptance of money by the government to settle tax liabilities gives it a positive fundamental value (that's FTPL which stands for Fiscal Theory of the Price Level). This point is not new nor original to Brian. That does not imply that Brian's formulation explains anything, which I don't believe it does.

Nick, my quick reading of your restatement doesn't make me want to disagree with you.

And again, it's very clear people hold cash well in excess of that needed to fund tax liabilities which implies it pays some sort of "yield" in real terms (even if not in nominal terms). The yield could be a convenience yield derived from liquidity services.

Once we agree the value of the stream of liquidity service has strictly positive value we are done, money has positive value whether it's other sources of value (FTPL or limited optionality) is positive or not.

[JKH]

Again, I return to this as in my first comment:

“Just use the liquidity demand function (we call it a "money demand function") to figure out the P (0) at which the ratio of market capitalisation to NGDP gives us an r=0%. Done.”

If you’re calculating a market capitalization ratio with NGDP in the denominator, then you must have a nominal measure of market capitalization of money in the numerator. That’s an obvious calculation for a non-money liquid asset. For money, you’ve defined M as the number of “shares” and therefore P(0) must be the nominal value of each share, which is the assumed face value – e.g. a US $ 1 bill. This is trivial. I see no “figuring out” of P(0) for purposes of an NGDP based ratio. It is M that must be “figured out”, or at least the relationship of M to NGDP, because P (0) is invariant in nominal terms. The latter is simply the assumed fixed nominal value of each “share” of M. Then, if M (the number of “shares”) relative to NGDP is small enough, the money demand function will hit an interest rate of zero.

I think your analysis using the demand curve amounts to a specification on the supply of money M with a fixed nominal value “per share” of P (0), where that nominal value is self-determined by P as the numeraire for itself. It all has to be nominal if you’re calculating an NGDP based ratio.

So this doesn’t answer the question about why P is what it is in nominal terms.

That’s answered by the finance guys.

[Oliver]

@ csissoko
I can't claim to understand more than a fraction of the paper you link to, but I find myself very much in agreement with the parts I think I do understand (also with your claim that government / tax system is not required to get a credit system working). This is the most detailed account of a banking school model I have ever come across in English. Thank you!

[Ramanan]

Nick R,

I am not sure what you are doing with money demands.

In the general case, I'd use Tobin's asset allocation theory to figure all this out.

But since the bond you are discussing is worthless, the portfolio preference parameter λ will be zero.

So even after you do supply-demand analysis, the equations would solve to give an answer zero as the value of the bond.

[Brian Romanchuk]

Nick,
My view (guess?) is that (what I would call) "mainstream" approaches to the valuation of money either end up as kludges (10 yen gives me the same real utility as 10 Canadian dollars), or the FTPL. (Or an institutional factor approach that is equivalent to the post-Keynesian view.) That's only based on my sampling of the theory, and arguments about scaling of monetary variables. Beyond the scope of discussion here.

Adam P.,

If you want to invoke real world examples, in real world pricers, "money" has a NPV of 1 by definition in real world pricers. You cannot argue with definitions.

What I demonstrated is that a sequence of putable perpetuals converges to the pricing characteristics of money, while option-free ones don't. This is not entirely useless; it is consistent with governments in unusual situations using bonds as a form of money.

Private sector debt is a multiple of the size of GDP, and a great deal of debt is rolled over at 30 days or less. Debt redemptions need money, and there is a legal 1:1 parity between private (bank) money and government money. Those rollovers dwarf the monetary base.

Saying that there is a "convenience yield" is not enough; why will that not vary over time? Since you need to capitalise that convenience yield fo get a valuation, the swings should be large as preferences change. A real store of value, such as gold, would be a more stable pricing unit for goods and services in this case, and that is hardly the case in the modern developed countries.

[Oliver]

@ csissoko / Nick

I am having a bit of trouble with your (csissoko's) definition of fiat money. This may come down to my complete inability to read equations (I'm not an economist), but when you say: the relevant rate of return on fiat money is not the interest rate that it pays but the interest that it enables borrowers to avoid paying I ask myself by what transaction fiat money comes to be. In a conventional OMO, as in a monetarist framework, the non-bank public gives up an interest bearing financial asset in exchange for CB fiat. Macroeconomically that does not square with the sentence of your's I quoted above.

You seem to use the term fiat to describe the stock of borrowed money held over from one period to the next and are arguing that, although contrary to a simple credit cycle model in which money balances disappear at the end of a period, your more complex analysis can explain why it might be rational for that not to happen, thus adding positive value to a stock of inside money. This is different from how I understand Nick's red & green model, which I take to be short Hand for inside & outside money.

But then again, I may have gotten both of you wrong and two wrongs might not make a right in this case.

