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Counting down to Too Much Fed in 5, 4, 3....

Determinant: what surprised me, as I was writing it, is that my position is somewhat closer to (what I think is) the MMT position than I thought it would be. 5,4,3...

They used gold coins in the "good" old times not because the coins were valuable or pecious but because that made them difficult to counterfeit.

shorter Nick: My imaginary history of money imagines money to have been an asset for most of it's history therefore money should still be thought of as an asset with now corresponding liability.

Nick,

Let's suppose I'm the B of C's magical accountant, I wave my wand, and a $20 bill appears.

I look at it and say "I now have an asset worth $20." Is this right? It seems right to me, I can use that $20 to buy stuff.

Then I say "I need to record it on my books." Do we still agree?

Being an accountant, I say "Everything has to be a double-entry, so to counterbalance my $20 asset, I have to have $20 somewhere else. There are only two possibilities, either liabilities go up by $20 or revenues go up by $20." I wouldn't put it past you to argue that the entire system of double-entry bookkeeping is incorrect, but I'm not sure that this is what you're actually saying here, is it?

I can see the $20 being revenue - and then in the long term being added to the B of C's accumulated surplus or owner's equity. But have no idea why this might matter.

"If we wanted to hold fewer Bank of Canada notes, the Bank of Canada would need to buy them back in order to keep its commitment of 2% inflation."

has exactly zero contradiction with

"If the demand for Bank of Canada notes will never fall, then the present value of a $20 liability at 0% interest that need never be paid off is $0."

The latter just has stronger assumptions!

The philosophical question of "if it's never going to be asked to be repaid, is it still a liability?" seems like a conundrum that applies to any very-long-lived institution that can make financial commitments, not merely central banks, actually. Worth comparing to public companies which never pay dividends, perhaps - are their shares liabilities? I should note that central banks appear to roll-over aggregate commitments rather than actually evade individual commitments.

Funny thing, after posting my last comment I went onto Youtube and this was the first thing recommended to me:

David Mitchell on the recession

It appears that he has a fine and subtle grasp of monetary policy.

Interesting thought experiment. I think that currency is indeed a liability of the central bank, but is more akin to deferred revenue than to debt.

When a private company receives money, but will (or may) have to perform some work in the future in order to earn that money, a liability is registered on the balance sheet. The Bank of Canada may, at some point in the future, exchange its government bonds to buy back outstanding currency in order to keep CPI (or NGDP, should its mandate change) from growing too quickly. Just because the currency is not redeemable on demand does not mean it is not redeemable at all.

Aha, it seems that balance sheet accounting does typically separate liabilities to shareholders into a separate column, so that one has assets = liabilities + equity, with equity being recognized as a funny kind of liability that isn't really like other liabilities.

This is for public businesses, mind you, not central banks, but I don't see why the intuition doesn't generalize.

Didn't Steve Randy Waldman (aka interfluidity) argue that state-issued fiat currency and state-issued debt are both better understood as equity?

@david

Public or private, long lived or short lived, shares aren't liabilities.

"But it wouldn't want to, under any normal circumstances, because people wouldn't want to hold that much 0% interest currency, so this policy would be incompatible with the 2% inflation target."

Probably, but it would be compatible with a -2% inflation target.

Gotcha. :-)

Anton: sounds plausible to me. I wouldn't know if something were gold or not.

Nathan: OK, so where exactly in my imaginary history did gold become a liability of the central bank?

Frances: "I wouldn't put it past you to argue that the entire system of double-entry bookkeeping is incorrect, but I'm not sure that this is what you're actually saying here, is it?"

I'm awfully tempted to answer "yes"!

Instead, the slightly more sober and careful me would answer "The BoC's net worth has just gone up by $20 in nominal terms, and slightly less than that in real terms, depending on the elasticity of the money demand function."

The David Mitchell thing was lovely. God, I'm so out of date with British comedy.

david: I tend to agree. Normally, for a private borrower, even if infinitely lived, the PV of the interest payments, discounted at market interest rates, equal the value of the liabilities. You can't finance a permanent stream of consumption by borrowing. But if I could borrow at sub-market rates of interest, (which central banks can), then I could lend the proceeds and consume the spread. Private banks, unless constrained by competition, could do the same. So could any monopolist.

Neil: OK. Airmiles are a good analogy. Think of them as an interest-free loan. As long as the stock demand for unredeemed airmiles does not fall, the present value of redeeming them is zero. Even if the demand does fall to zero at some future date, the Present value of redeeming them is less than the face value of the liability.


Frances Woolley: "Everything has to be a double-entry, so to counterbalance my $20 asset, I have to have $20 somewhere else. There are only two possibilities, either liabilities go up by $20 or revenues go up by $20."

There is a third possibility: it could be credited to equity...not exactly kosher by any means, but then again the BoC is not your usual firm...which I sometimes think is the point of MMT.

@Neil: "Just because the currency is not redeemable on demand does not mean it is not redeemable at all."
Just because it is not redeemable does not mean that, if need be "prudent and wise men " will abstain from doing what is needed to save the country. ( as said in the Report of the Bank of England on the 1825 Banking crisis, in preparation to the Bank Act of 1844). Everything is redeemable in at least something else.Unless,of course you forget that salvatio populi suprema lex esto...

david: "Didn't Steve Randy Waldman (aka interfluidity) argue that state-issued fiat currency and state-issued debt are both better understood as equity?"

