Bitcoin and the No-Arbitrage Condition

One of my favorite aspects of the Bitcoin phenomenon is that it has people talking about monetary economics and finance. Just as recessions tend to produce advances in academic macroeconomics, Bitcoin is forcing a wide cast of characters, from libertarian nerds to economic journalists, to think more deeply than they otherwise would about money and monetary institutions.

Nevertheless, monetary economics can be difficult, and there is a lot of confusion out there. It seems that most of the confusion is due to two errors. The first is that Bitcoin appreciation is deflationary, and therefore, recessionary. A variant is that Bitcoin volatility will create massive booms and busts in the Bitcoin economy. I think that this point has been decisively refuted by Jerry Brito. The macroeconomic effects of a currency have to do with its unit-of-account status, not with its medium-of-exchange status. Consequently, unless people begin (foolishly) denominating their long-term contracts in Bitcoin, the cryptocurrency won’t have any macroeconomic drawbacks.

As Bitcoin skeptics have come to terms with Jerry’s point, they have resorted to a second error, that Bitcoin’s long-run fixed supply would generate persistent, long-run deflation, which will cause hoarding of the currency. This would make it unsuitable as a medium of exchange, because no one would be willing to exchange it. Transactional demand for Bitcoin would be zero. Matt Yglesias and Matt O’Brien make versions of this argument.

I think that Tim Lee has done a good job of refuting this line of thinking both on Twitter and in two posts at Forbes. But his arguments haven’t satisfied everyone. O’Brien in particular seems to be doubling down on Twitter.

The problem is that in Yglesias’s and O’Brien’s posts on Bitcoin, I have not come across the word “arbitrage.” This is a pretty good sign that their claims about the long-run equilibrium are not rigorous. The long-run equilibrium must be defined by a “no arbitrage” condition—if arbitrage between currencies is possible, then we are not in equilibrium.

Let’s try to write down an equation that describes a first approximation of this condition:

$1 + i_\ = \dfrac{E_t(S_{t+k})}{S_t} - \pi_\sigma - \pi_l$

At a high level, this equation says that the expected return to holding dollars has to equal the risk- and liquidity-adjusted expected return to holding bitcoins. On the left side of the equation is the return to holding dollars, which is given by the nominal interest rate on dollars, $i_\$. On the right side of the equation, $\frac{E_t(S_{t+k})}{S_t}$ represents the expected appreciation in bitcoins from time t to time t + k, while $\pi_\sigma$ is the risk premium and $\pi_l$ is the liquidity premium. I am assuming for now that it is not possible to have a bitcoin-denominated loan, and therefore no interest rate on bitcoins, although I could imagine that there might be an overnight rate of some sort. But for now, assume that the equalization of returns has to happen via appreciation.

What this equation makes clear is that there is no free lunch from hoarding bitcoins. Bitcoin hoarders will be compensated for the risk they are bearing, for the illiquidity of the Bitcoin market, and for the opportunity cost of holding bitcoins, but for nothing else.

The fact that bitcoins are expected to appreciate in value does not increase the incentive to hoard bitcoins at the margin. Instead, all of the change in the value of bitcoins happens in the spot rate, $S_t$. The price of bitcoins adjusts now to accommodate any future expected increase in the value of bitcoins, and there are no further gains from hoarding bitcoins. There is therefore no disincentive to transactional use of bitcoins.

I expect further that in the future, forward contracts on the Bitcoin-dollar exchange rate will reduce or eliminate the risk premium, and more sophisticated entrants (read: hedge funds) into the Bitcoin market will supply additional liquidity, making even the nominal return to holding bitcoins about the same as that of holding other currencies. The model above is not meant to be a complete account of the market for bitcoins. But I think it serves as a good baseline for thinking about what claims about an incentive to hoard entail.

Finally, I’ll note that even if almost all of the eventual 21 million bitcoins are “hoarded,” a mere 1000 bitcoins would be more than adequate to supply the transactional needs of an economy as large as the United States. Each bitcoin is divisible into 10^8 “satoshis,” and there are only around 10^9 dollars, or 10^11 cents, in circulation. One thousand bitcoins would be 10^11 satoshis. If each satoshi equalled one cent, the market capitalization of bitcoin would have to rise to 2.1 quadrillion dollars. When the market capitalization exceeds that figure, I will concede that bitcoins have been over-hoarded.