[Nick Rowe]

JKH: You were doing fine up until this point:

"This suggests that a nominal, contractual interest rate of zero is determined by a unique quantity of money demanded/supplied for a given level of GDP (nominal or real)"

No. It's NGDP (either P and/or RGDP) that adjusts to equalise Ms and Md, since (as you say) the contractual rate of interest cannot adjust. NGDP adjusts until the ratio of market cap to GDP gives us a "desired" rate of return (i.e. a rate of return at which M will be just willingly held) equal to the actual rate of return.

All assets have a "desired" rate of return (given their liquidity, risk, etc.) at which they will be just willingly held. In equilibrium, the desired rate of return equals the actual rate of return. For most assets, it's the actual rate of return that does (most of) the adjusting. If the desired rate is above the actual rate, people try to get rid of the asset, so the price drops, raising the actual rate of return looking forward. But for money (or for any asset unique enough to have a downward-sloping demand curve), the drop in market cap/GDP is what drops the desired rate of return to equal the actual rate of return.

[Nick Rowe]

Feel like we are talking at cross-purposes.

One apple is worth one apple. One dollar is worth one dollar. To ask why one dollar is worth one dollar is not an interesting question; it's not even a question. (Though asking why Bank of Montreal dollars are worth the same as Bank of Canada dollars is a question, and an interesting question, and one with a straightforward answer.)

That is not what this post is about. This post is about: why is the dollar worth *anything* (in terms of apples, bananas, and other real goods), and what determines that value? The price of currency is 1/P, where P is the price of a basket of apples, bananas etc in terms of that same currency. Why is 1/P not zero? What determines 1/P? That is a real question, and an interesting question.

[Nick Rowe]

Assume FTPL is true. And just to keep it simple, let's consider a government that issues zero-interest currency only, and does not issue interest-paying bonds.

What interest rate do we use in the FTPL equation M/P = PV[real primary surpluses]?

[csissoko]

@Oliver

"the relevant rate of return" refers to the return required by someone who holds fiat money. The kind of equilibria that I (and many other macroeconomists) study has an initial level of the money supply at the "right" level and a path that the money supply follows in order for all agents to be optimizing. In my model -- where everybody borrows regularly, the effective rate of return for fiat money is determined by the fact that it reduces the need for the agents who hold it to borrow.

I've just dived into this literature and haven't played around with the issue of monetary policy in this kind of a framework. So I'm not actually sure how to relate it to OMO.

The distinction between fiat money (or outside money) and "borrowed money" (or inside money) in my model is the fact that money supply is a control variable, so the quantity of outside money can be set optimally (by for example the central bank). I do think that the distinctions commonly drawn between inside and outside money are often exaggerated, so it's not surprising if you find that in my paper one concept is very close to the other.

I'm just working from memory here, but the idea that red and green notes can be originated in pairs is a property of Nick's world that can be used by either the central bank or the private banks, I think. So I don't think that the distinction between inside and outside money is entirely clean in Nick's environment -- which is a good thing from my point of view.

[Nick Rowe]

csissoko: Off the top of my head (not really having thought this through):

I think the red/green distinction is separate from the inside/outside distinction. But not totally orthogonal.

I can hold either green money or red money at the Bank of Montreal (my chequing account can have a positive or negative balance). Inside money.

I can only hold green money at the Bank of Canada. But the Bank of Montreal can hold either green money or red money at the Bank of Canada (reserve account). Outside money.

[Nick Edmonds]

"But for money (or for any asset unique enough to have a downward-sloping demand curve), the drop in market cap/GDP is what drops the desired rate of return to equal the actual rate of return."

Not sure this is generally true. If by money we mean currency, then any mismatch in the desired and actual returns is corrected through the supply of currency, by drawings or reflux. If by money we mean balances with commercial banks, then it's the actual rate paid on those balances that adjusts.

This doesn't mean of course that if NGDP does change that it has no effect on desired or actual returns.

[csissoko]

Thank you, Nick. That clarifies the relationship nicely.

[Eric Tymoigne]

Adam P @5:46AM. The FTPL has nothing to do with it. When someone ask "what determines the market value of a zero-coupon perpetuity, like currency?" one is not asking about output-price level determination (what the FTPL, QTM, etc. are trying to address). The question is about why a particular security trades at the price it trades in the market; its fair (nominal) price: Why does a $100 FRN trade at $100 and not at $90, or $0?
While Nick seems to find the question uninteresting, it is actually very relevant to understand what creates an acceptance for monetary instruments and to understand monetary history.
Monetary instruments are priced exactly in the same way as any other security and the present value is relevant to understand that. One just needs to understand that:
1- a monetary instrument is not a consol, i.e. it does not have an infinite maturity (the issuer never promises to take it back). Monetary instruments have a zero maturity. This does not seem to be well understood because I have seen so many economists state that gov monetary instruments have an infinite maturity (in which case the fair price is indeed zero given that it is a zero-coupon security: a $100 will trade at $0 nominally).
2- the creditworthiness of the issuer is central to the acceptance of any security, including monetary instrument.