I think he did, and I think that's right. I said something similar myself once. Maybe, for an inflation targeting country, they are more like preferred shares. We can always break the inflation target if we really need to.

Max: if you followed Milton Friedman's Optimum Quantity of Money argument, and had a negative inflation target, so that nominal interest rates on bonds were pushed down to 0%, then seigniorage profits would go to zero, and currency really would be a liability of the central bank, because central banks would have zero net worth.

If the bank of candada is really committed to keeping the price level in canada rising 2%, then the paper money is a liability with a nominal interest rate of 0% and a real interest rate of -2%.

If the demand for currency should fall, then the bank of canada must pay off some of these loans.

If the demand for currency should fall to zero, then it must pay off all of those loans.

Rather than treating the paper money like gold, think the market basket of goods that defines the price level being like gold.

With a gold standard, the paper money is a debt payable in gold. Suppose rather than gold, you use gold and silver. Then gold, silver, and copper, then... a broad bundle of goods.

The paper money is still a debt. It is rather than a broad bundle of goods--the market basket of goods that defines the price level--replaces gold as medium of account.

Treating paper money like gold biases an economist to a base money quantity rule. If the quantity of base money is fixed, or grows at a fixed rate, then it is like paper gold and the government just spends the limited amount. Or, for that matter, if there is an unconstrained monetary authorty that just prints it and spends it, it is just like alchemy.

But if there is a commitment to a fixed price of something, then the paper money is a debt.

If you assume the demand for currency is always growing, for example, if you treat currency like it is the sole type of money, then maybe the debt framing isn't very good.

But this is all wrongheaded.

Of course, I favor a strong commitment to nominal GDP, and oppose prohibition on private issue of banknotes. Put those two things together, and treating paper money like gold--an asset--is wrongheaded, and danger.

A general comment on money and government bonds: central banks like to pretend there is a firewall between base money and government borrowing. In this view, the bond market restrains borrowing by imposing a default risk premium...unless the central bank commits the ultimate sin of 'monetizing' the debt.

In reality, the bond market acts as if government bonds are backed by their respective central banks. The fact that the debt could be monetized means it doesn't need to be. Hence a deflationary recession doesn't cause a default risk premium to appear. Bond holders fear prosperity, not recession.

@Rowe: Wait, if you do think it is equity, then what inspired the post?

"Is this a liability of the Bank of Canada?". They all answered "Yes". And then I said: "No, it's equity, and here's why...?"

"if you followed Milton Friedman's Optimum Quantity of Money argument, and had a negative inflation target, so that nominal interest rates on bonds were pushed down to 0%, then seigniorage profits would go to zero, and currency really would be a liability of the central bank, because central banks would have zero net worth."

This is a slight digression, but I had a revelation recently that currency could be de-monetized. Suppose that currency were auctioned instead of being issued at par. Then it would be essentially a bearer bond, and could trade above face value. No more zero bound!

Paul: "There is a third possibility: it could be credited to equity". Same thing.

Equity = the sum of revenues - expenses over all years.

Add the $20 to revenue and at the end of the fiscal year it gets added to equity.

Well, I was going to say you could call money degenerate debt. ;)

But then I thought, a debt is an obligation. Does the gov't have an obligation wrt the money it issues? Well, yes. If I have some of its money, the gov't is obliged to take it in payment of taxes, fines, and fees. If my tax bill is $600, they won't accept a toilet seat. ;)

Sort of like MMT says, eh?

If a business is not in liquidation, we should account for it as a going concern, and we should value its products at cost until they are delivered to customers. The BoC is a business that produces liquidity services at zero cost. The future liquidity services of your $20 note have not yet been delivered, so we should account for them at cost, which is to say, for balance sheet purposes, we should treat them as if the value were zero. In other words, for liabilities currently on the BoC's balance sheet, we should value them as if we lived in a world where their future liquidity services were worthless. In that world, the BoC would immediately need to shrink the money supply to zero in order to avoid hyperinflation and remain a going concern. It would have to sell all its assets to redeem its liabilities, and the value of the liabilities would thus be equal to the value of whatever assets it needed to sell to redeem them. Therefore, we should value $20 notes on the BoC's balance sheet equal to the value of the assets they can buy. They really are liabilities, because their future services have not yet been delivered, and their value to the BoC as a going concern depends on their ability to yield those future services.

Nick, interesting post. It's true that different liabilities (or promises) impose greater or lesser obligations on their issuers - there is a spectrum involved. For instance, some liabilities provide a first lien on assets, others are junior. Some require interest payments of their issuer while those like currency don't. Some are payable upon demand, others are perpetual. Some liabilities come with sinking funds that guarantee some basement price, peg, or whatnot, while others are fully floating. Obviously an entity wants to issue those liabilities that impose upon them the least constraints: interest free, perpetual, floating, junior liabilities is the ideal. (sounds like stock to me)

Nick, you go to great extents to argue that the side of the liability-spectrum that imposes the least obligations on issuers actually imposes no obligation whatsoever, and therefore should not be labeled as a promise/liability. I'd argue that while they admittedly impose less-binding obligations than your average liability, financial instruments such as paper currency are still on the spectrum of promises/liabilities. The moment some financial instrument loses its character as liability and promises nothing is the point at which it hits 0.

