In a couple of tweets to me and J. P. Koning, William Luther pointed out, I think correctly, that the validity of the backward-induction argument in my previous post explaining why bitcoins, or any fiat currency not made acceptable for discharging tax obligations, cannot retain a positive value requires that there be a terminal date after which bitcoins or fiat currency will no longer be accepted in exchange be known with certainty.
But if the terminal date is unknown, the backward-induction argument doesn’t work, because everyone (or at least a sufficient number of people) may assume that there will always be someone else willing to accept their soon-to-be worthless holdings of fiat money in exchange for something valuable. Thus, without a certain terminal date, it is not logically necessary for the value of fiat money to fall to zero immediately, even though everyone realizes that, at some undetermined future time, its value will fall to zero.
In short, the point is that if enough people think that they will be able to unload their holdings of a fundamentally worthless asset on someone more foolish than they are, a pyramid scheme need not collapse quickly, but may operate successfully for a long time. Uncertainty about the terminal date gives people an incentive to gamble on when the moment of truth will arrive. As long as enough people are willing to take the gamble, the pyramid won’t collapse, even if those people know that it sooner or later it will collapse.
Robert Louis Stevenson described the theory quite nicely in a short story, “The Bottle Imp,” which has inspired a philosophic literature concerning the backward induction argument that is known as the “bottle imp paradox,” (further references in the linked wikipedia entry) and the related related “unexpected hanging paradox,” and the “greater fool theory.”
Although Luther’s point is well-taken, it’s not clear to me that, at least on an informal level, my argument about fiat money is without relevance. Even though a zero value for fiat money is logically necessary, a positive value is not assured. The value of fiat money is indeterminate, and the risk of a collapse of value or a hyperinflation is, would indeed be a constant risk for a pure fiat money if there were no other factors, e.g., acceptability for discharging tax liabilities, operating else to support a positive value. Even if a positive value were maintained for a time, a collapse of value could occur quite suddenly; there could well be a tipping point at which a critical mass of people expecting the value to fall to zero could overwhelm the optimism of those expecting the value to remain remain positive causing a convergence of self-fulfilling expectations of a zero value.
But this is where network effects come into the picture to play a stabilizing role. If network effects are very strong, which they certainly are for a medium of exchange in any advanced market economy, there is a powerful lock-in for most people, because almost all transactions taking place in the economy are carried out by way of a direct or indirect transfer of the medium of exchange. Recontracting in terms of an alternative medium of exchange is not only costly for each individual, but would require an unraveling of the existing infrastructure for carrying out these transactions with little chance of replacing it with a new medium-of-exchange-network infrastructure.
Once transactors have been locked in to the existing medium-of-exchange-network infrastructure, the costs of abandoning the existing medium of exchange may be prohibitive, thereby preventing a switch from the existing medium of exchange, even though people realize that there is a high probability that the medium of exchange will eventually lose its value, the costs to each individual of opting out of the medium-of-exchange network being prohibitive as would be the transactions costs of arriving at a voluntary collective shift to some new medium of exchange.
However, it is possible that small countries whose economies are highly integrated with the economies of neighboring countries, are in a better position to switch from to an alternative currency if the likelihood that the currently used medium of exchange will become worthless increases. So the chances of seeing a sudden collapse of an existing medium of exchange are greater in small open economies than in large, relatively self-contained, economies.
Based on the above reasoning suggests the following preliminary conjecture: the probability that a fiat currency that is not acceptable for discharging tax liabilities could retain a positive value would depend on two factors: a) the strength of network effects, and b) the proportion of users of the existing medium of exchange that have occasion to use an alternative medium of exchange in carrying out their routine transactions.
Uneasy Money 
Mainly thinking out loud here:
Even with a certain event, the terminal date cannot be known until it happens (or at least is announced). But the probability of it happening can shift, including dramatically so. If we have no information about which specific time period it is likely to happen in, then it becomes an “infinite game”.
We know the network effects can be surprisingly powerful, from the end runs of actual currencies (think Confederate dollar) and terminal-hyperinflations. Nick Rowe’s point that the store-of-value aspect of money is by far its least significant feature of money is demonstrated by such cases–the use continues even as the value heads towards zero; people compensate by passing it along as quick as possible, not by not using it at all.
How much is bitcoin used as a medium of account? Less than it is used as a medium of exchange I suspect. Having a medium of exchange is useful, having a medium of account is even more so. But both those only work because there are connected lines of users.
Why did the Confederate dollar collapse in value? It was no longer useful for taxes if its issuing state disappears. But so did the political community underpinning it: so perhaps not as clear cut a point about the tax guarantee as it appears. The tax use provides a start-up expectation and potential end-point (the latter being ambiguous, as currencies are often ended with official swap rates to new ones) rather than a specific asset value. (I am not up for the fiscal theory of inflation, as government accepts money but does not in doing so set its output value.)
