Tag Archives: cryptocurrency

Bitcoin and Endogenous Nominal Rigidities

One supposed problem with Bitcoin taking over the world, critics say, is that lack of a central bank precludes countercyclical monetary policy. When aggregate demand grows more slowly than expected, you want the central bank to increase the money supply in order to induce people to spend. The argument is fair enough as far as it goes, but it is undercut somewhat by the growing literature on endogenous nominal rigidities.

At the core of New Keynesian models of monetary non-neutrality is price stickiness: how quickly do firms and workers update prices and wage demands in light of new information about nominal shocks? Most models follow Calvo in assigning producers an exogenous frequency of price changes.

But the endogenous nominal rigidities literature asks an important question: what if instead of changing prices according to an assigned schedule, firms can choose how often they update their prices? Furthermore, what if they make that choice in response to monetary policy? When monetary policy focuses on price stability, firms will choose to update their prices less frequently, conserving on the resource costs of changing prices (menu costs, as Mankiw calls them). When monetary policy focuses on the output gap (or, by extension, when monetary policy is erratic, which is important for analysis of Bitcoin), they will choose more price flexibility in spite of the higher menu costs. More price flexibility means both that nominal shocks have less bite and that monetary policy is less effective.

What does this mean for Bitcoin? If we simply model the Bitcoin money supply as set by an incompetent central banker, it means that in a world in which Bitcoin rules the currency roost, firms and workers will choose nearly complete wage and price flexibility and nominal shocks won’t matter as much.

That’s not such a bad world. The big downside is the menu costs—people will need to adopt systems that ensure complete pricing flexibility—but with improvements in information technology, menu costs are lower than ever before. For long-term contracts, people would index to a basket of goods, or as I’ve suggested, to GDP.

This world is also not unprecedented: for most of human history, we have not had central banks, and therefore humans have taken steps to decrease price rigidity. Consider Polonius’s advice, “neither a borrower or a lender be,” or the prohibitions on lending in the Abrahamic religions. These make sense when there is an erratic (or no) central banker. If cryptocurrencies displace fiat currencies, then we’ll say, “always index your debt contracts,” which is approximately an update of Polonius.

The bottom line is that recent advances in monetary economics somewhat undercut the macro-stability argument against Bitcoin. I would like to see this basic point acknowledged more widely, especially by people who style themselves the defenders of conventional economics against Bitcoin crackpottery.

Announcing btcvol.info, Your One-Stop Shop for Bitcoin Volatility Data

The volatility of Bitcoin prices is one of the strongest headwinds the currency faces. Unfortunately, until my quantitative analysis last month, most of the discussion surrounding Bitcoin volatility so far has been anecdotal. I want to make it easier for people to move beyond anecdotes, so I have created a Bitcoin volatility index at btcvol.info, which I’m hoping can become or inspire a standard metric that people can agree on.

The volatility index at btcvol.info is based on daily closing prices for Bitcoin as reported by CoinDesk. I calculate the difference in daily log prices for each day in the dataset, and then calculate the sample standard deviation of those daily returns for the preceding 30 days. The result is an estimate of how spread out daily price fluctuations are—volatility.

The site also includes a basic API, so feel free to integrate this volatility measure into your site or use it for data analysis.

I of course hope that Bitcoin volatility becomes much lower over time. I expect both the maturing of the ecosystem as well as the introduction of a Bitcoin derivatives market will cause volatility to decrease. Having one or more volatility metrics will help us determine whether these or other factors make a difference.

You can support btcvol.info by spreading the word or of course by donating via Bitcoin to the address at the bottom of the site.

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.

Bitcoin Volatility is Down Over the Last Three Years. Here’s the Chart that Proves It

Bitcoin’s detractors have for some time argued that the cryptocurrency’s high volatility makes it unsuitable even as a medium of exchange, because volatility increases the cost of hedging. Companies such as Bitpay and Coinbase, who process Bitcoin payments for merchants who only want to deal in dollars, take on the risk of currency fluctuations between the time they receive the coins and the time they can sell them. These companies have to hedge. They seem to be able to do so and charge fees of only 1%, so the cost of hedging can’t be prohibitively high.

Even so, it’s worth looking at Bitcoin’s volatility over time. As Bitcoin becomes more widely used and more liquid, we should expect volatility to decrease. And that is exactly what we find.


I calculated Bitcoin’s historical volatility using price data from Mt. Gox (downloaded from Blockchain.info), which is the only consistent source of pricing data over a long period. There is a clear trend of falling volatility over time, albeit with some aberrations in recent months. The trend is statistically significant: a univariate OLS regression yields a t-score on the date variable of 15.