It seems very important to a lot of economists that money be some intrinsically valueless token with no non-monetary uses, including being a liability/promise. Why is that? What wrench does money-as-a-liability throw into the works?

I wonder if there's a political economy explanation. To enter the $20 as equity, it would first have to be shown as revenue for the Bank of Canada. Does the government really want to show the B of C making such large profits?

Base money isn't really a liability of the central bank, but good monetary policy usually involves pretending that it is, e.g. by instituting a nominal GDP or inflation target.

Is there an analogy with monopolies acting competitive, in order to avoid competition?

Goven'ts act as if their currencies are liabilities, in order to avoid the real liability of using someone else's currency?

Willem Buiter: “These monetary (base money) ‘liabilities’ of the central bank are not in any meaningful sense liabilities, because they are irredeemable…..” See:

http://blogs.ft.com/maverecon/2008/03/wanted-tough-love-from-the-central-bank/

@JP, economists want valueless tokens for currency because that's one less superfluous reason not to trade, and economists are all about trading.

The ideal is to have synchronous trading, without the search costs. Those search costs are the reason we decouple things by using asynchronous trades, where money is the buffer. If people start valuing the buffer, they start holding the buffer, which can decrease throughput, leading to recession. It's a pathology of the system that doesn't happen with synchronous trading, and could theoretically be avoided.

jam: "Goven'ts act as if their currencies are liabilities, in order to avoid the real liability of using someone else's currency?"

Spanish Dollars (pieces of eight) circulated freely throughout the American colonies and remained in use well into the 19th century. No problem. :)

An increase in demand for base money is like lending to the central bank, and that's why base money is like a liability. Good monetary policy has the central bank acting like a financial intermediary; it should respond to an increase in demand for its liabilities by increasing its assets. A byproduct of this financial intermediation is an increase in the supply of base money to offset any increase in the demand, and the net effect on aggregate nominal expenditure should be zero.

Base money is only a 'liability' in the very broadest sense of the term. I don't move in circles that use the term frequently, and so perhaps I'm defying convention when saying base money is not really a liability. Whatever. No need to quibble over words. The point is that base money never matures and can never be returned for redemption. Central banks might pay off debts by selling assets, but there are no natural market forces to discipline them otherwise. They are removed from ordinary market feedback by design. To get them to behave as though base money were a liability (in the narrow sense I use the term here), it is necessary to create enforceable rules for central banks to follow, e.g. an inflation target.

moving away from the snide (it was that kind of moment when i first read it), a couple points. First, Gold is an asset with no corresponding liability because it's exists. It's that simple. It has nothing to do with being money. When money is issued by a central bank, no matter what substance it is made of, it is a liability of the central bank. Not the underlying gold. If you melted down the gold, the liability of the central bank shrinks even though the physical asset exists just like when you rip up a dollar bill. It is true that in our modern world (to quote Michael Hudson) central bank money is a "du jure not a de facto liability", but is still a liability. Note that this is true even if we acknowledge that the above history is a fantasy or if we pretend it is the truth.

Nick:

Compare two money-issuing banks: One stands ready to use its assets to buy back its money at par, and if the bank ever shuts down, people who hold its money will have a senior claim to the bank's assets.

The other bank dumps all its assets in the ocean.

Which bank's money will be valuable, and which will be worthless?

Reserve Bank of India on "I promise to pay ...." - (I think even the Bank of England does not answer it well)

What is the meaning of "I promise to pay" clause?

... The obligation on the part of the Bank is to exchange a banknote for coins of an equivalent amount.

So the central bank's liability is to deliver the State's liabilities ;-)

Nice joke about the airbag switches by the way.

"The demand for gold to use as money merely added to that industrial demand and made it even more valuable."

Corollory - which resulted of course in a social utility loss. (Mostly clearly seen during gold rushes.)

Nick,
are you really writing about Greece here?

Bill: suppose I sell a diamond. That diamond is not a liability to me. Suppose I sell the diamond, and also give the buyer a put option to sell it back to me at the same price any time in future. That put option is my liability. But the value of that put option is less than the value of the diamond, because it might not be exercised. Now suppose the strike price of the put option falls at 2% per year. The value of the put option is even less.

(Finance guys: what do you call that put option? American? European? Do there exist put options with strike prices that fall over time? Am I using words right here?)

Max @7.10: I basically agree. I like the bit about bond markets fearing prosperity, not recession. (The Eurozone is of course the exception that proves the rule, because they don't borrow in their own money.)

david: It was JW Mason's post that inspired mine. If money is like equity, it's one that doesn't pay dividends, and may (not must) be re-purchased in share buybacks, but at a falling price over time. It's closer to equity than debt, but still a strange form of equity.

Min: the government, like my supermarket, and my creditors, is happy to take payment in BMO dollars. I'm not even sure if I can pay my taxes in BoC cash. Plus, my taxes are (roughly) indexed for inflation, so you could argue I'm paying in real goods.

Andy: you lost me there. Sorry.

JP: On reflection, I think the "put option" view of the liability that I sketched above is the way to go. I need to work on that perspective. I think I need a little help with it though.

"It seems very important to a lot of economists that money be some intrinsically valueless token with no non-monetary uses, including being a liability/promise. Why is that? What wrench does money-as-a-liability throw into the works?"

Good question. No obvious clear answer springs to the front of my mind. Maybe because it's early ;-)

Frances: Dunno. The way it's done now is that the BoC only records profits as it earns interest on the assets it bought with the $20 note.

