Focal points, and how beta money becomes alpha money

This is my response to Tony Yates' lovely fairy tale about escaping the zero bound.

There is a Nash equilibrium in which each individual tosses a coin to decide which side of the road to drive on that day. But it's not a stable Nash equilibrium, in the old-fashioned sense of "stable". If I switch to always driving right, that creates a positive externality for others who drive right, and a negative externality for others who drive left, so it creates an incentive for others to switch to driving right too. There's a strategic complementarity, that is strong enough in this case to create two "stable" Nash equilibria: one where everyone drives right; and one where everyone drives left.

But how do millions of individuals coordinate on one of those two equilibria? They need some sort of focal point, and that focal point could be almost anything. History is the most plausible focal point. The drivers don't all hit the road at once. If the first to hit the road starts driving right, the others who see him will follow. But a sunspot -- some mere symbol or announcement that is publicly observed by all -- can get them all to switch sides. Like daylight saving time. It becomes a self-fulfilling forecast.

Money is (usually) both medium of exchange and unit of account. The two functions (usually) go together, simply because it's (usually) more convenient to announce prices in terms of the same good that people will actually be using for payment.

Both medium of exchange and unit of account functions have strategic complementarity. Each individual has an incentive to use the same medium of exchange and the same unit of account that others they trade with are using.

In the beginning there is alpha money. Then someone issues an IOU for alpha money. That IOU might itself be used as a medium of exchange, alongside the alpha money, if it is convenient to use it as a medium of exchange. That IOU is beta money, because the issuer of the IOU promises to peg the exchange rate between beta and alpha money by swapping the two monies at a fixed exchange rate in either direction. The issuer of the alpha money makes no such promise. It is that asymmetry in who promises to keep the exchange rate fixed that makes the alpha money the leader and the beta money the follower. The issuer of the alpha money can make his money more valuable or less valuable, and the issuer of the beta money just follows along.

We can observe which of the two monies gets used as medium of exchange. What we cannot observe, while the exchange rate remains fixed, is which of the two is the unit of account.

Suppose over time the beta money (mostly) displaces the alpha money as the medium of exchange. Now suppose the issuer of the beta money announces a 50% devaluation against the alpha money. What is the new focal point for the unit of account function of money? In other words, if prices are sticky, will they be sticky in terms of the old alpha money or in terms of the new beta money?

History is no use as a focal point, because by assumption the exchange rate has always been fixed between the two monies until the announced depreciation, so nobody can tell the difference.

Simple theory suggests that the beta money is likely to become the new unit of account, simply because the unit of account and medium of exchange functions (usually) go together, because it's (usually) more convenient that way for each individual price setter. But the whole point of focal points is that they are self-fulfilling prophecies, so anyone or anything can be a prophet, if enough people believe enough people ... believe he is a prophet. In examples like currency reforms, where the government deletes two zeros off the currency, price-setters likewise delete two zeros off the price tags. Because everyone expects everyone else will do this.

The whole point about focal points and sunspots is that there is no fundamental reason why one equilibrium should be chosen over another.

Tony's post is an extended metaphor about demand deposits replacing paper currency in the same way that paper currency replaced gold. And the consequences of some modern equivalent to e.g. Roosevelt's devaluation of paper dollars against gold. (I love his "cashbugs"!).

In the long run, theory suggests, and history seems to confirm, that the beta money will eventually become the new unit of account, so that beta money becomes the new alpha money for both functions. Because the convenience of using the same thing for both unit of account and medium of exchange is an ongoing force strengthening one focal point over another, and will eventually win out over past practice.

But the best case scenario, for a policy experiment like Roosevelt's, is for a bit of both, at least initially. People expect higher inflation when the beta issuer devalues against alpha, but they don't all jump their prices in terms of beta to neutralise the devaluation.

But the issuer of the alpha money could presumably do exactly the same thing by announcing a new focal point for (e.g.) an NGDP target.

And an announced ongoing crawling peg devaluation of beta in terms of alpha is equivalent to paying negative interest rates on beta.

Comments

[Majromax]

> We can observe which of the two monies gets used as medium of exchange. What we cannot observe, while the exchange rate remains fixed, is which of the two is the unit of account.