Historical volatility is different from implied volatility—the latter uses the price of derivatives to produce an estimate of volatility going forward, while the former looks at variation in past price movements. When we get a healthy Bitcoin/USD derivatives market going, we’ll have both a better measure of volatility and probably less volatility, since such derivatives make better forms of arbitrage possible.

Bitcoin is still about ten times more volatile than, say, the Euro priced in US dollars. But if Bitcoin’s volatility kept falling in half every three and a half years, it would be as stable as the Euro in less than 15 years.

If you want to check my assumptions or build off of this work, my Stata code to produce the volatility estimate is below. Mind the line breaks! Continue reading

Here’s How Cryptocurrencies Could Replace the US Dollar

Ever since Bitcoin started to capture the public imagination, I have downplayed the idea that it could ever represent a serious challenge to the US dollar. I disagree with the goldbugs who believe that simply fixing the supply of money is the best monetary policy, that inflation is theft, etc. Rather, I have argued that Bitcoin is a good medium of exchange despite being a bad unit of account and a risky store of value. These three functions of money tend to go together for reasons that Ludwig von Mises outlined over a century ago in The Theory of Money and Credit. But more recent research from the 1980s and 90s has explored the possibility of the separation of these three functions. A contemporary example of separation is that Treasurys are used to settle transactions in the shadow banking system, even though the transactions are denominated in dollars—the medium of exchange is different than the unit of account. Bitcoin could be just another example of the continuing separation of the functions of money as technology progresses.

I still think that this is correct—we are observing modest separation of the functions of money. Bitcoin doesn’t need to be a unit of account in order to be useful. On it’s own, Bitcoin makes a terrible unit of account.


This is speculative, but there is a scenario in which Bitcoin could create a real challenge for state-backed currencies. This scenario is not impossible.

As I wrote last week at The Umlaut, Bitcoin is not just money, it is a decentralized platform for generalized, programmable contracting, a transport layer for finance. It can be used to create all kinds of financial contracts, including, with the help of a trusted computer called an oracle, contracts contingent upon events in the real world. Suppose that an oracle existed that reliably provided information about the USD/BTC exchange rate. It would become possible to create a long-term contract, executed through Bitcoin, denominated in dollars. If the cost of querying the oracle were negligible (as we might expect it to be), then the cost of this trade would be the forgone interest on the funds used to meet the “margin requirements” built into the contract.

Now assume a second oracle that reports nominal GDP. By combining the two oracles, it becomes possible to write a contract, executed over Bitcoin, that is denominated in shares of NGDP. In fact, we could simply standardize this transaction and create a new currency unit, built on top of Bitcoin, that is equal to a trillionth of NGDP. We could call it a Sumner. Instead of getting a mortgage for $300,000 for a house, you could promise to pay 19,000 Sumners. That way, if the economy went south, you would owe less in real terms, and repayment would not become harder. If the economy boomed, you would owe more in real terms, and repayment would not become easier. Similarly, workers who had wage contracts denominated in Sumners would experience a real pay cut when the economy shrank, decreasing their employers’ incentive to fire them, and an automatic raise as the economy grew again. Sumners would have built-in monetary policy.

So by combining information from two oracles into a simple, standardized, tradable futures contract executed over Bitcoin, we create a cryptocurrency overlay that is superior to dollars, at least according to the market monetarists (see Scott Sumner’s 1989 paper and his recent Mercatus paper). As I said above, this is speculative; as far as I can tell, there are no oracles or Bitcoin-executed futures contracts yet. And there are at least two further (possibly surmountable) problems.

First, it remains to be seen what the long-term cost of hedging will be. The margin requirements built into a Sumner depend on how volatile Bitcoin is with respect to NGDP. It’s possible that over the long run, the volatility of Bitcoin will settle down a fair bit, even if it is never as stable as the dollar. If Bitcoin is some day only 3-5 times more volatile than the dollar, that should be enough to support the creation of Sumners. For now, Bitcoin’s price swings are still incredibly wide.

Second, there remains the puzzle of why we don’t see NGDP futures in the dollar economy. As far as I can tell, there are no regulatory barriers to creating them and using them to denominate transactions. Yet in spite of their supposed superiority to dollars, no one uses NGDP futures to trade, and indeed, there aren’t even NGDP futures markets. If it’s a question of there not being enough permissionless innovation in the financial system, then maybe market monetarists should embrace cryptocurrencies as a way to try out their ideas.

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.