Lee: "Base money isn't really a liability of the central bank, but good monetary policy usually involves pretending that it is, e.g. by instituting a nominal GDP or inflation target."

I like that. Yes, that works for me. I need to bring the put option idea together with that.

jam: "Is there an analogy with monopolies acting competitive, in order to avoid competition?

Goven'ts act as if their currencies are liabilities, in order to avoid the real liability of using someone else's currency?"

Maybe. But a government has to really screw up, Zimbabwean-style, to destroy even a crappy currency and letting it get driven out by a competitor.

Ralph: Yep, my views are close to Willem Buiter's on this.

jam: yes on buffer stocks and asynchronous trading. Where (what literature) are you coming from with this perspective, by the way? Anything in particular? Or just a whole line of monetary economics plus your own thoughts?


Frances: I wouldn't put it past you to argue that the entire system of double-entry bookkeeping is incorrect, but I'm not sure that this is what you're actually saying here, is it?

Nick: I'm awfully tempted to answer "yes"!

Go for it, Nick! The US dollar has not been a liability since Nixon broke the link.

Nick: "Frances: Dunno. The way it's done now is that the BoC only records profits as it earns interest on the assets it bought with the $20 note."

Yup, and the seignorage revenue is just buried in general government revenue under 'other' so it's really hard to actually work out how much it is. If it was recorded as revenue of the B of C it might be easier to work out. Or the B of C might be tempted to take the money and use it for something other than buying gov't bonds. The more I think about it, the more it seems that politics rather than economics underlies the decision about which entity the revenue from printing money is attributed to.

Nick:

That's not how a put option works.

The put option writer derives its income from the premium the buyers pays("time value"). For the buyer, the payoff is the max(K-S,0), where K is the strike and S is the spot. It's a kind of insurance policy.

You cannot say "the value of that put option is less than the value of the diamond" because you cannot compare option payoff and the spot price(see above).

"K" cannot fall by %2 as it is fixed by the contract.

Re. base money. When the central bank manufactures base money, it in fact writes receipts on debt paper (usually). So, the receipts possess value inasmuch as the debt paper may. That's why "they" occasionally say that fiat money is backed by debt (debt paper is the CB asset, the receipts are its liability).

Andy Harless has nailed it, IMO.

(Finance guys: what do you call that put option? American? European? Do there exist put options with strike prices that fall over time? Am I using words right here?)

Your option is american by definition, because it can be exercised at any time. There exist many varieties of options with time-varying strike. I am not aware of any special name for an option with declining strikes, perhaps because the structure is not common. The closest match traded in practice might be a bermudan swaption with a declining strike schedule. However, "bermudan" refers to the exercise style rather than the strike (a bermudan option is exercisable on a set of discrete dates. Swaptions are often bermudan because the coupon dates make natural exercise dates. But your option is exercisable continuously, which is american.) Your wording seems fine.

Thanks Phil.

The post on this subject I ought to write next:

1. Lead with that comment from Lee Kelly above.

"Base money isn't really a liability of the central bank, but good monetary policy usually involves pretending that it is, e.g. by instituting a nominal GDP or inflation target."

2. Then say that inflation targeting is like selling an American put option, with a strike price declining at 2% per year, bundled in with the $20 note.

3. Then say that the $20 note is not a liability of the BoC, but the put option attached to it is a liability.

4. Then say something sensible and useful about the value of that put option. That's the hard part for me, despite vjk's attempt to help me above.

OK, let's try this. The critical feature of a liability is not that it has to be repaid but that it has to be serviced. A perpetual bond would still be a liability. (After all, for a 100-year coupon bond with a substantial yield, the present value of the redemption proceeds is approximately zero, but we don't consider it any less of a liability than a shorter maturity bond.) Money is like a perpetual bond that yields liquidity services. As long as the BoC is to continue operations, its money must continue to provide those liquidity services. Rather than servicing its debt with monetary payments, it services its debt with "in kind" payments in the form of liquidity services, and its business model requires that it behave in such a way as to continue providing those services. Of course, if the BoC decides it wants to suspend operations, it has the option of defaulting, and its creditors will recover nothing (i.e., there is no collateral and no recourse), but in so doing it will destroy its business model. In general, neither collateral nor recourse is considered a precondition for a debt's being recognized as a liability. To the extent that we treat the BoC as a going concern, it has an obligation to service its liabilities.

Suppose I sell a car "as is". That car is not a liability to me.

Suppose I sell a car, and write on the bill of sale "If for any reason you are dissatisfied, I will buy back this car no questions asked at the original price any time over the next month". The car is not a liability to me, but the put option is.

It's the same when the BoC sells a $20 note, except the put option lasts indefinitely, has a declining strike price, and has no force in law.

Andy: OK. I think I get it now. But what is the cost to the BoC of providing those "liquidity services"? Mainly: stamp out counterfeiting; don't print too much new money.

I think I prefer my put option perspective.

Mike: If both monies were equally useful as a medium of exchange, and if there was no chance the demand for either would drop in future (or the supply would be increased), the ability of the issuer to use those assets to comply with the put option would be irrelevant.

Nathan: suppose I sold you 1 oz of gold, but at the same time promised to buy it back from you at the same price in future. Then there would be a liability attached to my promise. Same with paper.

