Thursday, April 11, 2013

Why do Bitcoins have market value?

This is not a "Bitcoin is a bubble" post, nor is it a "Bitcoin is not a bubble" post.

Why does currency have value? The main reason seems to be that money solves the “double coincidence of wants” problem--barter is tricky since I want what you have but you don’t want what I have, so money is useful. We have a large literature that explores this. We also have a lot of models that implement money in a more reduced-form way: money in utility (i.e., people get happiness just from knowing that they have some green pieces of paper under their pillow), cash-in-advance constraints (i.e., there is a law of the universe that stipulates that a certain currency must be used to buy certain goods), shopping time, etc.

How would we go about incorporating Bitcoins into one of our workhorse models?

I think it’s a worthwhile question--for people who think talking about Bitcoins is worthwhile. A nice thing about Bitcoins is that we only have to think about money demand; the supply path is deterministic.

The reduced-form approach would be simple. We clearly can’t put all goods in a Bitcoin cash-in-advance (CIA) constraint because most goods can be bought with other currencies (and most goods can only be bought with currencies other than Bitcoin). But I think, for now, we can put a select few goods in a Bitcoin CIA constraint--the illegal or otherwise taboo goods we keep hearing about.* If this were the only friction associated with Bitcoins, we would expect a few people to hold a few Bitcoins (relative to total currency holdings). I suspect that we wouldn’t see the kind of volume and value we are currently seeing on the Bitcoin exchanges.

Suppose we put money in the utility function (MIU). We know that, on its own, this tends to produce results that look pretty similar to a CIA constraint. But suppose we use it in addition to the taboo goods CIA constraint. Whether this further boosts the equilibrium value of Bitcoins depends on the weight of Bitcoins in utility; if the weight is small, having enough Bitcoins to satisfy the CIA constraint will already be enough. If the weight is large, we get a few more people holding a few more Bitcoins. With something as novel and hyped as Bitcoins, there are some people who get utility just from being able to say that they own some. We can include the people who like Bitcoins simply because they’re not printed by government in here, too.

So, now do we have enough money demand to explain what we see on the exchanges? Maybe, but I don’t think so.

Are we missing something by being too reduced form? We can go a bit deeper with “turnpike” or search-and-matching models, but I don’t see them giving us a lot of mileage beyond what we’re getting from CIA. Are there any buyers and sellers of regular goods that are having trouble transacting due to thin market problems or failure to achieve a double coincidence of wants with the currencies they already have? I don’t think so. The truth is that Bitcoins only do a handful of things for us that cannot be done by other currencies.

Where am I going with this? Obviously I’m not saying anything that everyone doesn’t already know. I’m just thinking aloud. The difference between the market value of Bitcoins and the value we’d expect to see if there were only the CIA constraint and a bit of MIU going on can probably be roughly attributed to speculation.

But... speculation about what? Do Bitcoin holders anticipate that, in the future, more goods will be subject to a Bitcoin CIA? Do they think that more people will get utility from Bitcoins in the future? I don’t think either outcome is very plausible. Simply getting more businesses to accept Bitcoins in addition to dollars will only make Bitcoins more valuable (relative to dollars) if Bitcoin transaction costs are far lower than dollar transaction costs. The problem is that the cost of electronic transactions with dollars keeps falling. And the MIU factor will wear off as the hype recedes (though I admit that I thought we were close to peak Bitcoin hype two years ago; it could last awhile). Also, Uncle Sam.

A lot of the speculation is driven by multiple equilibria stuff--people think Bitcoin has value because people think Bitcoin has value, and some people think that, in the future, even more people think Bitcoin will have value. But multiple equilibria are pretty tricky and unpredictable things.

By the way, we could replace the word “Bitcoins” with “gold” and change “illegal goods” to “jewelry and dental implants,” and all the above analysis would hold up pretty well.

I’m not a pundit, so I’m not making a prediction about the future value of Bitcoin. I’m not saying it’s a “bubble” in the sense usually meant by journalists and bloggers who are always calling everything a bubble because they think current values are “too high” and a crash is inevitable. Going around calling things "bubbles" and making big price predictions is a fool's errand (and risks drawing the scorn of Scott Sumner). Bitcoin almost certainly is a bubble according to certain technical definitions; in some definitions, all currencies are bubbles (not to mention subject to multiple equilibria). But it may not be the kind of bubble that is guaranteed to “pop” eventually. Who knows? Nobody, and me least of all. I don’t have a prior about whether Bitcoins will be worth $1000 or $0 in a year. In fact, neither will surprise me (but both will be entertaining).

But I think it’s worth thinking about the sources of Bitcoin value.


*This doesn’t actually ensure value for Bitcoins, but it may mean that there is a high probability that some crypto currency can have value.

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