The FBI is Completely Wrong about the Size of the Silk Road

Over the past two years, I’ve collected and analyzed data from nearly 300 Bitcoin users to estimate the size of the Bitcoin economy – how much stuff, legal and illegal, people have bought with Bitcoin.  The FBI estimate is that Silk Road was a massive billion dollar black market. Yet, all of the data I have collected, along with research by security expert Nicholas Christin, points to a market a tiny fraction of the size.

Forbes reported that “[g]iven the current price — $140/Bitcoin — that’s $1.2 billion in sales and $80 million in commissions[1].” This is not just bad economics – it is bad math. Of course, the price of Bitcoins has fluctuated from less than a dollar to a high of $300 U.S. over the past two years. Silk Road transactions from even a year ago would have taken hundreds of times more Bitcoin for the same street value of drugs.

The first price spike in 2011 and ensuing fervor for the virtual currency left me with a huge unanswered question. Are people actually buying with Bitcoin? Or is the whole Bitcoin market driven by recurrent manias? I needed to know what users were buying, so I surveyed them directly about spending habits, and combined the results with estimates for the number of active Bitcoin users.

When I first surveyed Bitcoin users in March 2012, the average user reported purchasing around $1,600 U.S. of goods and services. I surveyed users on Bitcoin Talk Forums – Ulbrich’s account there led in part to his arrest – and the Reddit subforum dedicated to Bitcoin[2]. The users on these forums are the most ardent supporters of Bitcoin, so I would suspect that the average spending per user was on the high side compared to everyone who has ever purchased Bitcoin. Based on 18,000 users actively buying things with Bitcoin (I based the number of active users on the number of reported active accounts from the largest Bitcoin exchange MtGox), I figured Bitcoin users paid for just under $29 million U.S. in goods and services from March 2011 to March 2012.

My survey also revealed that 62 percent of users made purchases to hide their identity. Assuming that all of these users purchased exclusively on Silk Road, the trade on Silk Road from March 2011 to March 2012 was about $17.9 million.  Despite the crude, back-of-the-envelope calculation, security expert and Carnegie Mellon computer engineering professor, Nicolas Cristin – who directly accessed the site and counted transactions – found a similar market of $14.4 million[3]. My estimate was probably a little high because the 62 percent of users who used Bitcoin to hide their identity likely bought both legal and illegal goods and services from a variety of sites that accept Bitcoin.

Was there an astounding increase in sales on Silk Road over the next year that can even remotely explain the FBI’s $1.2 billion figure? Absolutely not. I repeated a modified version of the survey in March 2013 on the same online forums. I had over double the response rate, and I asked more in-depth questions to get a better grasp of what users were actually buying. For March 2012 to March 2013, I estimated that the total Bitcoin economy had more than doubled in size to $63 million U.S. and might have been as high as an impressive $119 million U.S. No other economy on earth can claim a 100 to 300 percent growth rate.  Still, this pales in comparison to the FBI claim of a $1.2 billion underground economy.

In fact, I was surprised to find that users reported buying relatively more legal goods and services.  In 2013, only 31 percent of users reported that they used Bitcoin to hide their identity, half the share of the year before. I suspect that the growth in legitimate places to spend Bitcoin offered users other venues to spend their virtual currency. Over the past year, a number major websites, including WordPress, Reddit, and 4chan, have started to accept Bitcoin, and a number of storefronts selling everything from computer parts to DVDs to books to kitchenware have made it easier to shop with the virtual currency. Using the same crude method as before to calculate the size of Silk Road, I would peg the annual Silk Road black market around $20 to $40 million. In a July interview, Nicholas Christin said that Silk Road revenues of “[s]omewhere between $30 million and $45 million a year would not surprise me[4]”. Again, his expectation is well within the range of my findings.

Both Nicholas Christin and I have corroborating evidence that the total revenues for Silk Road in the past two years were in the range of $35 million to $65 million U.S. I should say that gathering data on the Bitcoin and Silkroad market is imperfect, because, by design, Bitcoin and Silk Road hide as much information about users and transactions as possible. Furthermore, the users I surveyed were probably less likely to admit buying illegal goods because of the risk. Yet, Nicholas Christin and I, using entirely different methods, both found similar market sizes over the two year period the FBI was monitoring Silk Road. I doubt that we simultaneously underestimated the market by a factor of 40.

To support my efforts to increase knowledge about the Bitcoin market for goods and services, user sentiment, etc, please make donations to 1EySGJWKjN5U4gQwkvPjNApKxL1KwpCZ9L

[2] I collected results anonymously, so I have no way to know if Ulbritch participated in my survey.

[3] His initial estimate in a draft paper was $22 million, slightly above mine.


What is the real price of Bitcoin? Measuring Bitcoin hoarding, irrational exuberance and the inevitable crash

In any first year macroeconomics course, students are introduced to the concept of the quantity theory of money. The quantity theory of money can be expressed as an intuitive and basic formula.

M * V = P * Q

M = Money supply (measured in $)

V = Velocity of money (a constant)

P = Price level ($)

Q = Quantity of goods sold

Generally, P * Q is the final demand for goods and services sold in an economy in a year (C + I + G + X – M). So, V, the velocity of money, is the usually measured as the ratio of the size of the liquid monetary base relative a country’s nominal GDP – the final goods and services consumed by consumers, governments, businesses, or exported net of imports.

A higher velocity means that money changes hands faster in an economy.

