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.
Worthwhile Canadian Initiative 
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.
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:
Click to access cochrane_stock_as_money.pdf
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.
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.
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.
Eric: monetary instruments are also immediately redeemable in goods and services, the ultimate definition of liquidity.
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”.
Aha – I should point now to the excellent Cameron Murray http://www.fresheconomicthinking.com/ .
Money is an OPTION not a bond.
Brian Romanchuk’s “put option” and the author’s “liquidity demand” seem like the same thing to me.
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)
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 ?
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.
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.
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.
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
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.
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.
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).
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.
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.
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?
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.
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).
If you want to relate to real goods, then it seems the following formula is quite peculiar:
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.
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.
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..
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.
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.
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?
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)
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.
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.
@ 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!
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.
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.
@ 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.
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.
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.
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]?
@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.
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.
“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.
Thank you, Nick. That clarifies the relationship nicely.
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).
@ 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.
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
@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.
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”.
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.)