I am not saying that issues of output price level are irrelevant for monetary analysis, I am just saying that one must make clear difference between what determine the fair price and the purchasing power of that fair price. Fair price relates to financial characteristics and creditworthiness, the second is a more macro issue. The two issues are at work in monetary history but are not usually well distinguished. With that one can understand what in the past $100 notes did circulate at a discount or a premium (again in nominal terms).

[Oliver]

@ csissoko & Nick R.

An inside money only world has equal amounts of red and green money, an outside money only or mixed world will have an overhang of green money. I take that overhang to be what the fuss is all about and what csissoko calls fiat money. My point is that that fiat money comes at a price - namely at the price of the interest income foregone through the sale of interest bearing financial assets to the central bank. So you have to subtract the interest saved by the non-bank public by not having to borrow from the interest foregone by the sale of the asset. Something tells me they cancel out. Hope that makes sense. And thank you for engaging.

[David Beckworth]

Brian, there are interesting examples of money maintaining value without government backing or being treated as legal tender. For example, the Somali Shilling continued to circulate as money after the Somali state collapsed in the 1990s. Also, unofficial dollarization that spontaneously emerges in many developing countries is another example. Finally, there is bitcoin.

This is not to say the state is inconsequential, but only that there is 'convenience yield' due to money's network effects that is distinct from any government backing story.

Nick and Brian, this podcast with Will Luther is really good on this point:https://soundcloud.com/macro-musings/willluther

[csissoko]

@Oliver

I think you're a little confused here. If $1 of FM is exchanged in an OMO for an equivalent value of (positive) interest-bearing bonds, then the face value of the bonds must be less than $1. That is the amount of FM that you get will compensate for the interest that the bond bears using a present value formula. In short in an OMO the seller of the bond doesn't lose the interest, but instead gets paid cash upfront for it.

[Nick Rowe]

David: Bitcoin is the cleanest example. Especially since it is not (usually) used as the unit of account, so we don't get muddled when we talk about the price of Bitcoin. If it survives another 10 years, and gets generally used as a medium of exchange, it will be a great example.

Nick E: Yes. That depends on the central bank, and what it is targeting. If the central bank targets M, it's NGDP that adjusts. If the central bank targets NGDP, it's M that adjusts. If the central bank targets the price level (or inflation), it's M (and maybe RGDP in short run) that adjusts. Plus, other interest rates may adjust too in the SR.

Oliver: "An inside money only world has equal amounts of red and green money..."

I don't think that's right. Suppose commercial banks refuse to allow anyone to have an overdraft in their chequing account. Then there's no inside red money. "Red money" is not the same as "debt".

[Brian Romanch]

David B.,

I agree that it is possible for a currency to survive without state backing. Furthermore, you could have a state currency without "taxes" (gulf oil states could easily do it). Although I am closest to the MMT camp, I fit somewhere in broad post-Keynesianism where the answer to what what determines the prices level is: "it's complicated." Not sure what the "official" MMT stance is on the question; I think they have an explanation (their academic views are more nuanced than what you see repeated on the internets).

Nick,

Assuming your question about the FTPL is aimed at me, I think that would be the equation for the standard setup, where bills were abolished. You treat money as a bill locked at 0%; since in the standard setup, nobody holds money (dominated by bill holding).

I will eventually write a longer version of my wild assertion about the FTPL; but I will note that you could generate a similar effect with private debt contracts. I guess what I really want is a GFTPL (Generalised FTPL.) This would cover models where there is no government, rather just a pair of households. The key is that you need a monetary obligation that creates a scaled demand for money. (Otherwise, we are in what I think are kludges; I will have to explain why I dislike them elsewhere. I am pretty sure that my complaints about them are well known. I just have no idea why the GFTPL is not discussed more.)

[Nick Rowe]

Brian: well, my FTPL question was aimed partly at you, but also at anyone else who happened to be reading and who thought FTPL a useful approach ;-)

[Eric Tymoigne]

David B.
For theory of inflation in MMT and PK check section "income distribution and inflation" in this: http://neweconomicperspectives.org/2016/04/money-banking-part-11-inflation.html

[Oliver]

@ Nick R.

Suppose commercial banks refuse to allow anyone to have an overdraft in their chequing account. Then there's no inside red money.

OK, so I've had that wrong all the time. But then for there to be green money in an inside money only world, banks must be able to issue by fiat, too (I thought the idea was that they couldn't). And my observation about interest income and debt service cancelling out remains, independent of the bank setup.

[Nick Rowe]

Oliver: suppose banks issue green money (positive balances in chequing accounts) as liabilities, and hold bonds (that are not used as money) as assets. This is the simplest textbook model of banks.

