Monday, April 29, 2019

The difference between two colourful bits of rectangular paper

David Andolfatto had a provocative and open-ended tweet a few days back:
We see two coloured pieces of paper, both with an old dead President on it. They each have a face value of $500. Both are issued by a branch of the government, the $500 McKinley banknote (at right) by the Federal Reserve while the $500 Treasury bond (at left) by the Treasury. Both are bearer instrument: anyone can use them.

So why do we bestow one of them the special term "money" while the other is "credit"? I mean, they seem to be pretty much the same, right?

The word money is an awful word. It means so many different things to different people that any debate invoking the term is destined to go off-track within the first fifty characters. So I'm going to try and write this blog post without using the term money. Why are the two instruments that David has tweeted about fundamentally and categorically different from each other?

One of them is the medium of account, the other isn't

Being a veteran of the monetary economics blogosphere, David's tweet immediately made me think of the classical debates between Scott Sumner and Nick Rowe about the the medium-of-exchange vs medium-of-account functions of assets like banknotes and deposits and coins. (For those who don't remember, here are some posts.)

As Scott Sumner would probably say, one of the fundamental differences between the two bits of paper is that the McKinley $500 Federal Reserve note has been adopted as the U.S.'s medium-of- account. The $500 Treasury bond  hasn't.

Basically, if Jack is selling his car for $500, this price is represented by the $500 note (and other sub-denominations like the $50, $20 etc), not a $500 bond. Put differently, the bill is used as the medium for describing the accounting unit, the $. The bond does not have this special status. Now it could be that Jack is willing to accept bonds as payment, but since he doesn't use bonds to describe his sticker prices, he'll have to do some sort of calculation to convert the price into bond terms. When something is the medium of account, the entire language of prices is dictated by that instrument.

So why has society generally settled on using banknotes and not the bonds as our medium of account?

First, let's learn a bit more about the bond in question. The image that David has provided us with isn't actually a bond, it's a bond coupon. A coupon is a small ticket that the bond owner would periodically detach from the larger body of the bond in order to claim interest payments. The full bond would have looked more like this:

This format would have hobbled the bond's usefulness as a medium of exchange. The bond principal of $100 is represented by the largest sheet of paper. Attached to it are a bunch of coupons (worth $1.44 each) that haven't yet been stripped off. To compute the purchasing power of the bond, the $100 principal and all of the coupons would have to be added up. Complicating this summation is the time value of money. A coupon that I can clip off tomorrow is more valuable than the one I can clip off next year.

So if Jack is selling a car, and Jill offers him a $500 Treasury bond rather than a banknote, he'll have to spend a lot more time puzzling out the bond's value. A $500 McKinley note, which pays 0%, is much easier on the brain, and thus less likely to hit some sort of mental accounting barrier. (Larry White wrote a paper on this a while back).

Another hurdle is that there are many vintages of $500 Treasury bonds. A $500 bond that has been issued last year will be worth more than one that has been issued ten years ago and has had most of its coupons  stripped off. Put differently, Treasury bonds are not fungible. Banknotes, on the other hand, don't come in vintages. They are perfectly interchangeable with each other. So in places like stores and markets where trade must occur quickly, banknotes are far more convenient.

Further complicating matters is capital gains tax. Each time the $500 Treasury bond changes hands its owner must go back into their records to find the original price at which they received the bond, compute the profit, and then submit all this information to the tax authority. The $500 note doesn't face a capital gains tax. Better to use hassle-free banknotes, and not taxable bonds, to make one's day-to-day purchases.

Which finally gets us to why notes and not bonds are the medium-of-account. Since banknotes are such a convenient medium of exchange, everyone will have a few on hand. And this makes it convenient to set our prices in terms of notes, not Treasury bonds.

Why is it convenient? Say that Jack were to set the price of the car he is selling at $500, but tells his customers that the sticker price is in terms of Treasury bonds. So the $500 Treasury bond will settle the deal. But which Treasury bond does he mean? As I said earlier, at any point in time there are many vintages of $500 bonds outstanding. The 1945 one? The 1957 one? So confusing!