The Utopia of Infinite Elasticity

In 1993, James Carville famously said, “I used to think if there was reincarnation, I wanted to come back as the president or the pope or a .400 baseball hitter. But now I want to come back as the bond market. You can intimidate everybody.” Even if your goal is not to intimidate people, it is undeniable that bond markets have a lot of power. If bond markets express their displeasure with the state of a government’s budget, it matters little in the long run how big that government’s army is; financial repression does not work forever, and at some point the government’s spending will decrease.

It’s tempting to think that the bond market is powerful because of corruption, but that is at most a proximate source of power. The real source of power is elasticity. The supply of financial capital is highly elastic; it moves around the globe in milliseconds. Try to tax it and the incidence of the tax will go elsewhere; burden it with regulations and it will flea to a more hospitable climate.

Imagine a world in which all factors of production were as mobile and elastic as financial capital. If labor and physical capital could flea instantaneously and at low cost from bad policies, there would be little danger from either the predatory or incompetent state. In short, it would be a libertarian utopia.

This utopia seems hard to realize. It’s hard to believe that labor and physical capital could ever be as elastic as financial capital is today. Nevertheless, I think this framework provides a way forward for libertarians who have given up on political reform (and maybe even those who haven’t yet). Even if we can’t make the supply of most factors of production infinitely elastic, maybe we can make their supply more elastic. To the extent we succeed, we reduce the power of governments around the world.

Here are a few ideas for building a more libertarian world through higher elasticity:

1. Labor would be more internationally mobile if there were no language barriers. Consequently, libertarians should (without coercion) support the removal of barriers to language standardization. In practice, this means subsidizing English, which is already the globally dominant language of business and science. As a libertarian, I obviously do not support forcing anyone who does not wish to use English to learn it, but Rosetta Stone’s market capitalization is only around $150 million as of this writing. It should take only a fraction of that amount to induce it to release the English version of its language learning software for free. Alternatively, other methods of learning English could be developed on an open-source basis. Because language has network externalities, this endeavor would not only improve the wellbeing of those who would learn English, it would help those who already know English by giving them more exit options. 2. We need better and more secure options for telecommuting and for being paid for work. In particular, it would be very good if people could telecommute across legal jurisdictions without the government in the jurisdiction in which they reside being aware of it. It’s hard to imagine how the modern state could be as redistributive as it is without income tax withholding. If people who live in the US, say, could work in a jurisdiction that does not have income tax withholding and be paid covertly, the power of the US government to tax would be greatly diminished. And if workers could shop around between jurisdictions in which to work, the governments in which the firms were located would be forced to adopt efficient policies to attract economic activity. Consequently, libertarians should support an Internet infrastructure that is decentralized, encrypted, and hard to tap, and a payments system that is hard to track, such as Bitcoin or some successor that operates along similar principles. 3. Almost all factors of production would be more elastic if we could open up new frontiers. Libertarians are excited about seasteading and space colonization. I am not so sure that they will be feasible in the medium term, but I do hope they succeed. 4. As I argued in a previous post, there are more mobile forms of physical capital in development, and these would serve to limit the amount of control the state can exercise. 3D printers are more mobile and elastic than assembly lines, and solar power is more mobile than the electricity grid. Science fiction has even better examples; witness the (Seed-driven) matter compiler in The Diamond Age or Mr. Fusion from Back to the Future. I’m not sure what other options there are. Maybe commenters or other bloggers will weigh in. But if I were Peter Thiel or a Koch brother, something like this framework would guide my philanthropy. Libertarian ideas will never be popular; this is how we can create a better society anyway. No, we’ll never get to the utopia of infinite elasticity, but the land of pretty high elasticity is not such a bad place to live. What Would Stateless Internet Courts Be Like? Last year I wrote that there are benefits to operating a business that is subject to state law. As Schelling says, the right to be sued is the power to make a promise. Increasingly, however, there seems to be interest in running profit-making internet ventures that are immune to state control. There may be a market, therefore, for a private court that accommodates such activity. In this post, I’ll present an outline of what such a court might be like. There are a number of private arbitration firms in the world, but in general they are not suited to deal with stateless actors, particularly those who wish to avoid state control altogether. First, they themselves rely on state law to a large extent. Firms who go to arbitration often do so because their contracts prescribe arbitration; these contracts are the ordinary state-enforceable sort. Because state law casts its shadow on private arbitration (and the disputing firms prefer it), judgments are typically secret. The secrecy of judgments creates problems. Secret judgments increase the incentive for lazy arbitrators to split the difference, rather than search for actual fault. Recently, in order to combat difference-splitting, arbitrators have relied increasingly on American-style procedural rules, which has increased the cost of arbitration and eroded one of the major benefits of private adjudication, its lower cost. Second, private arbitration firms to my knowledge are not typically prepared to accept disputes between pseudonymous parties. Firms on the internet who seek to avoid state control must use pseudonyms; otherwise states would be able to track them down and interfere with their businesses. It’s imperative that the arbitration firm or court not have access to any concealed real identities of the parties. Otherwise if the identity of the arbitrator is discovered, the government could extract the real identities and prosecute accordingly. Since a private internet court must attract business without the machinery of the state, most of its rulings would need to be public. It would want to develop a reputation as a truth- and fairness-seeking body. Its opinions would need to be clear, well-reasoned, and principled. Past rulings would serve effectively as advertisements to bring in future business. It could occasionally offer secret proceedings if both parties publicly agreed to be bound by them, but in equilibrium, these would cost more since they could not be used as advertisements. Since the court could not rely on the state to enforce its rulings, it would need to maintain a publicly accessible database of the compliance of defendants with its rulings. Market participants should be able to query the database with the pseudonym, trade name, or public encryption key of any online business and be able to see immediately whether that entity is out of compliance with the court’s ruling, and if the proceedings were public, the evidence and explanation of the ruling. To bring a case, a plaintiff would have to pay the court’s fee up front. If the plaintiff won his case, the defendant could be ordered to reimburse the plaintiff for this fee. This ensures that the court always gets paid, and it is the only system I can think of that is fully compatible with the purely voluntary nature of the trial. What if the defendant declines to participate in the trial? The court cannot force him to participate, but this is less of a problem than it at first seems. The court still has an incentive to supply a fair ruling (which, again, will be publicly verifiable). If it does not, then its database of out-of-compliance defendants becomes worthless. No one will pay attention to a database of people that plaintiffs sued in a corrupt court. For the database to have value, it must at least correlate with fair rulings. Once one private internet court gets started, it will likely face competition. Courts will compete on fees and reputation for fairness. This will generate a search for efficient rules of civil procedure: what rules of procedure make the optimal tradeoff between cost and information? My intuition is that for the kinds of cases we’re discussing, the rules will need to be very low cost. Since the enforcement mechanism relies entirely on reputation, and firms can always “declare bankruptcy” on their reputation and start over, the cases that will be brought will be relatively small, at least at first. Therefore, the cost of litigation must be low enough to make adjudication worthwhile. I would expect there to be no discovery, which is very costly. In equilibrium, private courts would probably receive a complaint from a plaintiff and a response from the defendant, and then have the opportunity to question both parties. It would then issue a judgment. While the scenario I have sketched above may seem far-fetched, there are lots of parallels between it and the actual development of merchant law and Anglo-American common law. Early courts in these traditions had little power to enforce their rulings. They also faced competition from other courts, and issued public rulings in order to establish reputations for fairness and efficiency. If Bitcoin can get past its recent struggles (1, 2, 3, 4), or if some successor medium of exchange is more successful, then demand for state-free adjudication may increase. I’m not ready to abandon my current career plans yet, but given my academic interest in private governance, the internet, and law and economics, I’m willing to hear cases on an ad hoc basis. If you think you’ve been ripped off by a merchant on Silk Road, get in touch. I’m ready to claim universal jurisdiction. Hail Neal Stephenson! *Snow Crash* Comes to Life Via Roderick Long, this New York Times article documents the fascinating case of Gurgaon, a quasi-anarchic city of 1.5 million people in India. While the city is subject to state and national law, there is no municipal government to speak of. Services are provided by an archipelago of private communities. In between the private communities there are miserable slums (this is India, after all), but life inside the communities is good. Alex Tabarrok also has a good post offering commentary with which I largely agree. See also The Voluntary City, coedited by Tabarrok. As I read about Gurgaon, I could not help but think of Neal Stephenson’s 1992 postcyberpunk novel Snow Crash (Kindle version). Snow Crash envisions a future in which most people live in sovereign gated communities called burbclaves, or in the big business version of the same, franchises like Mr. Lee’s Greater Hong Kong. The US government still exists, it just has no power and little territory. Gurgaon is on its way. Builders of the private communities there, such as Tata Housing, have properties in other Indian cities. This is a lot like the franchising that Stephenson imagined. There are other parallels between Snow Crash and reality. In the novel, the US government has gone bankrupt and had to resort to hyperinflation—quadrillion dollar bills circulate, alongside private currencies. The private currencies in Stephenson’s world are issued by popular franchise communities; they are not decentralized peer-to-peer currencies like Bitcoin. Nevertheless, it seems that a number of governments around the world are in the process of bankrupting themselves through overreach and dysfunctional politics. We may all learn more about private currencies in the near future. In the novel, there is a flourishing private intelligence industry. Several of the characters are freelance intelligence gatherers for the CIC, the private commercial successor to the CIA. So far, the analogous real-world “private intelligence” organizations like Wikileaks and Anonymous are non-profit, but can for-profit variants be far behind? Or maybe Google is the CIC. Google Earth, for instance, resembles software described in the book, and it has long been alleged that Google has CIA ties. Finally, there is The Raft, a flotilla of thousands of boats fastened to a former aircraft carrier and each other that functions as a floating city. Seasteading anyone? N.b. that an actual Raft as described in the book would not work. The chop of the ocean would cause the boats to smash each other to bits. So a seastead is the closest possible real-world analog of this element of the novel. Are there other ways in which Snow Crash is coming to life? Readers are advised that although this post did not contain major spoilers, commenters may need to reference important plot elements to add to the analogy. If you haven’t yet read Snow Crash, beware, and remedy that problem soon. Can the War on Drugs Bootstrap Bitcoin? A few weeks after my last post on Bitcoin, the cryptocurrency was featured on EconTalk. From there it captured the imaginations of libertarian geeks everywhere. When I last wrote about it on March 12, one Bitcoin was worth 88 cents; today one is worth$17.14. There are now numerous startups dedicated to serving as Bitcoin exchanges, banks, e-wallets, etc. Notably, there are not yet any futures markets, which has led many commentators to quite reasonably cry bubble.