[Mike Sproul]

Nick:
For interest rate R and convenience yield Y, the price of a security paying 1 oz of silver in 1 year is

PV=1/(1+R-Y)

So if R=5% and Y=2%, then the security will be worth about .97 oz at the start of the year, and will grow to 1.00 oz at the end of the year.
Throw in printing and handling costs of C=3%, and the formula becomes

PV=1/(1+R-Y-C)

So if R=5%, Y=2%, and C=3%, then the security will start the year worth 1 oz and end the year at 1 oz.
Call the security a dollar, and call the convenience yield "liquidity" and the value of a dollar is always 1 oz. The rules of finance explain money.

[Nick Rowe]

Mike: Let's change your example slightly.

Suppose the Bank of Canada keeps a lot of CPI baskets of goods in its basement. (Yep, the haircuts and fresh food are a bit tricky to store, but allow me some literary licence). Then targeting 2% CPI inflation would be very easy. The Bank stands ready to buy and sell currency for CPI baskets at a crawling peg exchange rate that depreciates at 2% per year against the CPI basket.

That determines the price level path. And we talk about the liquidity of currency, and the downward-sloping demand curve for liquidity, to explain why people demand to hold a positive stock of currency despite it yielding negative 2% real interest.

In the special case where the supply curve of apples is perfectly elastic, the supply curve determines the price of apples, and the demand curve determines the quantity at that price. But in the general case we need both supply and demand curves to determine both P and Q. Same with money.

[Nick Rowe]

Put it another way: the "rules of finance" do fine -- provided you add a downward-sloping liquidity yield demand function.

[Oliver]

@ Nick
Yes, and it is money that is produced in such a ways that I believe csissoko refers to as fiat and in her paper is reserved for the central bank. Commercial banks, OTH engage only in acceptance banking.

Her claim then seems to be that a: acceptance banking is sufficiently self stabilising that it can be viewed as a stand alone theory of money creation. and b: that fiat banking can be added as a bonus because it relieves the non-bank public of having to borrow.

My point, which is probably idiotically trivial, is that the privilege of fiat comes at a price. Namely at the price of the income attached to the bond, which would otherwise accrue to the non-bank public. Seignorage, in other words. The non-bank public can either borrow and pay interest or pay seignorage to the banking sector.

[JKH]

Nick,

From your post and later comment:

“Just use the liquidity demand function (we call it a "money demand function") to figure out the P(0) at which the ratio of market capitalisation to NGDP gives us an r=0% ………………. Put it another way: the "rules of finance" do fine -- provided you add a downward-sloping liquidity yield demand function.”

That’s 3 slightly different terminologies for presumably the same thing.

Can you indulge me - and describe more precisely what you intend by this function – the axes and what it applies to?

E.g. my starting point for trying to understand what you mean by the money demand function is my understanding of it as portrayed along with the supply function that go into constructing the standard (old fashioned) LM curve in ISLM. So the demand for money is downward sloping with respect to some general level of interest rates on the y axis and quantity of money on the x axis. And the old fashioned fixed supply cuts that vertically. And then logically trace an upward sloping LM curve as you expand NGDP. That all seems intuitively consistent with what you are describing.

But you have also generalized to non-money liquid assets, extended somehow to P and 1/P, and have also talked about a demand/desire for yield on money.

I think I see this all intuitively, but I’m struggling to see exactly what this particular demand function you’re referring to looks like. As with other things, do you construct this sort of thing differently from other monetary economists, or is it all standard? Is there an implicit iterative development of curves here? Does it apply to bonds as well as money?

Sorry, this is a bit of a teaching request, and probably ponderous for you to respond to.

(After that, I have a comment on why I think you've gotten the nature of the finance responses you have, given the particular logical organization of your post.)

[Nick Rowe]

JKH: Here is the conventional textbook money demand function:

Md = P.L(Y,r)

(It is conventional to use L( ) rather than F( ) as the letter for that function, following Keynes' "Liquidity Preference".)

L( ) is a positive function of Y (real GDP) and a negative function of r (the interest rate on "other" (non-money) assets.

I have simplified it slightly, by assuming Md is strictly proportional to Y (not a bad assumption, empirically), so we can re-write it as:

Md = P.Y.F(r) or (Md/NGDP) = F(r)

That implicitly assumes M pays 0% interest. If instead M pays rm% interest, we can re-write it as:

(Md/NGDP) = F(r-rm) (Note that r-rm is the opportunity cost of holding M instead of "other" assets.)

Now any demand function or curve can be inverted, so we talk about the "demand price" Pd for apples as a function of quantity of apples bought (the amount people would be just willing to pay for that quantity of apples). We can do the same for this one, and write it as:

rmd = r + H(M/NGDP) where H is some function that starts out as a negative number and gets bigger (less negative) as M/NGDP increases.