Ramanan: there's something similar in Canada. The Mint gets seigniorage from coins. The BoC gets seigniorage from notes. (I ignored coins in this post, to keep it simple). I'm not sure if the BoC is obliged to redeem in coins.

reason: the airbag switches was a deliberate anachronism, just in case somebody missed the "fake" history bit!

Yep, there are two social costs to using gold as money: it means less gold gets used in teeth; all the resources used to dig it up. Adam Smith said something similar IIRC, about how Britain could be better off if it replaced gold with paper and exported the gold.

This wasn't really about Greece, though I think it's relevant.

Arthurian: I should stay away from the temptation to say things too wild!

Frances: the BoC reports its profits on the annual accounts, IIRC. Last time I looked it was $2B annually. Probably more now.

A typical variable strike price option is the cliquet option.

Both swaptions(puttable or callable swaps) which are in 99% of cases fixed strike price options and cliquets are exotics.

If one assumes the vanilla put with varible stike, one has something other in mind than the vanilla put.

One is free of course, given a willing counterparty, to create any sort or crazy contracts (and does).

The traditional view of money as a liability of the central bank comes from thinking of the central bank as a regular bank. Just like how regular banks issue loans and invest in securities, which comprise the bank's assets, the central bank issues loans (as lender of last resort) and buys government securities in open market operations. These are the assets of the central bank. The central bank has two sources of funds to finance its purchases of assets: reserves from private banks, and newly created money. Thus, as the source of financing, money is a liability of the central bank.

It is true that central banks no longer have to exchange money for gold on demand. But money is still redeemable in some sense--its just that it is redeemable for money, and the central can simply "buy" back your money by issuing more money. In that regard the central bank acts as the only legal ponzi scheme--it is exactly the same as a bank who pays out liabilities by borrowing even more.

Nick:

I am not sure whether the option vocabulary clarifies. What is it that the CB obligated to buy from the note holder, even at the strike price 2% lower ?

Why not look at the notes or reserve money as possessing value equivalent to the debt it was exchanged for, at the open public market, as I mentioned above ?

If one assumes that base money possesses such value, then it is easy to understand why it can be used as a medium of exchange, in addition to other functions, by various market players, I think.

May be wrong of course :)

If BoC wanted to redeem in coins, it could but the Mint and BoC are unrelated. BoC redeem in money ( 4 Wilfrid Laurier for one Queen).
We pretend the BoC is a bank by listing his "assets", most of which are CDN gov'ment bonds. Bonds backed by the "full faith and credit of the Crown".
Turtles all the way down.
Why not be honest and stop at the elephant? Because most people, having barely survived the shock of "no gold in the vault, arrgh!" shouldn't be frightened even more by "nothing in the vault arrrrrgggghhhh!"?

I agree with the statement below.

"It is true that central banks no longer have to exchange money for gold on demand."

The notion of the CB being liable towards the note holder is meaningless and antiquated in the direct sense of being obligated to exchange the receipt for gold.

There may be indirect societal "liability" or the "duty of care" in the sense of providing a reliable measuring stick (no counterfeiting) or conducting a sensible monetary policy by manufacturing a proper amount of receipts to enable interbank settlement to proceed smoothly with a desired overnight rate.

re: put options. Didn't you go over that back here?

http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/03/liquidity-and-risk.html

Issuing a security with a put option is just another way of adding a redemption-upon-demand feature to that security.

I'd agree that BoC liabilities have puts attached. Each day banks can "put" BoC liabilities back to the BoC in exchange for bonds held on the BoC's balance sheet at the lower operating band. The BoC promises that the value of the bonds you can put back to the BoC will not fall by more than 3% a year.

Firms can issue puttable stock too, it's rare. But if the stock has its puttability stripped away it remains a security for which the issuer is ultimately liable. It won't lose all its value, just the value of the lost put feature. Likewise the BoC could have its puttability feature stripped - as such it would no longer be redeemed on a daily basis for central bank assets - and it would fall in value by the amount of the loss of the put... but as a financial instrument it would still be worth more than zero as it is still an ultimate liability of the issuer.

Nick,

The perpetual American put on a log-normal asset is classroom problem with a very simple closed form solution as I remember it. The reason it's so simple is that all parameters of the solution must be stationary so the problem reduces to a simple, solvable, ODE instead of a PDE. The usual problem is with a constant boundary but an exponentially declining strike might be a simple change of numeraire. I can try to find it if necessary, but before that, I'm not sure I understand the put model of money.

What exactly does the bearer have the right to exchange $1 for? Is it a diamond minus 2%/year? If so, that doesn't sound like money. It would be if the holder was entitled to receive the target (effectively a real return bond), but she isn't. She's only entitled to diamond minus realized inflation which might be more or less than 2%. The right to exchange two assets at the current market price isn't an option. All I see is a changing dollar/diamond price ratio. (Maybe this is the same thing as vjk is saying.)

BoC can exchange money for money. It can exchange money for bonds.
One is about its role of providing the medium of exchange. The other is about conducting monetary policy. The two roles are very different. Shouldn't they be conducted by different institutions?

Jacques René Giguère: "Turtles all the way down."

:)

I should probably just write the post, get as far as I can with it, then let you guys finish it. You would need to make an assumption about the variance (distribution?) of the demand for base money, instead of making an assumption about the price of base money (which is what's normally done with options), in order to value the put option.