Jack's customers will all have a few notes in their wallet, having left their bonds locked away at home. But if Jack sets prices in terms of bonds, that means they'll have to make some sort of foreign exchange conversion back to notes in order to determine how many note to pay Jack. What a hassle!

If Jack sets the sticker price in terms of fungible notes he avoids the "vintages problem". And he saves the majority of his customers the annoyance of making a forex conversion from bond terms back into note terms. Since it's better to please customers than anger them, prices tend to be set in terms of the most popular payments instrument. Put differently, the medium-of-account tends to be married to the medium-of-exchange.

Alpha leaders vs beta followers

There is another fundamental difference between the two pieces of paper. Say that the Treasury were to adopt a few small changes to the instruments it issues. It no longer affixes coupons to Treasury bonds. And rather than putting off redemption for a few years, it promises to redeem them on demand with banknotes at any point in time. This new instrument would look exactly like the McKinley note. Without the nuisances of interest calculations, Treasury bond transactions should be just as effortless as the those with Federal Reserve notes.

But a fundamental difference between the two still exists. Since the Treasury promises to redeem the bond with banknotes, the Treasury is effectively pegging the value of the Treasury bond to the value of Federal Reserve notes. However, this isn't a reciprocal relationship. The Federal Reserve doesn't promise to redeem the $500 note with bonds (or with anything for that matter).

This means that the purchasing power of the bond is subservient to that of the banknote. Or as Nick Rowe tweets, "currency is alpha leader, bonds are beta follower."
This has much larger implications for the macroeconomy. In the long-run, the US's price level is set by the alpha leader, the Federal Reserve, not by the beta follower, the Treasury.

The Treasury could remove the peg. Now both instruments would be  0% floating liabilities of the issuer. Without a peg, their market values will slowly diverge depending on the policy of the issuer. For instance, a few years hence the $500 Treasury bond might be worth two $500 Federal Reserve notes. We could imagine that in certain parts of the U.S., custom would dictate a preference for one or the other as a medium of exchange. Or maybe legal tender laws nudge people into using one of them. And so certain regions would set price in terms of Treasury bonds while others will use Federal Reserve notes as the medium of account.

The Treasury's monetary policy would drive the price level in some parts of the U.S., whereas the Fed's monetary policy would drive it in the rest. This would be sort of like the 1860s. Most American states adopted Treasury-issued greenbacks as the medium of exchange during the Civil War, but California kept using gold coins issued by the US Mint. And thus prices in California continued to be described in terms of gold, and held steady, whereas prices in the East inflated as the Treasury printed new notes. (I wrote about this episode here.)

In conclusion...

So in sum, the two instruments in David's tweet are fundamentally and categorically different because one is the medium of account and the other isn't. Treasury bonds just aren't that easy to transact with, so people don't carry them around, and thus shopkeepers don't set sticker prices in terms of Treasury bonds. But even if the Treasury were to modify its bonds to be banknote look-alikes, they are still fundamentally different. Treasury paper is pegged to notes, but not vice versa.

This peg can be severed. But for convenience's sake, one of the two instruments will come to be used as the medium-of-account within certain geographical areas. And thus in its respective area, the issuer of that medium-of-account will dictate monetary policy.

Wednesday, April 17, 2019


The U.S. $10,000 was available till Nixon nixed it in 1969

For the last few years the conversation about cash has been dominated by Ken Rogoff's proposal to remove high-denomination banknotes. In an effort to broaden the discussion, last year I wrote an essay for Cato Unbound about introducing a new U.S. supernote. The value of the current highest denomination note--the $100 bill--has deteriorated over the decades thanks to inflation. Is it time to restore the purchasing power of U.S. cash by bringing out a $1,000 note?