In words, the rate of interest paid for holding money, at which people would be just willing to hold that stock of money, is less than the rate of interest paid on other assets, and is an increasing function of money's market cap (M/P) as a ratio to RGDP.

In the *simplest* case, where M=Ms is fixed, r is fixed, and RGDP is fixed, P adjusts until rmd=0%. (That's what macroeconomists call the Long Run equilibrium, where P is perfectly flexible.)

The same should be true for any asset that performs some sort of unique service, where the demand for that service slopes down.

I'm still puzzled about the reaction this post has got from finance people. I really thought: "OK, they understand that people are willing to accept a lower yield on more liquid assets. All I need do is note that the demand curve for liquidity slopes down, so people will be willing to pay a lot for liquidity if the market cap/GDP of the very liquid asset is small, and less as it gets bigger. Done." I reckon it's got something to do with the unit of account function. "A dollar is a dollar is a dollar"?

[Min]

Nick Rowe: "The face value (and market value) of one apple is one apple. But that says nothing about the price of apples in terms of other goods."

What other goods do you wish to evaluate money in? Nothing else appears in your equations.

[Nick Rowe]

Min: simplest answer: all the goods in RGDP, which does appear in my equations.

[Oliver]

I reckon it's got something to do with the unit of account function. "A dollar is a dollar is a dollar"?

I reckon it has something to do with separating the money - goods nexus from the money - other financial assets nexus. As far as the latter is concerned, my guess is finance people would agree with you.

[Nick Rowe]

Oliver: so they keep thinking about Wall Street, not Wall Street *and* Main Street? ;-)

[JKH]

Thanks Nick

“In words, the rate of interest paid for holding money, at which people would be just willing to hold that stock of money, is less than the rate of interest paid on other assets, and is an increasing function of money's market cap (M/P) as a ratio to RGDP.”

You see, I get that word intuition pretty readily. But for some reason, I really struggle with the algebraic notation in this area. My brain, like yours, is old, and in my case, exposure to introductory economics was just too long ago. You would think that with the number of your posts I’ve read over the years, the intuition for the algebraic notation would have sunk in by now. I’ll try to work on this.

“I'm still puzzled about the reaction this post has got from finance people.”

I will comment later today or tomorrow morning on how I interpret the reason for this reaction. I think it is interesting.

[Oliver]

The other way around, really. They accuse economists of thinking you're solving 'real' problems, whereas what you're doing in their eyes is just stirring around in a sea of nominal claims. Or are you just pulling my leg?

[JKH]

Nick,

Again, regarding:

“I'm still puzzled about the reaction this post has got from finance people.”

In summary, you started out by exploring a “nominal space” calculation for the price/value of money as represented in the form of a 0 coupon perpetual bond and concluded that this doesn’t work. You then switched over into a “real space” more macro analysis of what determines the price of money P (t) in real terms - although your market capitalization/GDP ratio criterion can be expressed in nominal terms as well.

I think you’ve gotten the reaction you have from the finance types because you abandoned that nominal space bond calculation under what they would allege to be false pretences.

In fact, money is not properly represented as a (plain vanilla) 0 coupon perpetual bond. It has optionality that makes it exactly the opposite of that from a maturity perspective. Its effective maturity is immediate - as I think all of Eric, Brian, and Nick E. explain or at least infer in their own way.

This is more subtle and meaningful than "a dollar is a dollar”, although I suspect you may disagree.

My own interpretation is probably more general than the others’ from an optionality perspective. Start out by acknowledging that the underlying form of money is that of a zero coupon perpetual bond. Attach to that bond a put option. And I would say that it is a put option in a most general way. Money can buy anything at any time. Viewed this way, it is an option to put a special type of perpetual bond at any time for any purpose.

The put option converts a zero coupon plain vanilla perpetual to something that contingently represents what is in effect a “stripped” bond in form. A stripped bond is a derivative of a regular bond where the bond has been stripped of its coupons and what remains is the final maturity cash flow only. That cash flow becomes a “bullet” payment at maturity without any intervening coupons.

In the case of a plain vanilla zero coupon bond, the bond has already been “stripped” of its coupons – in effect. Moreover, nothing of substance remains in terms of cash flow because the final maturity payment has already been extinguished the perpetuity condition. Such a bond is worth zilch in nominal terms.

But attach a put option to that bond, and it effectively converts to an immediate maturity cash flow on exercise, sans any intervening coupons. And because that cash flow is continuously available, until the option is exercised, it is trivial to conclude that it is worth the face value of the money that constitutes such a “bond”. The effective term of the bond is continuously zero. Moreover, it doesn’t matter what the discount rate is – because the discount rate operates over a zero time horizon.

This is more than “a dollar is a dollar”. It is an option adjusted explanation of how money resembles a particular type of bond. I’ve explained it intuitively, while Brian has gone into an explanation using legitimate option math heuristics. (I don’t know if Brian would agree with my intuition).