Nick Rowe: "It's the same when the BoC sells a $20 note"

When the BoC sells a $20 note, what does it get in exchange?

Interesting. But I would like to tell a different story.

Once upon a time people had many different heterogeneous claims on each other. I was obliged to offer my daughter in marriage to your son, you were obliged to say prayers for my ancestors, we were both obliged to follow our lord in war, and so on. Also people promised each other pigs and roof repairs and things like that.

Over time, these claims became quantified so that they could be netted out against each other. They also became transferable to third parties. As promises became more general in this way, eventually it became unnecessary for them ever to be settled, since the holder of a liability could more easily get payment by transferring the liability to a third party. You fixed my roof. I promised you a pig. You transferred the claim on the future pig to someone else. When payment time came, I provided 20 bushels of wheat instead. All this required agreement about the respective value of wheat and pigs, and confidence that I would be good for my promises. If these two conditions held, my promise of a pig in the future could circulate widely and be exchanged by other people for all kids of other things. And if the promise of the pig can itself be exchanged for something of value, actually getting the pig can be put off for a long time without anyone minding.

As promises became generalized in this way, it became convenient to set up clearinghouses for them, so that instead of A, B, C, D... having to track their commitments to and from each other, everyone only had promises to and from B. Call B the bank. (So for A to make a promise to C, A would make a promise to B, and B would make an equivalent promise to C. ) This allowed promises to circulate more widely.

Now a second thing has happened during this evolution. The banks stop being passive clearinghouses for promises between third parties and start making promises of their own. Let's say in the old days, C has something A wants, and A has nothing, for the moment, that C wants. Then A makes a promise to give something to C in the future. With the evolution of banks, as above, the promise from A to C now takes the form of two promises, from A to B and from B to C. C is happier to accept B's promise because B is very reliable, and more importantly because -- in part for that reason -- promises from B can be exchanged with third parties. So there's no reason for A and C to reach agreement first, and then "register" their mutual agreement with B. B can just make a generic promise to A, which A can then transfer to C in exchange for whatever A wants. So while promises from B are formally just like promises from anyone else, they are now the only ones that circulate between third parties,so it can be convenient to give them a special name, like "money".

Meanwhile, as it gets easier and easier to get tother people to accept your promises from B in lieu of whatever you owe them, actual delivery from B becomes less urgent. In fact, delivery from B can be delayed indefinitely without creating any problems, as long as you can just transfer your promise from B to someone else when you need a real good or service or to settle an obligation of your own. Promises from B get an ever-increasing share of their value from the fact that other people will accept them. Since it makes no difference how far into the future delivery is deferred, we can reach a point at which B never even expected to make delivery, without anything changing.

Now since there are more than one B type player, these banks also have to make promises to and from each other, and to convert their claims into each others'. So eventually we get a B of the Bs, a bank of the banks. Every relatively closed economic community should have just one. This bank of the banks, while still formally a private entity, then takes on increasing responsibility for maintaining the trustworthiness of the system of promises as a whole. But we may eventually reach a point where the "B of B"'s responsibilities for the system as a whole result in it acquiring a formally public status. And while its promises are formally no different from the other Bs, they may be considered especially trustworthy and circulate exceptionally widely. They are also, of course, what the Bs use to net out promises among each other.

Now once this whole evolution has taken place, the "bank of banks" may find that its strategic place in the system of promises also allows it to play a macroeconomic role. if it can influence the extent to which banks allow other people to make promises, it can influence the demand for real goods and services with the goal of keeping demand at some desirable level. But both logically and chronologically, this role comes after its role in interbank settlement.

Now having told this story of the evolution of central banks, I can ask the same question you did, but from the other direction: When in this history did the liabilities of the central bank cease being liabilities?

My story has the advantage, also, of describing the evolution of money in the real world, not just as it happened in the past, but as it continues to happen today. Short-term Treasury bonds, for example, currently pay no interest. But there is plenty of demand for them, in part because they are extensively used for settling large transactions between financial institutions I short, they are well on their way to being money in every sense. But I don't think you would deny that they also remain liabilities of the federal government?

Without meaning to push the analogy too far, base money is like funny money to a counterfeiter.

Suppose an economy with no central bank. All money is gold coins. Each unit of funny money is, in the broad sense, a liability to the counterfeiter--it might be traced back to him. The counterfeiter can get into trouble if he is found out. It's like the counterfeiter has an implicit inflation target determined by the benefits of additional funny money traded off against the risk of getting caught. As a going concern, so to speak, it's important that the counterfeiter regulate the quantity of funny money in circulation. He can even sell goods and services to get some of the funny money to take it out of circulation, though that's obviously much harder for a counterfeiter than a central bank for logistical reasons.

Is the funny money a liability for the counterfeiter? Kind of. Again, I don't want to quibble over words. Calling base money a liability of the central bank is, at least, misleading. Regular connotations of the word 'liability' imply something quite different. In an accounting sense, base money is recorded as a liability, but in the economic sense it is, at least, a very peculiar kind of liability.

A bit of a mind bender, but very interesting, particularly in that it makes sense. As someone else mentioned, I would suppose that it hasn't been a "true" liability since it was delinked from gold (or any fundamental underlying value other than confidence).

tl;dr of my very long comment above: Our counterfactual economy without central bank money should be one based on private credit, not one based on gold coins.

