Are Cryptocurrency Exchange Rates Indeterminate?

Last week, I was chatting with Garett Jones about Bitcoin, and he asked about exchange rate indeterminacy. It’s an issue that Tyler Cowen has raised as well. What is exchange rate indeterminacy? Do cryptocurrencies suffer from it? Here’s my rough sketch of an answer.

The classic paper on exchange rate indeterminacy is by Kareken and Wallace. Suppose, they say, we have two countries, two fiat currencies, no capital controls, and floating exchange rates. Each currency is, in expectation, just as good as the other, since they are both fiat currencies not redeemable for any assets, and some version of interest rate parity holds. Why, they ask, would anyone prefer to hold one currency versus the other? The equilibrium does not need to be the one most commonly assumed in economics, that currency holdings will be split along national borders. Kareken and Wallace show that under these assumptions, there are actually an infinity of equilibria. For any given exchange rate, there is a valid equilibrium in terms of money holdings.

In reality, I don’t think exchange rate indeterminacy holds between fiat currencies. One reason is that economies are still territorial, and therefore optimal currency area considerations still apply. Central banks, it is hoped, adjust the money supply of fiat currencies in an attempt to optimize against the local business cycle. Ex ante, I am somewhat better off holding the money that will respond countercyclically for my actual physical location. In addition, governments still accept and make payments in particular currencies, and this helps bootstrap a local network that prefers to accept those currencies, in part because it is costly to accept multiple currencies.

These modest frictions perhaps explain why exchange rate indeterminacy doesn’t hold between fiat currencies. We can adopt flexible exchange rates and laissez-faire for capital movements without too much trouble, contrary to Kareken and Wallace’s predictions, at least in countries with reasonably competent central banks.

However, those frictions disappear when we’re talking about exchange rates between multiple cryptocurrencies. We have multiple currencies, no capital controls, floating rates, no countercyclical policy (indeed, cryptocurrencies are not generally used as units of account, so they have no macro effects), no government acceptance, and it is super-easy for merchants to accept multiple currencies. Shouldn’t we then expect cryptocurrency exchange rates to be indeterminate?

I’m still working out a full answer, but I’ll start with two points.

1. Fiat currencies are basically all the same—paper money, for instance, has the same basic properties whether it is stamped with Andrew Jackson or Elizabeth Windsor. You can spend, store, and transport it the same way. The major cryptocurrencies, however, tend to have different properties from each other. Bitcoin, for example, is zero-trust, uses a proof-of-work system (SHA256), produces a new block every 10 minutes or so, and so on. Litecoin uses scrypt instead of SHA256 (which is supposed to make in less susceptible to ASIC mining) and produces blocks more often. Ripple is an entirely different beast: users must extend trust, there is no proof-of-work system, and the system can be used to exchange other cryptocurrencies. Ethereum, which hasn’t formally launched yet, uses a totally different mining system, and a much more powerful (Turing-complete) scripting language. And Zerocoin, one of the most interesting prospects, is a lot like Bitcoin, except it features automatic mixing—transactions using Zerocoin are truly anonymous, not just pseudonymous as with Bitcoin.

Since all of these currencies differ along multiple dimensions, the basic Kareken and Wallace observation that all money is basically the same doesn’t really apply to them. If mining collusion turns out to be a big deal, you’re going to want to hold Litecoin instead of Bitcoin. If, on the other hand, bugs turn up in both Litecoin and Bitcoin that require rapid coordination of mining pools, you’d rather hold Bitcoin since the pools are more concentrated. If you value private transactions, you would have greater demand for Zerocoin, whereas if you favor the law enforcement seal of approval, you would rather hold Bitcoin. Because these currencies differ in their technical characteristics, they are not perfect substitutes. That non-substitutability should be able to pin down exchange rates between them.

2. This doesn’t solve the problem of perfect cryptocurrency clones. Suppose that I create a Bitcoin2 network using the Bitcoin source code. I don’t change any of Bitcoin’s technical characteristics, I just launch a new network that is exactly the same. Bitcoin and Bitcoin2 operate in exactly the same way. What pins down the exchange rate between Bitcoin and Bitcoin2?

I think the answer is governance. Bitcoin is developed by a rather competent and conservative group of core developers. They don’t take a lot of stupid risks, they make changes to the core protocol very deliberately, they have responded well to the handful of governance crises that have occurred to date, and the miners seem to trust them. Even if I, as Bitcoin2 lead developer, simply copy their behavior, who is going to trust me in a crisis if I don’t really know what I’m doing? Unless there is some other advantage to using Bitcoin2, which is ruled out by the assumption of identical protocols, then no one is going to use Bitcoin2 when they could simply use Bitcoin.