So I think you are getting the finance push back you are on this – not necessarily because of the way you are modelling the price/value of money starting out in real space – but because you departed nominal space with an incorrect interpretation of the bond math you started out with - as it should apply to money. You may be getting additional push back on the real value approach with the demand curve, but you’re probably getting more of it because of your premature/incorrect abandonment of the nominal bond approach.

I think of the two approaches as entirely complementary. I think I understand what Brian is doing and I think I understand the intuition of what you are doing. So I don’t think your approach displaces the validity of the option adjusted bond approach. It may well be more interesting, but I think it is incomplete in that it presumes to displace what I think is a legitimate micro optionality approach.

(I have a feeling you will disagree with all of this, and maintain your “dollar is a dollar” reaction.)

[JKH]

As a distant corollary to the above, I absolutely loathe the proposal by some hard core helicopter droppers that the central bank should extend 0 coupon perpetual loans as a way to right its balance sheet optics upon making drops. Such loans are plain vanilla, and are worth zero. The perpetual loan proposal is a ruse in an attempt to circumvent the indignation expressed by some (I wonder who) that central banks should not be running negative equity as an accommodation to facilitate helicopter drops. Plain vanilla perpetual loans don't change that negative equity result.

[csissoko]

@Oliver

Yes, my view is that money can be private or public. What you need is some reason to "trust" the issuer, so that the value of money is expected to be maintained.

When the finance people say money should be represented as a put option, they are making assumptions about the behavior of the issuer that will support the value of the put option. There's no reason properly calibrated incentive constraints can't be used to support the private sector as issuer.

Yes, when people substitute fiat money for inside money the banks lose income -- and this affects their incentive constraints. My paper -- and many others -- find that the Friedman Rule is sub-optimal because it is incompatible with the incentive structure of the banking system.

[Too Much Fed]

JKH said: "Start out by acknowledging that the underlying form of money is that of a zero coupon perpetual bond."

Why can't currency be viewed as a commodity that yields 0%?

Let's assume there is no paper currency and gold is used as MOA and MOE. Wouldn't gold be considered a commodity that yields 0%, and wouldn't gold be considered "money" then?

[Nick Rowe]

Oliver: I wasn't pulling your leg.

JKH: I think it's easier if we start out thinking about money *not* being the unit of account, so it is a very liquid asset (used as medium of exchange) that has a price Pm, just like stocks and bonds do, in terms of some other numeraire (like apples or gold). So then the market cap of money is just Pm.M, just like bonds are shares. And we ask what determines Pm (or the market cap Pm.M). Then, after we have explained what determines Pm, or Pm.M, or Pm/NGDP, we do a last minute flip, and say "Hang on, we measure prices in money, not apples or gold, so Pm is just 1/P".

But as a way of explaining my thinking to finance people, it seems to have failed badly, just making things harder.

[Min]

Moi: "What other goods do you wish to evaluate money in? Nothing else appears in your equations."

Nick Rowe: "simplest answer: all the goods in RGDP, which does appear in my equations."

But not as a vector, right?

[JKH]

Nick,

Here’s what some of the finance oriented people have said:

Nick E:

“If I take a $100 bill to the bank, I can have $100 credited to an account of my direction, creating an asset or extinguishing a liability. The earliest date I can do so is today. So its discounted value is just its face value.”

So he’s responding to your exploration of a bond calculation for money by pointing out the discounting period is 0 (i.e. 0 days, since the liquidity/put can be exercised intraday).

Ramanan:

“Nick R, as Brian says, you ignored the optionality in valuation of the bond …”

Same issue

Eric T:

“Monetary instruments are not perpetual, they have an instantaneous maturity (zero term to maturity) i.e. due on demand. While some of them are not convertible, they are all redeemable at face value to the issuer on demand…”

Same issue

And:

“Nick R about Nick E: issues of bond valuations are about determining the nominal value not real value….

Same issue

“Main point though is that one must make a difference between what determines nominal value (structure of financial instrument and creditworthiness of issuer) and real value (theory of inflation)”

That’s the issue of the difference between nominal bond valuation (including the value of money when interpreted as a puttable bond) and your real valuation using the money demand curve.

And so on.

The point being that people at the outset are not rejecting your approach to real valuation. They are objecting to your methodology whereby you rejected a nominal bond valuation approach outright – because you’ve ignored the liquidity option in the underlying bond analogy for money as a perpetual zero coupon bond. And those are two different things. I don’t see anybody else paying much attention in comments to your real valuation approach, so it’s actually hard to tell what they may think of it.