There turns out to be a non-trivial demand for bitcoins as a substitute for state money. But it is still relatively trivial. So the demand must be for its specific features: demand which is clearly pretty limited. The blockchain provides integrity in an IT-geeky appeal way while it limits supply. So it both is key to the appeal while blocking its wider use.
Even though bitcoin’s exchange value shoots around, it continues to have an exchange value, so is, in at least part, parasitic on the wider money system.
Having a medium of account is really useful. Having a medium of exchange with various features can also be useful. Particularly in a highly taxed-and-officially-observed world.
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I think Bitcoin is absolutely useless as a (commercial) medium of account and fraudulent as a store of value. Its worth now lies in its attractiveness as a libertarian medium of exchange, with that being leveraged by purely speculative option value. If forced to choose, I would model it as an option with zero intrinsic value and an expected 15 year life, trading according to purely technical patterns of speculative frenzy. Over time, its time value will decay and its intrinsic value of zero will win out, with the speculative forces gradually dropping out and moving to other technology platforms and trading ideas. It doesn’t have to go to zero to become irrelevant at some point. It will just languish until it putters out, like a bad stock. I view Bitcoin as the currency equivalent of Bre-X mining stock. Bodies may fly out from helicopters yet. In fact, Bitcoin is nothing more than a purely speculative stock itself with some currency value attached.
I didn’t buy the backward induction argument of your first post. But I do think there is an asymptotic force in play as described.
And while “network effect” may be an important economic idea, I think it is only descriptive of something that is so inherent in the idea of a currency that its relevance is better explained from first principles, without relying on the jargon.
(I’m also surprised you haven’t mentioned medium of account considerations in your two posts.)
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I agree. Except for the role of taxes. Taxes only eliminate the worthless money equilibrium if taxes would be used to make the nominal stock of money zero if it did become worthless, creating an excess demand. Otherwise there’s an equilibrium where people pick up worthless dollars off the floor to pay taxes, and the government hands them back to people as transfers, and they get thrown back on the floor, like any free good with satiation.
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Esperanto: purely the network-phenomenon.
Silver lost fiscal value around 1870, and gold at latest one century later. We do see a kind of halftime, and we also see – even among scholars and central bankers – mixed feelings. Each complex has a real part and an imaginary part; ask your local mathemagician. (Numbers can be complex.)
I see pieces of the puzzle fitting.
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May 7th, 2140 is potential terminal date. At that point the blockchain no longer yields bitcoins as a reward for mining, switching to a fee-only incentive structure. At that point, the cost of accounting for the bitcoin transaction must be carried by one of the parties engaged in the transaction. Currently, miners are rewarded by the system for verifying transactions at no cost to parties (though some platforms may charge a fee to speed up transaction time).
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Lorenzo from Oz – “There turns out to be a non-trivial demand for bitcoins as a substitute for state money. But it is still relatively trivial.”
Not sure I agree with this. Sure people use bitcoin as money but it really isn’t a substitute, at least not in a complete sense. Consider using euros vs using dollars; they are two completely independent currencies in the sense that the use of one as a medium of exchange has little direct correlation to the other. For instance, I could go my entire life and never use a euro for exchange and vice versa.
However, Bitcoin does not have an independent economy. It’s more or less just an ultra-liquid form of cash, particularly whatever fiat currency with which it is exchanged. It’s more of a currency intermediary than an actual currency. I can’t transact in BTC without transacting in dollars, but I can very much do the opposite.
JKH – “I think Bitcoin is absolutely useless as a (commercial) medium of account and fraudulent as a store of value. Its worth now lies in its attractiveness as a libertarian medium of exchange, with that being leveraged by purely speculative option value.”
This. As I’ve stated though, Bitcoin suckles at the teat of fiat currency. You can’t price with it non-relative to fiat, and its short-term and long-run prospect as a store of value is pretty terrible. Whatever perceived advantages as a medium of exchange may be nontrivial but they also aren’t exclusive. If there is a use case that makes it more than niche, it hasn’t been determined yet.
I can’t seem to get around the simple facts that currency use as mediums of exchange boil mostly down to rule of law, convenience, and habit. I also think that its purpose as a unit of account is underrated. Being able to set prices with a currency on which there can be general agreement is a pretty profound factor when you think about it. No one can even conceive of what a Bitcoin independent of fiat currencies would actually be worth in goods and services. I think that is an underrated weakness in it.
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aren’t your points a and b at the end just away of saying that currency is an invention with a social function(s) only one of which is the settlement of tax obligations?
there are social groups which explicitly find value in a currency that can’t be used as settlement of taxes.