Don't we observe just this with ordinary retail transactions, given different kinds of beta money in circulation?

Stores price their wares in dollars, but they accept payment in cash, debit, cheque, and credit (which is beta money from the store's perspective). Each of these payment methods has different associated processing fees, but very few stores try to impose a credit-card surcharge, for example; lately I've seen few stores even have minimum transaction sizes for card-based payment.

> Now suppose the issuer of the beta money announces a 50% devaluation against the alpha money. What is the new focal point for the unit of account function of money? In other words, if prices are sticky, will they be sticky in terms of the old alpha money or in terms of the new beta money?

Alpha money, to the extent that beta money has only a small liquidity premium over alpha money.

You've ignored the store-of-value role of money here, but that's a first-order factor when you contemplate a 50% devaluation. Less serious valuation risks than that led to the seizing of the ABCP market in Canada in the financial crisis, where suddenly the asset went from very-moneylike to not-at-all-moneylike.

[JP Koning]

Good post. Just some scattered thought from me:

"We can observe which of the two monies gets used as medium of exchange. What we cannot observe, while the exchange rate remains fixed, is which of the two is the unit of account."

Riffing on your point, I've argued before that we're already on a credit card dollar standard of sorts, at least in the retail world, and not on a central bank dollar standard. In order to pay onerous credit card fees, shopkeepers mark up all their prices by the size of the fee (and sometimes offer cash discounts). Another way to think of this is that the peg between the sorts of deposits that shopkeepers receive in payment and all other deposits is around 1:0.98. If shopkeepers were allowed to levy a surcharge on credit card use (or if that became standard practice) then they would go back to pricing in terms of central bank dollars. We are sort of in Tony's weird world where the betas can influence the economy's price level, in this case by increasing credit card fees.

"History is no use as a focal point, because by assumption the exchange rate has always been fixed between the two monies until the announced depreciation, so nobody can tell the difference."

A real world example of this problem is Miles Kimball's plan to establish a crawling peg between cash and electronic money in order to be able to get to deeply negative rates. The government needs to be a 'prophet' to ensure that shopkeepers are pricing in electronic money, not cash. If not, deeply negative rates have no effect on the price level. Miles likes to use the analogy to daylight savings:

"Moreover, just as the government can point to an equilibrium for the details of daylight savings time and most people follow the suggested equilibrium in order to coordinate with everyone else, within reason the government can probably determine the unit of account simply by pointing to a particular equilibrium."

https://www.imf.org/external/pubs/ft/wp/2015/wp15224.pdf

[Majromax]

> In order to pay onerous credit card fees, shopkeepers mark up all their prices by the size of the fee (and sometimes offer cash discounts). Another way to think of this is that the peg between the sorts of deposits that shopkeepers receive in payment and all other deposits is around 1:0.98.

That's why I think the MoA is still central bank money. Since shopkeepers don't charge differential prices, they are acting as if they accept the official 1:1 exchange rate even though the unofficial rate is 1:0.98.

As an example with a wider spread, consider a stylized Cuba where officially the peso and USD trade at par, but the black market rate is closer to 2:1. If stores offer the same selection of goods at the same prices for both dollar and peso purchases, then the peso is in fact the unit of account.

Of course, if the true exchange rate differs too much from the official accounting exchange rate, we're in the territory of Gresham's law with bad money driving out good money. That doesn't happen in retail because the unofficial exchange rate is within the liquidity premium of use, but you can see market forces working at the margin with American Express and Discover cards (and their non-universal acceptance).

[Nick Rowe]

JP (and Majro): Ah! As I was writing that bit about observational equivalence of unit of account, I had your post at the back of my mind, and wondered if you would chime on on that point. Suppose the fees on debit cards fell. Which price would stay sticky?

Majro: "You've ignored the store-of-value role of money here, "

Yep. My canoe is a store of value, but I would not list "store of value" as one of the defining functions that makes something a canoe. Did a post on this a couple of years back.

JP: Yep, Miles and I are roughly on the same page here, I think. But people can get terribly confused about this sort of announcement. I am old enough and Brit enough to remember the famous Harold Wilson "Pound in your pocket" speech.