In the same essay I also floated the idea of taxing the supernote. Why a tax? A new $1,000 bill could be used for both good and nefarious purposes. Given that nefarious supernote usage (tax evasion and crime) could impose costs on society, a tax would make up for this by transferring wealth from note users to the rest of us. (I also blogged about the idea of taxing cash here and here). 

Josh Hendrickson, Will Luther, and Jamie McAndrews all had responses. Do read them, as they give a good sense of all the various nuances and complications involved in issuing a supernote and taxing it.


Say we introduce a new supernote worth $1,000. What would Walter, a seasoned drug dealer, think about this new policy? Let's walk through the day-to-day costs that Walter absorbs as an illicit cash user.

Walter makes large value payments using banknotes. He also stores plenty of the stuff. A million dollars worth of $100 notes (i.e. 10,000 notes) takes up a lot of space. But one thousand $1000 bills can be packed into a container a tenth the size. This will make Walter's business much easier to expedite. His costs of counting, transporting, storing, and sorting notes will all drop significantly.

The risk of detection will also be much lower with supernotes. Hiding twenty supernotes in a car is a lot easier than hiding two-hundred $100 notes. Detection by authorities imposes costs on Walter and his associates. Banknotes can be seized under civil asset forfeiture laws. In many cases the police can seize cash on mere suspicion of wrongdoing--they don't even have to charge the owner with a crime.

Example of an asset forfeiture case involving cash [source]

These seizures can be contested by Walter and his associates, but this will involve significant time and legal expenses. There are also non-pecuniary losses associated with detection. If Walter or one of his associates is pulled over for speeding and the cops find a bag full of $100 notes in his car trunk, that may provide law enforcement with information and insight into his network.

Finally, Walter also incurs a "tax" on his cash holdings. Specifically, his cash does not earn interest. If Walter regularly stores $100,000 in cash, and the interest rate is 3%, he is effectively forfeiting around $3,000/year. This loss is the same whether Walter holds his stash in $100 notes or supernotes. Walter's $3000/year loss goes directly to the public. He is providing the rest of us with an interest-free loan, or a subsidy.

Weaving this all together, from Walter's perspective the new supernote is a great product. It reduces his storage & handling costs (S) as well as any costs arising from detection (D), and does so without increasing his taxes (T).

Civil society isn't quite as well off with a supernote. We've provided Walter with a superior means of avoiding detection. Not only does this mean that we've increased the odds of Walter staying out of jail. We've also reduced asset forfeiture revenues. Since law enforcement agencies uses forfeitures to fund their operations, any diminution in this flow means that the rest of us will have to pay higher taxes to compensate.


Why don't we strike a deal with Walter? If supernotes allow him to enjoy lower S and D, why don't we ask for higher T in compensation? Setting a higher T involves an increase in the tax rate on supernotes relative to $100 notes.

One way to do this is to make the supernote depreciate a bit each day. The central bank will buy the note back today for $1000, but tomorrow it will only buy it back at $999.95. This constitutes a 5¢/day transfer from Walter to the public. At a yearly interest rate of 3%, he also loses around 5¢/day in forgone interest. This combination of a capital loss and forgone interest comprise the supernote tax.

Now when Walter and his colleagues switch from using the $100 bill to the supernote, society's decline in forfeiture income is compensated by higher tax income. Even with the higher tax, Walter prefers the supernote to the $100 because he saves enough on S and D to make it worth his while. So everyone wins if we issue a supernote.

Or as Hendrikson says in his response essay:
"the introduction of the supernote is in this instance welfare-improving (given the premise that illegal trade creates a social cost) because it allows policymakers to engineer a transfer from criminals to law-abiding citizens that would not be available otherwise."

There may be some additional improvements in efficiency to be gained by replacing a bad tax--asset forfeiture--with a good one. Having the police directly raise funds by confiscating people's property is ripe for abuse.
By contrast, a supernote tax is automatic, predictable, transparent, and easier to collect.