I think this is why it is considered one of the risks of ‘bitcoin’ that it will be made illegal.
in other words – governments worry that their value is based on the currency rather than the currency being based on the government’s blessing.
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Nick,
I don’t think the threat of incarceration can be understated. Let’s play your game where people pick up dollars to pay taxes, government pays out that tax revenue in the form of transfers, and people throw that money back on the ground.
Imagine that the government incarcerates anyone that fails to pay taxes.
In a competitive environment – I produce and sell shoes and my neighbor produces and sells shoes, I have a non-zero chance of putting my neighbor in jail (out of business) by picking up more dollars than I need to pay taxes so that my neighbor cannot fulfill his tax obligation.
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These later responses begs the question: what is Bitcoin’s utility. Under what circumstances does it serve as a better money than standard fiat currencies?
As a medium of exchange, Bitcoin shows no particular or acute advantage. As a standard of account, also none. That leaves store of value.
I’m biased against the store of value argument because I personally don’t understand the persistence of either gold or silver as anything other than a math exercise. It makes more sense to view Bitcoin purely as a speculative vehicle. So far, the Chinese have used it as a method for escaping capital controls. OK. What is the long-term prospect for that?
The majority of Bitcoin mining operations are in China and I’m beginning to wonder if Bitcoin is merely a proof-of-concept for the Chinese until they design their own currency. After that, my expectation is for their BTC mining operations to be properly nationalized. Until then, expect Bitcoin’s exchange price to mysteriously remain safely above their marginal price but not more so. But, ultimately, short of a new use case, I expect Bitcoin to tank at some point.
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James,
“These later responses begs the question: what is Bitcoin’s utility. Under what circumstances does it serve as a better money than standard fiat currencies?”
The advantage (if you want to call it that) that Bitcoin has is the block chain record of transactions that is not available in fungible traditional currencies.
The uniqueness of each unit of currency (each block chain is unique) would allow illicit private activity to be tracked more easily as well as providing the public a fuller account of government expenditures and campaign finance.
In addition, I suspect a niche market would be developed for individual pieces of currency that were used by certain people, groups of people, or for certain special events assuming that the transaction histories for each piece of currency were a matter of public record.
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Frank,
Though I was aware of that, the manner in which you presented it was very useful.
This begs a new question: how does Bitcoin leverage this? While I see the benefits of distributed ledger technology in general, how useful is such a record for an everyday medium of exchange, particularly Bitcoin?
At the least Frank, you’ve succinctly pointed out a unique feature in Bitcoin that has the potential to give it some value (fairly certain that David Glasner also pointed it out but in a larger context). But the feature is not unique to Bitcoin, other alt-cryptocurrencies have the same capability or potential for it. And the desirability of such a feature is still questionable.
While it’s apparent that the blockchain itself has enormous potential as a system for storage of value, there’s no evidence that Bitcoin itself as a currency is particularly essential to that function, at least specifically and in its current incarnation.
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Since the value of any currency, including that of metal currencies, is based on network effects, The place to look for its value is in the mathematics of its attractors, that is, in the topology of the differential equations that define the network. There’s also a selection effect. No one is going to use a currency that doesn’t have some modicum of stability. Good money drives out the bad.
That’s why Canadians consider Canadian Tire coupons as good as money. http://www.macleans.ca/society/life/7-surprising-things-bought-with-canadian-tire-money/ Unlike bitcoin, you can buy stuff, like tires, with Canadian Tire coupons. As best I can tell, bitcoin is the new numbered Swiss bank account.. It lets you store and transfer money anonymously. The problem is that so few places accept bitcoin, and, unlike Swiss bank accounts, the bitcoin exchange rate is more volatile as the markets have had less experience with them.
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Kaleberg – “As best I can tell, bitcoin is the new numbered Swiss bank account.. It lets you store and transfer money anonymously.”
Bitcoin is actually pseudonymous. It’s possible to attach transactions directly to a person with some effort. My understanding is that Zcash is truly and unbreakably anonymous but its token limit gives it the same challenges as Bitcoin. If I were going to actually invest in a cryptocurrency, I pick Zcash of Bitcoin. Why? Because in a world of pervasive surveillance, privacy will become scarce.
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James,
“This begs a new question: how does Bitcoin leverage this? While I see the benefits of distributed ledger technology in general, how useful is such a record for an everyday medium of exchange, particularly Bitcoin?”
The benefits of the technology (distributed ledger) extend beyond currency. Think about transferrable loans (mortgages, etc.) and other securities that may have extensive backing paperwork (loan application, credit / employment history, record of current assets, etc.). That paperwork can get lost in the shuffle if the company that originally made the loan / sold the security goes belly up.