Majro: "As an example with a wider spread, consider a stylized Cuba where officially the peso and USD trade at par, but the black market rate is closer to 2:1. If stores offer the same selection of goods at the same prices for both dollar and peso purchases, then the peso is in fact the unit of account."

I know you said "stylized", but when I was there it shot up to 80:1 IIRC, then stabilised around 20:1 when they opened some markets! There were peso stores (where you could hardly buy anything) and dollar stores. If prices were quoted in pesos, they were nearly always very keen to accept dollars, but would easily accept an unofficial rate.

[Majromax]

@Nick Rowe:

> Suppose the fees on debit cards fell. Which price would stay sticky?

Neither, I think. Since the merchant can't control the mix of payments its customers use, falling fees on debit cards would look like a general reduction of cost-of-sales. Price changes would depend upon elasticities.

If we're talking about sticky prices because of menu costs, then central-bank-prices (the ones on the price stickers) would stay sticky.

> Yep. My canoe is a store of value, but I would not list "store of value" as one of the defining functions that makes something a canoe. Did a post on this a couple of years back.

I'm not thinking of a long-term store of value, but rather a short-term one. The very act of the beta bank changing the exchange rate peg would undermine confidence that it won't happen again, in the same way that the early credit defaults undermined confidence that ABCP would hold its value.

> I know you said "stylized",

It was stylized in part because I couldn't quickly figure out the modern system. Apparently Cuba now has a split between "convertible Pesos" and "nonconvertible Pesos." But your experience with storekeepers being willing to accept an unofficial rate for dollars points to dollars being at least part of the unit of account in Cuba.

[LWest]

Hi Nick,

Not directly related to your main point - but some years ago I was doing a bit of reading on mediaeval money, and I think there was some evidence for the French Crown using a unit of account (livres tournois, if my memory serves) that was not actually issued as a medium of exchange. So taxation liabilities were denominated in the UoA but extinguishing in (one of) the MoE.

Thinking through how this would apply in your model, I think the key difference is that there was no fixed exchange rate between the official UoA and MoE. I believe the exchange rate was more of a crawling peg (which also assisted the Crown in reducing the real burden of its debts).

Obviously, mediaeval monetary systems are of limited consonance with contemporary money - but an interesting sidelight on your post.

[Nick Rowe]

LWest: actually, I think that is very closely related.

I've done a little related reading, but my memory is so totally cr*p and muddled I can't remember any of the details. Isn't the Argentinian(??) Real(?) similar? And Eunadi(??) wrote a book on imaginary monies. Then, in my own UK childhood, auctions were held in Guineas (1 pound 1 shilling) which didn't exist, though did have a fixed exchange rate (my father's theory: the pound was for the seller, and the shilling for the auctioneer).

IIRC, "imaginary" units of account were used when the coinage was a bit of a mess, so each coin had to be inspected to figure out its worth.

This is the sort of topic that JP loves to delve into, and does so well at!

[Henry]

"There is a Nash equilibrium in which each individual tosses a coin to decide which side of the road to drive on that day."

In the 1970s, there was an interesting novel published, The Dice Man by Luke Rhinehart. It gained cult status. The protagonist would every day assign activities to be carried out to one of the six numbers on the die. For instance, today, 1 would be a policeman, 2 would be a minister etc. etc. The activities got out of hand eventually such that activities included rape and bank robbery. Needless to say the protagonist more or less lost his mind. A monetary system based on stochastic market equilibria could in the same way devolve into a spastic non functioning system - I can't see strategic complementarity working. Would it not seem that the "focal points" that are required to make the system work are the "rules of the game" - removing risk and increasing certainty and therefore workability. The "rules of the game" requires an overarching authority accepted by all players. The late 19th century Gold Standard did not emerge from a probabilistic primordial ooze.

[Nick Rowe]

Henry: I remember that book. Read it as a teenager. My God. Suddenly remembered a friend who was enamoured of that book at that time. Couple of years ago a big scandal broke, that he had been up to since about that time! Probably just coincidence.

But that is unrelated to this post. The guy who tosses a coin, when everyone else is doing the same, really is indifferent between driving right and driving left. Same chance of collision either way. That's not the same when everyone else chooses one side.