JP:

"I'd agree that BonkC liabilities have puts attached. Each day banks can "put" BoC liabilities back to the BoC in exchange for bonds "

The CB sells/buys bonds on the open market, not to/from the individual bank in the normal course of business. The bank does not have a right to buy a bond from the CB with the previously issued receipts, thus the bank does not hold a "put" option.

Likewise, a private bearer of the currency note does not have a right to buy a security from the CB.

@Nick: "suppose I sold you 1 oz of gold, but at the same time promised to buy it back from you at the same price in future. Then there would be a liability attached to my promise. Same with paper."

what does that have to do with my comment? My point was that what a liability is represented by doesn't affect how much liabilities a central bank has. The scenario you pose is a different one. Your scenario is a repurchase agreement of gold. There still isn't any liability attached to the gold itself, only to you. It's still an asset with no corresponding liability. just because someone takes a mortgage out to buy a house, doesn't mean the asset exists with a liability. it is a physical structure. you have a liability and the bank has an asset. I actually think we're agreeing on this point.

Nick:

1) Since the demand for money always fluctuates, then money issued by a bank with adequate assets must be valuable, and money issued by a bank with no assets must be worthless.
2) You admit that if the issuing bank uses gold or something similar to buy back its notes, then the notes are a true liability, but if the bank only uses bonds to buy back its notes, then the notes aren't a true liability. As JP observed, you are bending over backwards just to preserve the idea that the money we use is a worthless token. I can see where the money-is-a-liability thing throws a monkey wrench in the works though. Pretty much all of monetary theory would have to be dumped, and textbooks would have to be rewritten.
3) Checking account dollars are like paper dollars now, in that they don't pay interest. All the private banks have to do is keep their checking account dollars out there forever, while earning interest on their loans, and then you'd have to say that even checking account dollars are not a true liability of the issuing bank.

JW: Your blog post has already inspired me to write two. And I'm only just beginning, because I was responding only to a small part of what you wrote!

Let me respond to just a small part of your comment. "Short-term Treasury bonds, for example, currently pay no interest. But there is plenty of demand for them, in part because they are extensively used for settling large transactions between financial institutions I short, they are well on their way to being money in every sense. But I don't think you would deny that they also remain liabilities of the federal government?"

Normally, if I have a liability it means I am poorer than if I didn't. It is a promise that is costly for me to fulfill. If I have a 0% interest loan, and if I can roll it over forever, you might say I have an obligation, but is it a liability? Does it make me poorer? A sustainable Ponzi scheme is net wealth. It's an asset to whoever holds it, and makes them richer, but does it make the issuer poorer?

Currency is a sustainable Ponzi scheme. If those 0% Tbills stay at 0%, (so the nominal interest rate is less than the NGDP growth rate indefinitely, like in Samuelson's Exact consumption Loan model), I would say they would be a sustainable Ponzi scheme too. And I would deny that they are liabilities of the Federal government in any normal sense.

@Nick: exactly. In our modern fiscal system currency is a de jure, not a de facto, liability to the government

Normally, if I have a liability it means I am poorer than if I didn't.

Sure, normally. But lots of things are true normally, but not always, or not by definition. Heavier than air objects don't normally fly. But a 747 is, nonetheless, heavier than air.

The meta issue here, I think, is that you are coming from a tradition that sees the quantity of central bank money as playing a key role in macroeconomic outcomes. So it makes sense that you would look for ways i which central bank money is special. Whereas if moneyness is an attribute that inheres in lots of assets, the vast majority of which are created by private credit transactions, it gets much harder to tell a coherent monetarist story.

Your blog post has already inspired me to write two.

It's funny, isn't it? Write an academic article, you have to practically beg people for feedback. But write a blogpost, and you get a bunch of smart responses immediately. Kind of makes one wonder why bother with other forms of writing at all...

"The CB sells/buys bonds on the open market, not to/from the individual bank in the normal course of business. The bank does not have a right to buy a bond from the CB with the previously issued receipts, thus the bank does not hold a "put" option."

In the BoC's case, it promises to defend the target for the overnight rate. If the rate falls below its target, it'll conduct unlimited open market sales - the BoC calls them SRAs. The result is that, as a bank, you know you can always sell your money back to the bank for bonds via SRAs at some rate below the overnight rate. It's no different than the put option that exists in a gold standard... you know you can put unlimited amounts of gold to the central bank at $x.

"a private bearer of the currency note does not have a right to buy a security from the CB."

Yes. Though a private bearer can sell it to a bank for a deposit, and the bank can put the note back to the BoC in exchange for a central bank deposit. And this deposit can be put back to the BoC for bonds at some price below the overnight rate.

JW: "Kind of makes one wonder why bother with other forms of writing at all..."

I'm tenured, getting on in years, less ambitious than I was as a young guy, thinking of retirement, so I can afford to say "why indeed!" ;-)

I see money (the medium/media of exchange) as being crucially important in macroeconomic outcomes. And if you start from that perspective, you look around for the policy lever that is most influential, and that's the central bank, given the current institutional structure. There might be other institutional structures, including better ones. There's room for "blue sky money" thinking too. But we can't wait for that to reach fruition. We drive the car we've got as best we can in the meantime.

JP:

"It's no different than the put option that exists in a gold standard... you know you can put unlimited amounts of gold to the central bank at $x"

I disagree.