But since you asked about the benefits in regard to use as an everyday medium of exchange, I will try to answer.
There is the clean money / dirty money aspect to consider. Clean money (that never used in illicit activities) may have a certain moral appeal to people.
There is the niche aspect of collectible money – that used by your favorite celebrity / sports star / personality.
There is the possibility of floating savings / checking accounts that are not centered on any one bank. This has some intriguing legal and accounting aspects since all deposits (as liabilities) would essentially be removed from a bank’s balance sheet and deposit insurance would disappear with it. Everyone would essentially carry all of their money around on an electronic card / device.
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Frank,
I get distributed ledger tech, my background is actually in IT. My point was that the use cases you just mentioned can’t be facilitated by Bitcoin in its current incarnation. Most of what you mentioned are capabilities that the Federal Reserve wants to implement in a proposed “Fedcoin.”
If the question is “why does Bitcoin have value?”, the answer seems to be the potential afforded by the blockchain but it is not exclusive to Bitcoin. Bitcoin leverages almost none of the blockchain’s capabilities right now. So the question of its value is still that… a question.
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James,
Okay, thanks. I don’t know a whole lot about Bitcoin, it’s inventors (patent holdings, trademark / licensing agreements), or the underlying technology (digital ledgers).
If a central bank did adopt the technology of Bitcoin or some other digital currency, would there be associated royalties / patent infringement concerns?
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Frank,
No, the blockchain is open source. There is no real competitive moat for Bitcoin though its fans claim its “network effects” can’t be surmounted by competitors, which is highly doubtful.
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“That’s why Canadians consider Canadian Tire coupons as good as money. ”
No, Canadians don’t consider Canadian Tire money to be as good as regular money. See: http://jpkoning.blogspot.ca/2016/04/why-hasnt-canadian-tire-money-displaced.html
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JP Koning: Sigh, it sounds like the tire coupon thing was an urban legend. They’re more like trading stamps in that they have a fixed currency relationship, so they are unlike airline miles which have their value subject to the whims of the airlines.
BTW, I just learned why people on Yap Island used those big stones as currency. According to Atlas Obscura, they were limestone. Limestone is not commonly found on little islands in the Pacific. They are usually volcanic, and limestone is an old sedimentary stone. The ones they used for money weighed tons and had to be hauled in by canoe from Palau, 300 miles away. It sounds like they were as good as gold for a while.
http://www.atlasobscura.com/places/rai-stones
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Way OT but I wanted to bring David Glasner’s attention to the following:
Click to access sr541.pdf
“The boom-bust in U.S. house prices has been a fundamental determinant of the recent financial crisis. The securitization process that eventually lead the financial sector to the brink of collapse crucially relied on expectations of ever-increasing house prices. Understanding the causes of these house price dynamics is crucial for preventing a repeat of a similar situation in the future.
Large and widening current account deficits accompanied soaring house prices, especially during the five years before the eruption of the crisis (figure 1). These two variables were perhaps the most discussed indicators of U.S. imbalances (Greenspan, 2005). Interestingly, the negative correlation between house price dynamics and current account balances is not specific to the U.S. but rather a robust global phenomenon, affecting advanced and emerging market economies alike(figure2).1 Countries that witnessed house price boom and substantial external deficits (such as Greece, Iceland, Ireland, Spain and the U.S.) also experienced among the highest degrees of financial turmoil during the crisis.2”
Fascinating. Run a big trade deficit and boom your house prices….leading the Fed to disastrously raise rates?
Huge trade deficits lead to gigantic and unstable house price booms?
Who knew? But I think the mechanism still requires property zoning….
I do not see how the topic of “free trade and big deficits” can be addressed in a vacuum that specifically excludes what happens due to ubiquitous property zoning and the propensity of banks to lend on real estate…..
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David Glasner’s name being bandied about everywhere….
http://www.themoneyillusion.com/?p=32286
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Some might say that Bitcoin might be more appropriately named “Bitchcoin”.
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Apologies for the long lag in my responses to comments. Other activities sometimes get in the way of blogging.
Lorenzo, Good overall summary, but I still see a huge downside risk to holding bitcoins.
JKH, I agree with much of what you say even though it doesn’t exactly agree with Lorenzo’s comment which I also like. I don’t get why you dislike network jargon, but to each his own. What should I have said about “medium of account considerations?”
Nick, Did I say that taxes do more than eliminate the worthless money equilibrium?
Yope, Sorry, but your comment was a bit too cryptic for me to penetrate.
escapedonfoot, No it’s a way of making a conditional prediction in principle about the circumstances under which we might see a fiat currency not acceptable for discharging tax obligations retain a positive value.
Benjamin, Thanks for keeping me well informed.
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