There is a sense in which all fiat currencies are based on bubbles. After all, by definition fiat currencies have no intrinsic value; they are valuable because they are liquid, and they are liquid because they are valuable. This circular reasoning is not far from the information cascades that economists discuss in the context of bubbles.

Let’s call the process by which a currency comes to circulate as a widely-accepted medium of exchange “bootstrapping.” For fiat currencies, bootstrapping typically involves some coercion: the government demands that taxes be paid in its fiat currency, which creates demand for the currency. If the currency has other properties that make it useful as money—it’s divisible, transportable, and a reasonably good store of value—then this coercion is enough to make the currency widely-accepted for non-tax payments as well.

Bitcoin does not have a sponsoring government that demands Bitcoin-denominated tax payments. But it has something close: the black market. This week Gawker ran a piece describing Silk Road, an online black market where you can buy everything from marijuana to heroin, plus drug lab supplies and small weapons (no WMDs—yet).

Silk Road is only accessible through the encrypted and decentralized Tor network, so I did what any anarcho-curious geek would do. I downloaded and configured Tor and merrily browsed the Silk Road website (link only works if you have Tor running). I can confirm that it is like a candy store for drug users. According to the merchant reviews, the drugs are shipped in vacuum-sealed packages that emit no odor to be detected by the drug-sniffing dogs. Furthermore, each merchant lists the country from which he ships; pick a merchant based in your country and your package won’t have to go through customs, further decreasing the likelihood of detection. Most customers seem very happy with the care taken in shipping as well as the quality of the products they have received.

Nearly all payments on Silk Road are made using Bitcoin. Bitcoin is an excellent fit for the black market because it is pseudonymous—every payment is made from and accepted at a public 33-character address, but users can generate as many addresses as they want to preserve anonymity.

The question remains of whether the quasi-anonymity of Bitcoin is enough to keep the Feds from being able to shut down Silk Road or to make it unsafe to use the site. As Jerry Brito points out, we are now observing a natural experiment on the anonymity of Bitcoin. The hacker group LulzSec has recently undertaken some activities that make it a prime FBI target and solicited donations at a publicly-listed Bitcoin address. Assuming that the address is a real one and not devised to throw the FBI off the scent, we’ll soon know whether the government is able to identify people on the basis of their Bitcoin transactions.