Again Eric:

“To Adam P: the fact that gov accepts its monetary instruments at any time at face value value in payment of gov dues is what makes its monetary instrument perfectly liquid (i.e. constant nominal value). Again, mon instruments are securities, we all agree on that, but their term to maturity is not infinite, it is zero so promise of issuer to take back its instrument at face value is central… Point is creditworthiness is central like for any other securities to determine the nominal value at which an instrument circulate. Now issues of what determine the purchasing power of that nominal value is a different issue.”

Again, he’s referring to money liquidity as optionality and money being representable as a type of bond with optionality. And the real value issue is separate. But no criticism or actual rejection there of your real value approach.

Etc.

[JKH]

The entire reaction can be boiled down to a collective focus on the fact that you ignored the put option in your bond analogy.

Apart from that, I see little push back on your real value approach, which as Eric says is quite a separate issue.

[JKH]

i.e. ships passing in the night

[JKH]

and you may find the liquidity optionality approach to be uninteresting (perhaps in the sense of "a dollar is a dollar"), and your P(t) demand curve approach more interesting - which is fair - but the optionality approach is in fact the correct reconciliation of the bond analogy that you introduced at the start of your post

[Nick Rowe]

Min: simplest answer: as a scalar. The GDP Deflator tells you (one way) to convert that vector into a scalar.
More complex answer: strictly speaking, I could and should leave it as a vector. Md is a function of that whole vector of prices of new and used goods. But that's taking way off into unconventional territory.

JKH: "i.e. ships passing in the night"

That's the metaphor I was looking for! I was moving my hands together, offset a bit.

Here's the way I see it: the (canadian) dollar is *defined* as Bank of Canada currency. The Bank of Montreal dollar is not *defined* as being worth one dollar, but we can explain why it is worth one dollar (as long as BMO is solvent and liquid and lets you convert your BMO dollars into BoC dollars at par). So what Eric said (for example) is great for explaining the value of the BMO dollar in terms of BoC dollars. But it gets us nowhere if we want to explain why *either* of those two dollars has any (real) value. It's circular: explaining BMO dollar in terms of BoC dollar, then BoC dollar in terms of BMO dollar. "But what makes any of those bits of paper or electrons worth *anything*?" The finance guys can't get out of Wall street.

[JKH]

You might say that the finance types in their comments on this post have for the most part have provided an answer to the following question:

"Why does money viewed as a 0 coupon perpetual bond not have a value of zero?"

(Similarly, I think of Chartalism/MMT answering the question "Why does fiat money not have a value of zero" - i.e, why is fiat money "accepted")

Whereas I think you are answering the question:

"What determines the real value of money?" (including how the interest rate earned on money (zero or non-zero affects that determination)

I think these are all legitimate, complementary questions

[JKH]

Nick,

"The finance guys can't get out of Wall street."

To be fair, they are responding in this post mostly to a specific point on the bond analogy that you introduced.

And the rest of it depends on what question one is interested in answering.

The real value of money is a specific question. There are others.

I think one of the benefits of the blogosphere SHOULD HAVE BEEN more integration of finance and economic perspectives by now. There has been a general massive failure in this regard, in my view. That said, you've probably done more than your share in the attempt. However, I do think that the economics profession in general deserves its share of the blame for failing at this.

[Eric Tymoigne]

Yep JHK, that's exactly the point. Finance guys like to deal with nominal values (one must keep that balance sheet in shape), most of my fellow economists just want to talk about real values (focusing merely on that may end up killing that balance sheet). One needs both to get a complete picture of what goes on in the economy.
Nick: the argument about nominal value is not circular. It all boils down to the creditworthiness of the issuers.
-I accept BMO monetary instruments because BMO promised that I can convert at par into BoC mon instrument and that I can pay BMO with its monetary instruments at par. Redemption at par (via conversion or payment) was not a given in the past and BMO mon instrument would trade at a discount relative to face value.
-I accept BoC mon inst at par because BoC promised that I can pay gov with BoC mon inst at anytime at par (either directly or through the banking system).

If BoC or BMO decide to default of their promise by removing convertibility (or changing it) or by refusing their monetary instruments at par (or at all) in payments, then their instrument will trade below face value.
None of this relies on the circular argument that "I accept a $100 at $100 because I expect someone else to accept it at $100." The creditworthiness of issuer is the anchor that allows to get rid of the circularity.
Also, with all this stuff, one can understand why bitcoins that were alluded above have a fair price of $0 and are not monetary instruments.

[Nick Rowe]

Eric: Great, so they are all "creditworthy", meaning they can all fulfill their promises to convert their bits of paper into each others' bits of paper. They all trade "at par" with each other. So what? How come all those bits of paper aren't equally worthless? And we give worthless bits of paper to government at tax time, and it gives us back worthless bits of paper as welfare cheques. Like a giant game of Monopoly.

How come I can buy a kilo of apples with one of those bits of paper?