A supernote would provide at least some benefit to non-criminals. Say that Sarah wants to sell her car for $8000. She may be wary of accepting a check from the buyer, Todd, who she doesn't know. If she provides the car to Todd but his check bounces, then she's out of hand. Cash is a simple way to solve this problem. The moment that cash passes hands from Todd to Sarah, the payment is 100% certain.

Without a supernote, Todd will have to pay for the $8000 car with eighty $100s. Wouldn't it be more cost effective for him to make the payment with just eight $1000s? Less counting is required and the bills easily slip into a wallet. So S is reduced. (Detection, or D, is not a cost that licit users need worry about.)

Unfortunately the imposition of a tax will reduce the supernote's potential for improving the lives of non-criminals like Sarah and Todd. Since the tax raises the cost of the supernote relative to alternatives like the $100 note, many people who would otherwise have consumed the supernote just won't bother. Put differently, the  consumer surplus (for licit users) that is created by the introduction of a taxed supernote will be small than if the supernote was untaxed.

If the tax is set quite high, then usage of supernotes may be entirely confined to criminals. This the sort of monetary future that David Birch would probably say was first described by novelist William Gibson in Count Zero. Cash still exists, but it will have disappeared from polite society.


A taxed supernote is a neat idea, but does it qualify as a "fancy monetary standard" i.e too abstract and academic to inspire confidence? "Fancy" is the word that Irving Fisher's critics used to denigrate his early ideas about price targeting.

Admittedly a taxed supernote doesn't present a very clean user interface. Having a round face value is one of the conveniences of a note. This feature ensures that it can be easily divided into smaller amounts. But the supernote tax means that the face value of the note will very quickly fall to some inconvenient number like $999.33. As McAndrews points out
"...the differential rates of exchange among the different denominations of notes is an inconvenience. The cost of all those calculations required to make change and set different prices based on which note a customer offers must be counted against whatever benefit a tax might achieve."
It might be possible to avoid the rounding problem by finding a different means for assessing the tax. In his paper Taxing Cash, Ilan Benshalom describes a withdrawal tax. This tax would be assessed whenever money is taken out of an ATM or bank teller. However, supernotes will probably circulate for long periods of time without every being deposited, which means the withdrawal tax will rarely be activated.

For now, taxed supernotes are science fiction. But who knows? Irving Fisher's fancy monetary standard was science fiction for decades, but it has slowly become the standard way of doing monetary policy these days.

Wednesday, April 3, 2019

Banknotes in bottles in coal mines

[This is a guest post by Mike Sproul. Mike has posted a few times before to the Moneyess blog.]

“If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coal mines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well tried principles of Laissez Faire to dig the notes up again (the right to do so being obtained, of course, by tendering for leases of the note-bearing territory), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. It would, indeed, be more sensible to build houses and the like; but if there are political and practical difficulties in the way of this, the above would be better than nothing.”

-J.M. Keynes, The General Theory.

Keynes’ ruminations about bank notes and coal mines are a good place to draw a dividing line between classical economists and Keynesians.  In contrast to Keynesian optimism about the coal mine scheme, classical economists tell us that the newly dug-up bank notes will only succeed in causing inflation, while wasting the labor of those who dig up the notes.

Surprisingly, there is some middle ground about burying bank notes. Economists of both stripes generally agree that money shortages cause recessions. If there is not enough money for people to conduct business conveniently, then people are forced to revert to barter or other less efficient means of trade. Trade slows, and productivity suffers.  Some economists will call it a “money shortage”. Others will say “liquidity crisis”, “credit crunch”, “tight money”, “failure of aggregate demand”, and so on. Whatever the terminology, economists have been saying for centuries that money shortages cause recessions.
In the year 1722-3, the Governor and Assembly…thought themselves obliged to take into their serious consideration the distressed circumstances and sufferings of the people, through the extreme want of some kind of currency…These bills being emitted, their effect very sensibly appeared, in giving new life to business, and raising the country in some measure, from its languishing state. (Pennsylvania Assembly to the Board of Trade, 1726. Cited in Brock, 1941, p. 76)
Now we begin to see the middle ground. Both Keynesians and Classicals agree that the coal mine scheme could potentially provide badly needed liquidity and thus end a recession. Once this is agreed, the rest is just dickering over the size of various forces. A Keynesian might think that the misallocation of labor spent digging up bank notes might drag down national production by 5%, but that the notes dug up might lubricate trade enough to boost production by 20%.  A Classical might put the figures at 10% drag and 15% boost.