Assume that it turns out to be safe and convenient to use Bitcoin in the black market. This fact may then turn out to be enough to bootstrap Bitcoin. As I wrote above, bootstrapping a fiat currency involves coercion. In this case, that coercion is supplied by governments who enforce the illegality of black market activities. They are coercively creating demand for the currency that is most convenient to use in the black market. Once there is enough demand for Bitcoin for black market purposes, Bitcoin may become more widely-accepted for legitimate transactions, just as the demand for fiat currency that governments create through taxation spills over to non-tax payments.

In the short run, Bitcoin will likely become more widely associated with the black market and therefore demonized. If you want Bitcoin to succeed, you should be OK with this, since it’s pretty much inevitable. Read up on Agorism and counter-economics. The demonization of Bitcoin may make some legitimate users hesitant to adopt the currency. In my view, this is silly. I will happily accept your Bitcoin-denominated tips and donations at 1FMxbQLh2hEoWXgM4GggbSAMoR61iL7zdp.

I am by no means certain that Bitcoin will succeed. The rapid rise in value that it has experienced may in fact be because there is a Bitcoin bubble. This guy is evidence of that. But it’s hard a priori to differentiate between a bubble and the successful bootstrapping of a currency (this is one reason we need Bitcoin futures). However, I am confident that if Bitcoin succeeds, it will be because of the War on Drugs and other policies that increase demand for a quasi-anonymous, internet-transportable currency to engage in online black market activities.

The Economics of Cryptocurrency

Is there a word for serendipitous Wikipedia browsing? Yesterday I started out seeking information on punk music and I ended up discovering Bitcoin, an open source peer-to-peer digital currency. Bitcoin uses strong cryptography and decentralized computing to produce scarcity in the money supply, which grows at a predefined rate that is clearly visible in the source code. Tamper with that growth rate and your software becomes incompatible with the rest of the cloud, and your Bitcoin holdings become valueless. Double-spending is impossible unless at least half the computing power of the cloud is in on the attack against the currency. You can read all the technical details here.

The total supply of Bitcoins is scheduled to grow geometrically and will asymptotically approach 21 million. This means that if the currency becomes successful and its velocity does not accelerate proportionally to its use, we should expect long-run deflation in Bitcoin-denominated prices. Bitcoins are technically divisible to 8 decimal places to accommodate this. Notably, if I am reading the data correctly, Bitcoins have appreciated by a factor of 300 against the dollar in the last year. One Bitcoin is worth around 88 cents as of this writing.

I have a number of questions. Perhaps my readers know some of the answers, or perhaps some enterprising young monetary economist will address some of these in an academic paper (calling Will Luther).

1. Currencies are based on trust, and trust in money is accomplished through scarcity. Bitcoin is cryptographically guaranteed to be scarce since its supply will never exceed 21 million. But there is reason to believe that a perfectly fixed supply is not optimal. If people suffer from money illusion, it is better if prices increase gradually over time. If money has real effects, then it is best if the money supply is countercyclical. These two facts are at least part of why Sumner advocates a fixed NGDP trajectory. Is it possible to create a cryptocurrency that targets NGDP instead of the money supply?
2. If there are competing currencies would we still want any one currency to target NGDP? MV ≡ PT, but notably T only represents transactions denominated in a particular currency. In general, what is the optimal path of the various money supplies when there is more than one currency in use in a given economy? When there are competing currencies, is there less money illusion? Does money continue to have real effects?
3. What are the monetary implications of the fact that governments will probably have difficulty regulating banking in cryptocurrency? Does cryptocurrency provide a test of the legal restrictions theory developed by Fischer Black, Neil Wallace, and others?
4. What if prices come to be denominated in Bitcoin (with its fixed supply), but different media of exchange and settlement are used? How does that change any of the above?
5. In a number of the above scenarios, there may not be much deflation in Bitcoin-denominated prices (since the money supply is not defined, say, under the absence of legal restrictions on financial intermediation). Putting these scenarios aside, if deflation were consistent, then Bitcoins would yield a positive return due to appreciation. Would we see more money hoarding during recessions? Would the world finally see a real liquidity trap? With monetary policy out of the picture, would fiscal policy become necessary? Is crypto-anarchy self-defeating because it requires big government interventions?
6. Decentralization of the currency means that it cannot be debased, but it also means that it cannot be confiscated at an institutional level. What are the political effects of this change?

I suppose I should add that I am not exposed to Bitcoin and am long USD. And by the way, thinking about Bitcoin reminded me of David Friedman’s Future Imperfect, which you may want to read if you enjoyed this post.

Update 4/4/11 — Bitcoin is the subject of today’s EconTalk.