An American put option gives the holder the unconditional contractual right to exercise it *any* time he wants.

The bank cannot clearly do the same. It is fully dependent on the CB willing to sell the bond, the bank is a completely passive reactor, not an active actor, it cannot initiate the bond buy from the CB.

Thus, the point of view the that there is a put option attached to the note does not hold. There is simply no contractual obligation for the CB to accept your currency note/or bank reserves for a bond in exchange.

Just thinking some more. I've decided that I disagree the with the "put option" analogy.

Money itself remains a liability. It's a bit more straightforward to see how it's ultimately a liability of the government, which agrees to accept it in return for government services, or for taxes owed. (instead of "IOU one passport," they have instead sent out $120, which I can collect and return to them in exchange for a passport). This looks at the government and it's wholly owned subsidiaries as being a single entity, which isn't unreasonable (other complex organizations are required to consolidate their own balance sheets and financials with any subsidiary in which they have a controlling interest.)

Even if you want to separate the Bank from the rest of the government, the government is able to do this because they can then deposit that money with the Bank of Canada, which accepts it at face value, and agrees that turning it in to them means they in turn owe it back to the government. We wouldn't think too much of this with a commercial bank, but when you're the central bank, it's a bit different because it's something you created in the first place.

If the bank was selling, and had no further obligations in relation to that money, why are they now accepting it at face value?

Non-exchange traded options can come with all sorts of conditions. They can have limited windows, vesting periods, and such. The option the central bank provides a deposit holder is not free from limitations - it has conditions attached to it. But it still provides a deposit holder with an option to sell a deposit to the BoC at certain times and prices.

I agree there is no contractual obligation for a central bank to allow the option be exercised. But some sort of obligation is implied by the evolution and structure of the system. The BoC *has* to initiate SRAs if the overnight rate falls below its target if it is to maintain the integrity of the present system, and banks know this. So if such a situation arises, the banks know they have the option to participate in an SRA and sell deposits for bonds. That option, conditional though it may be, must have some value.

Nick Rowe
"Yep, there are two social costs to using gold as money: it means less gold gets used in teeth; all the resources used to dig it up. Adam Smith said something similar IIRC, about how Britain could be better off if it replaced gold with paper and exported the gold."

Careful, you'll have the gold bugs going nuts before you know it. Gold is the solution to life the universe and everything - didn't you know?


Sovereign fiat money is not a liability, because the holders cannot compel the sovereign which has a monoply over its currency.

Fiat money is an equity, redeemable for relief of state taxation, whose value is a fine balancing act between confidence and compulsion.

Isn't the case that damaged bills (and they all will be damaged or retired) are returned to the BOC by banks? In such a context, the 20$ note is a liability (will have to be replaced by another one when it comes back damaged) and revenue is booked when this happens as the BOC has been generating interest income on the asset side.

Are coins debt? A $1 coin today serves exactly the same way as a $1 bill.

'Twas not always so. In the gold standard era a $1 bill was a liability *and* a debt because it was a promise to deliver a $1 gold coin. But with the elimination of the gold standard and that promise, the $1 bill became the "base" so to speak, and stepped into the role of the coin. ISTM bills now logically should be accounted for as coins, as there is no meaningful difference between them in this regard.

This means they would not be a "debt", as they do not represent a claim of any sort, while their manufacture would be a cost and whatever is received for would be revenue. With the Federal Reserve Banks being corporations (I'm in the USA) the net revenue over cost would be profit and add to their equity, as others have said.

Instead, the gold standard era accounting method for paper money continued onward after nation went off the gold standard as a matter of historical contingency, bureaucratic inertia, path dependence, sloth, whatever.

Of course, equity *is* a liability on the corporate balance sheet -- it is just not a debt. Not all accounting liabilities are debt. So the liability would stay on the balance sheet, but on a different line.

Which brings up another existential question: What does it *mean* to talk about the "equity" of a central bank? Certainly not the same thing as the equity of business.

And a political practicality: If voters were told the central bank was reaping vast "profits" for itself by printing money (especially in a Great Recession) what would they think? In a lot cases I imagine it would be "Yikes!" or a lot worse.

An interesting historical fact: after the German hyperinflation, the German fovernment could quadruple the amount of 'hot money' - without inflationary pressions. I should restate this: the German Central Bank could not do anything else than quadrupling the amount of money, as people wanted to rebuild their cash balances, which enabled monetary financing of the Weimar Republic.

In more or less the same way, a government can issue T-bills, instead of paper money, if people want them. Bills have te be redeemed and carry interest, unlike money. However, when paper money is badly damaged - the government is still obliged to change it into a new note. It has to be redeemed - and does carry interest, 0% to be precise. In that sense it's still a debt.

Keynes wrote about this, in the twenties, by the way, I owe the comparison to his writing but didn't manage to find the exact quote at short notice.

The fact that a liability can decrease in value doesn't mean it isn't a liability.

Currency is just subject to rather precipitous declines, like hyperinflation. Sort of like insurance doesn't pay off, until it does, and generates a big payout. Currency is insurance: You pay the premium (inflation) to hold a widely pooled asset that declines only relatively predictably across the whole economy. That would explain why currencies continue to work even during sustained periods of inflation as long as it's *PREDICTABLE* ... 25% /year is a high insurance premium but may be better than holding less "tenderable" assets in such a volatile economy.

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