The backing theory of money gives us a way to clear up some confusion between these two views, and provides a liquidity-based theory of recessions that both Keynesians and Classicals can live with.

The backing theory is summed up in figure 1:

In line (1), the bank (which may be a central bank or a private bank) receives 100 ounces of silver on deposit, and issues $100 of bank notes in exchange. Each dollar note is worth 1 ounce of silver.

In line (2) the bank issues another $200 in exchange for 200 ounces worth (or dollars’ worth) of bonds. The backing theory view is that even though the bank tripled the money supply, the bank also tripled the assets backing that money, so it remains true that $1=1 ounce.

Now suppose that the $300 in circulation is 10% less than the “ideal” quantity of money, and that the economy is therefore in recession. A well-functioning bank would respond to the money shortage by issuing another $30 of bank notes, while getting 30 ounces (or $30) of bonds or other assets in exchange. This open-market purchase of bonds would relieve the money shortage, end the recession, and leave the value of the dollar at $1=1 ounce. The open-market purchase method gives excellent results. Keynesians would not be surprised at this, but Classicals might be surprised that the money injection caused no inflation.

Next, let’s try the bottles-in-coal-mines method. The bank prints $30 of bank notes, places them in bottles, and buries them in coal mines. Workers will waste (at most) $30 worth of labor digging up the notes. The bank gets no new assets as it issues the $30 of bank notes, so the value of the dollar falls by about 10% relative to silver. While there are 10% more dollars in circulation, each dollar is worth 10% less silver. The real value of the aggregate circulating cash is thus unchanged. There is no relief of the money shortage, and so the recession continues. The bottles-in-coal-mines method gives terrible results, just as Classicals would expect. Keynesians might be surprised to see that even in a recession, the money injection still causes inflation and fails to stimulate production.

We can improve on the bottles-in-coal-mines method by following Keynes’ suggestion and issuing bank notes in exchange for houses and such. The bank prints $30 of bank notes and spends them acquiring 30 ounces (or $30) worth of houses. The bank’s assets (including houses) rise in step with its money-issue, so the value of the dollar remains at $1=1 ounce. This method relieves the money shortage, ends the recession, and causes no inflation. Excellent results, and not especially surprising to either Keynesians or Classicals. The problem is that it is not always easy for the bank’s assets to keep up with its money-issue. If the bank had spent its $30 of new notes on houses that were only worth 29 ounces, then money-issue would outrun the bank’s assets, and inflation would result. Overall, it’s safer for the bank to spend its $30 buying bonds than buying houses.

There are many more methods of issuing banknotes, but I’ll mention just one: Print $30 of bank notes and give them away to passers-by outside the bank. Then have the government give $30 of bonds to the bank. The bank’s assets will rise in step with its note issue, so there is no inflation. At the same time, the real money supply rises by 10%, so the money shortage is relieved and the recession ends. Excellent results once again. The only problem is that the government will eventually run out of wealth, and will be unable to help the money-issuing bank’s assets keep up with its money issue.

1) Money shortages cause recessions, and the solution is to issue more money.
2) Issuing new money won’t cause inflation, as long as the new money is adequately backed.
3) It is best to issue new money via conventional open-market purchases of bonds. Failing that, it’s ok to issue new money for houses, or even to give it away, provided the government can cover the give-away. But whatever you do, don’t bury the money in coal mines.