Eli Dourado

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.

  1. 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.