[Henry]

"That's not the same when everyone else chooses one side."

But that's the point isn't it Nick. What has everybody spontaneously choose one side?

[Jacques René Giguère]

Nick: not some chance of collisions. First chaos. Then paralysys. Then , maybe, slowly emerging order. Like trying to figure out who arrived first at a 4 stop corner.

[Majromax]

@Henry:
> But that's the point isn't it Nick. What has everybody spontaneously choose one side?

Because variance, and because an observation of a random variable is not the same as its expected value.

Because of strategic complementarity, I will choose to drive on the side of my road favoured by the local traffic. Even if the a priori chance of each car driving on the left is 50%, the observed pattern of traffic may be RRLR at this very moment.

If everyone is a strategic thinker, this will quickly lead to sections of road with uniform traffic flow, separated by relatively sharp transition regions if the flow of traffic is opposite elsewhere. (Unlike the development of magnetic domains, there is no large-scale pressure towards 50/50 flow.)

[Oliver]

Wikipedia on right- and left-hand traffic:

The history of the keep-left rule can be tracked back to ancient Greece, Egypt and Rome, and was more widely practised than right-side traffic. Ancient Greeks, Egyptians and Romans adhered to the left side while marching their troops. If two men riding on horseback were to start a fight, each would edge toward the left. Thus, they would be able to draw swords from their right and uphold a defensive position. Eventually, this turned into custom, and later, a law.

...

In the late 18th century, the shift from left to right that took place in countries such as the United States was based on teamsters’ use of large freight wagons pulled by several pairs of horses. The wagons had no driver's seat, so a postilion sat on the left rear horse and held his whip in his right hand. Seated on the left, the driver preferred that other wagons pass him on the left so that he could be sure to keep clear of the wheels of oncoming wagons.[46] He did that by driving on the right side of the road.

[JP Koning]

LWest, if you're interested in medieval monetary systems, read John Munro.

https://www.economics.utoronto.ca/wwwfiles/archives/munro5/MONEYLEC.htm

The phenomenon you're talking about is what Munro labels "ghost monies" The concept is a bit different from the "imaginary money" concept Nick mentions, which envisions a unit of account that is completely dissociated from any real good. In the case of ghost money, people set prices in terms of a coin that has long since ceased to exist. However, a ghost money isn't dissociated real goods since it takes the historical quantity of gold ounces in the expired coin as its fixed point.

Majromax: "Since shopkeepers don't charge differential prices"

But where surcharges are not allowed, shopkeepers *do* charge differential prices by offering cash discounts. It's just that people are too lazy to ask for them, and its only worth asking for at large amounts. You definitely see them at gas stations, for instance:

https://nudges.files.wordpress.com/2008/08/img_2587.jpg

In Australia, where shopkeers are allowed to surcharge, its the inverse. Shopkeepers use cash as the medium of account and then surcharge at the till. See this Australian's comment:

http://jpkoning.blogspot.ca/2015/06/how-monetary-systems-cope-with.html?showComment=1435443530993#c4210161235521739955

[Henry]

@ Majromax

There a great deal of presumption in your explanation?

If everybody tosses the coin everyday, how can there be strategic complementarity? Surely gridlock is the most likely outcome in this circumstance whether we're looking globally or locally?

The a priori chance of vehicles driving left and right might be 50/50, but what is the a priori chance that they will line up together on each side?

Even if everybody is a strategic thinker, it still begs the question, what is it that has those that want to travel in a given direction all choose the one side?

There either has to be some overarching control or some natural, inherent tendency to choose one side. The former will have the coin tossing cease. Even in the latter case there will initially be chaos. How long will it take for a non-entropic order to develop? But what could these natural inherent entropic-behaviour sapping factors be?

[Jacques René Giguère]

Everybody is complaining about credit card fees. Forgetting the stupefying cost of handling, sorting,counting,securing and transporting cash.
My family had a store in the '70's. The joy of counting the cash at the end of the, getting out of the store and going to the local bank. Our town was rather calm and we were never robbed (though we had three hold-up. SOme of our colleagues weren't so lucky.