[Eric Tymoigne]

Nick, remember there is also that "payment" promise. One is dealing with the value of the promise for itself not relative to others. All this is similar to the valuation of a stock or a bond. One is merely concern with what goes on with the creditworthiness of that issuer in terms of itself, not relative to the creditworthiness of others.
Regarding the worthless bit, given what has been said above, one must recognize that there are two cases of worthlessness:
1- Hyperinflation: The note themselves still trade at par but one needs a truckload of them to buy anything.
2- Default: The notes suddenly trade at a heavy discount (relative to face value of those same notes) instead of parity, even though the price level of goods and services has not changed since the beginning of time.

Finance people in the comments are focused on case 2 and apply that to the nature and analysis of monetary systems. Starting with issues of present value, perpetuity, and coupon, usually puts a reader in a frame of thought related to case 2, not case 1. Your post mixes both to talk about case 1 so that is confusing.

[JKH]

I believe the full chartalist argument depends in part on the capacity of the government to influence prices by spending on some non-trivial subset of goods and services - i.e. not just transfer payments. Taxation enforces the acceptance of those payments in the relevant currency (at those prices).

[Oliver]

@ csissoko

Thanks for clarifying. I think I agree with that.

@ Nick

OK, thanks. Not that that would have been a problem.

[Min]

Nick Rowe:

"Min: simplest answer: as a scalar. The GDP Deflator tells you (one way) to convert that vector into a scalar.
"More complex answer: strictly speaking, I could and should leave it as a vector. Md is a function of that whole vector of prices of new and used goods. But that's taking way off into unconventional territory."

It's not only unconventional, it's problematic. At least as far as the GDP is concerned, the vector is different in every time period.

[Min]

Nick Rowe:
"How come all those bits of paper aren't equally worthless? And we give worthless bits of paper to government at tax time, and it gives us back worthless bits of paper as welfare cheques. Like a giant game of Monopoly.

"How come I can buy a kilo of apples with one of those bits of paper?"

Somebody gives you something of value in exchange for them. When nobody does, they quickly lose value, like the Continental Dollar did.

[Jussi]

"I guess what I really want is a GFTPL (Generalised FTPL.) This would cover models where there is no government, rather just a pair of households."

I think the question can and should be first thought in the most simple setup. Having two parties and some monetary contracts (plus their enforcement system) will already create some demand for money. And also it is simply to see that money needs to be backed by real assets to have real convertible value.

I think Brian is correct that money always has the optionality and thus its discounting period is zero days and NPV is the face value. But this tells us nothing about the real value in terms of other stuff.

Money is just a liability which derives its value from a pool of real assets (usually through many layers of financial assets). The pool of asset might be an asset side of a legal entity (like a bank) or just a pool of collateral. Nowadays the biggest asset is usually the future value of currency issuer's tax payments. But going back to two household economy: it can be also the assets pledged against the money used (eg borrower might have pledged some physical assets or future production to secure the loan).

[Min]

Brian Romanch: "I guess what I really want is a GFTPL (Generalised FTPL.) This would cover models where there is no government, rather just a pair of households."

Jussi: "I think the question can and should be first thought in the most simple setup. Having two parties and some monetary contracts (plus their enforcement system) will already create some demand for money. And also it is simply to see that money needs to be backed by real assets to have real convertible value."

Enforcement system = gov't.

As for real assets, it depends on what you mean by real. If social obligations are real liabilities, no problem.

[Jussi]

Min: I would say social obligations are the most basic enforcement system, which allows the economy to create liabilities and (financial) assets. Rule of law is just a set of formalized social conventions.

By real assets I meant something that is (or will be) a factor of production (ie capital goods) or inventory of real goods. In the end of the day a financial asset is just a legal ownership claim on real assets or other financial assets that are linked in the end to real assets (aside of speculative assets like bitcoin). That applies to money as well. I think that is easy to see if we think very simple economy. One might argue that doesn't hold if the economy is complex enough but I do not see what is the critical step after money doesn't need to be backed by real assets anymore?

[Frank Restly]

Nick,

"How come all those bits of paper aren't equally worthless? And we give worthless bits of paper to government at tax time, and it gives us back worthless bits of paper as welfare cheques. Like a giant game of Monopoly."

"How come I can buy a kilo of apples with one of those bits of paper?"

Not sure about the Canadian Government, but:

https://en.wikipedia.org/wiki/Article_One_of_the_United_States_Constitution
Section 8: Powers of Congress

"To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures."

You ask why you can buy a kilo of apples with bits of paper and I would answer for the same reason that you will always get the same amount of apple when you request a kilo (or 2.20 pounds U. S.) of it.

Seriously, that is all you think that a government does (welfare cheques)?

[Denys]

Bank notes are fundamentally different from zero coupon perps. . That seems clear.
A better description of bank notes is that they are securitised government bonds.

Bank notes could be issued by an SPV Which owns only treasuries.