Cryptocurrencies of a given set of characteristics seem like a winner-take-all market. Once I have decided on the set of characteristics I want in my currency, I am going to choose to hold and use the currency with those characteristics with the best governance institutions and the most competent leaders. Because there are no macro effects or optimal currency area considerations, the network effect for cryptocurrencies may be stronger than it is for fiat money, just as the network effects for credit cards appear to be stronger than those for fiat currencies. If given-characteristic cryptocurrencies really are winner-take-all, then exchange rate indeterminacy will never apply because the major cryptocurrencies in circulation are always going to be imperfectly substitutable.

So my first reaction to the question of exchange rate indeterminacy is that it probably won’t play as much of a role in the economics of cryptocurrency as most economists might imagine. Nevertheless, I am interested in reading analyses that go beyond the above, so if you have or see one, send it my way.

11 replies to “Are Cryptocurrency Exchange Rates Indeterminate?

  1. JP Koning

    “I think the answer is governance. Bitcoin is developed by a rather competent and conservative group of core developers.”

    So if Gavin Anderson and the Bitcoin Foundation start Bitcoin2, then the exchange rate between BTC and BTC2 should be 1:1?

  2. sflicht

    RE: JP Koning’s comment — Interestingly, some have proposed that Gavin Andresen (i.e. the Bitcoin core dev team) should do exactly that, the idea being that Bitcoin2 would be used as a development testbed for introducing new features.The current status quo, where new features are explored in altcoin blockchains and only then implemented in Bitcoin, is supposed to have certain disadvantages, which I don’t recall at the moment, except for the following. Using Bitcoin2 would enable the developers to enforce a 1-way peg between Bitcoin and Bitcoin2 at the protocol level, allowing users to experiment with the new features without bearing FX risk, while protecting the Bitcoin network from the potential adverse effects of a horrible bug in an experimental feature.

    On the other hand, I’m aware of exactly one case in which Bitcoin adopted technology first implemented in an altcoin — namely, Litecoin developers fixed the database error that was causing Bitcoin (and Litecoin) to be unusable on Macs, and their code was then integrated into the main Bitcoin protocol. This seemed to work just fine.

  3. D

    A far more relevant analysis would involve a two-currency system where one currency is fiat and the other is crypto. I wish you would have focused on that instead of the mostly academic questions you indulged in.

  4. Alois k

    “Ex ante, I am somewhat better off holding the money that will respond countercyclically for my actual physical location.”

    Are you sure? I think I would rather be in debt in this currency.

  5. David Rangel


    Interesting post. I’ve enjoyed your blog.

    With regard to this post, I agree that the network effect for cryptocurrencies is stronger than for fiat currencies. In fact, I would go further and say that it is probably *much* stronger. The reason is that cryptocurrencies don’t just have the network effects you see in the 2 comps you mention:
    1) fiat currencies – the more people are using a given currency, the more useful it is to me (i.e., standard network effect)
    2) credit cards – the more merchants accept a card, the more useful it is to me as a consumer and vice versa (i.e., 2-sided effects)

    In addition to those, there is one more important network effect to consider. Cryptocurrencies also depend on a willing army of miners to actually do the work: validate, process and certify transactions. A new cryptocurrency could have a fantastic theoretical set of features, but if it does not have a critical mass of miners, then transactions won’t get processed or will be at risk of being tampered with. But miners won’t start mining for a given cryptocurrency unless they believe that they will make money from doing so. And they won’t make money from doing so unless there are lots of people using it and there is a good chance that those coins will be worth something in the future.

    My opinion is that all these network effects taken together make it unlikely that any cryptocurrency other than Bitcoin will get enough traction to become truly viable (and valuable), with 2 possible exceptions:

    1) There is a fatal bug in Bitcoin. In this case, Bitcoin would likely get replaced by a currency that did not suffer from that fatal flaw.

    2) “Niche” cryptocurrencies. By this I mean that there could be certain ecosystems/industries that require “special” rules or regulations that make them un-addressable by Bitcoin but that would still benefit from a cryptocurrency (but I don’t have a great example for what these could be). In that case, you could see a coin emerge to serve that niche, provided that the niche is large enough (i.e., enough transactions taking place) that it could entice enough miners to dedicate resources to it.


  6. Tim Makarios

    Ripple only requires you to extend trust in order to hold IOUs for other currencies. You don’t need to extend trust to anyone in particular (only to the Ripple system as a whole) in order to hold Ripple’s own internal currency.

    But regarding the indeterminacy of exchange rates, I argue that the value of a fiat currency derives from the value that can be extracted from debtors. If the currency becomes too valuable relative to real goods and services, then debtors will default more often, reducing the value of the currency for creditors, as well as for those who hold the currency that would otherwise be demanded by debtors. See

    I wonder to what extent there are net debtors in various cryptocurrencies. Have many people short-sold BTC, for example?

    Coming back to Ripple again, I also argue that there is something that may put a floor on the value of XRP, other than what can be extracted from short-sellers. Each transaction within Ripple destroys a fraction of an XRP, of which there are only finitely many, so “the total value of all XRP in existence shouldn’t fall below the expected total of the time-discounted marginal values of all future transaction services provided by the Ripple system”. See and its follow-up with corrections and clarifications,

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