For complex economies, there can be many ways to measure the money supply. The narrowest definition is M0 – the value of currency in circulation. Obviously, the deposits in chequing and savings accounts are also as liquid currency. M1 is the sum of all currency in circulation and demand deposits or checking accounts at financial institutions.

In the U.S., the current velocity of M1 is about 7. That is, the nominal GDP of the U.S. is about 7 times greater than the amount of money available in currency and held in chequing and demand deposit bank accounts.

So, what is the velocity of Bitcoin?

MB * V = (P * Q)B

One can easily convert this into $U.S. by multiplying both sides by the exchange rate

MB * eUS/B * V = (P * Q)B * eUS/B

In my last post, I estimated that the value of goods and services bought with Bitcoin was between $62 million and $116 million U.S in the last year.

Currently, the Bitcoin market capitalization is valued an astronomical $1.88 billion!

So, if $1.88 billion * V = $62 million to $116 million

The current velocity of Bitcoin is about 0.032 to 0.062.

On average, Bitcoins are changing hands for final goods and services at a rate 110 to 210 times slower than U.S. dollars. A year ago, the velocity was nearly a factor of 10 higher. In April 2012, the final demand for goods and services in the past year was $28.3 million compared to a market capitalization of $44 million. The velocity of Bitcoin was 0.64. Clearly, the amount of Bitcoin hoarding, which was already high, has gone illogically parabolic as speculators flood into the market.

With some modifications, the M * V = P * Q formula can actually be used to determine what the exchange rate of Bitcoin will be if suddenly people stop hoarding and return to the relatively stable market of last April.

Let’s assume that the velocity of Bitcoin returns to 0.65. To use this method, we have to also assume that the number of Bitcoins in existence does not influence the demand for goods and services. I think this is a very sound assumption. There is no Bitcoin economy interest rate that can fall with growth of the monetary base. Demand for Bitcoin goods is based entirely on the fact that Bitcoin transaction fees are lower and that it provides some anonymity in transactions. Basically, there is no reason to suspect a real-financial linkage in the Bitcoin economy.

(P * Q)B * eUS/B = (P * Q)$U.S.-> The final demand in U.S. dollars is the final demand expressed in Bitcoin multiplied by the exchange rate.

So, if MB * V = (P * Q)B then,

MB * V = (P * Q)$US / eUS/B

Right now, MB is about 11 million, I’m assuming that a more appropriate V is 0.64, and that the current final demand for goods and services in U.S. dollars is up to $116 million.

Substituting in my assumptions,

11 million * 0.64 = $116 million / eUS/B

eUS/B = $116 million / (11 million * 0.64)

eUS/B = $16.4 U.S.

Now, this assumes that the velocity can return to 0.64, this might be troublesome. Recent speculative activity might cause many Bitcoins to be effectively destroyed – either deleted, forgotten or lost. According to, in the past year the number of Bitcoin days destroyed – a proxy for the amount of Bitcoin effectively out of circulation – has nearly doubled.

Even then, if the velocity of Bitcoin were halved to 0.32 as a result of lost/destroyed Bitcoin, the exchange rate should be around $32.8 U.S. per Bitcoin and nowhere near the currently absurd level of $190 U.S.

Of course, there are other factors I haven’t considered. After such a huge crash the amount of goods and services (whether legal or illegal) people want to buy in Bitcoin could collapse as well. This would drag the exchange rate even lower.

Survey Results

Bitcoin Survey Purpose

One of the unanswered questions about Bitcoin is one of the absolute most basic – how much stuff do people actually buy with Bitcoin?  It’s an important question. It will tell us if people actually use Bitcoin or if people are still just speculating on the future exchange value.

If it’s the latter, Bitcoin is doomed to failure. No market for goods or services means that the Bitcoin market is just waiting for a negative shock to permanently bury the currency.  On the other hand, if the current userbase utilizes the currency because it provides identifiable benefits to them there is a chance that it will remain an online fixture, barring a technologically superior alternative.

As far as I know, my very basic survey is the first effort to make any effort to quantify how much people actually use Bitcoin for buying goods and services, and how much speculation is going on.


I conducted the survey using a SurveyMonkey basic account, which unfortunately limits the granularity of data I could collect, and somewhat limits my analytical abilities (I can’t automatically do cross-tabs, for instance). Furthermore, the survey is pretty unscientific. It was posted on two popular forums of discussion for Bitcoin – the Bitcoin Talk forum and r/Bitcoin. It is certainly possible that the users of these forums are not representative of the population of Bitcoin users.

Nevertheless, some very interesting patterns emerged.

How long have people been using Bitcoin?


N = 93

Of the 93 users who answered the survey (which was posted on Reddit r/Bitcoin and the Bitcoin Talk forum) most users had been using Bitcoin for at least 6 months (77.4%). Although I didn’t collect granular enough data to estimate an average, it seems that on average those polled had been using Bitcoin for about a year.

The Bitcoin Market for Goods and Services

N = 93

Out of everyone who answered the survey, 72% had purchased goods and services with Bitcoin. Unsurprisingly, the longer someone has been using Bitcoin the more likely they were to have purchased something. All users who had been using Bitcoin more than two years had purchased something. Ninety per cent of all users who had been using Bitcoin for 1 to 2 years had purchased something.

Furthermore, it seems that most people plan on making a purchase in the future. Ninety-four percent of people polled plan on making a purchase in the future. It seems that it just may take some time before people are comfortable with making a purchase.

So how much, on average, have people spent? After converting to U.S. dollars (the native country of most users), the average user has spent $1,549 on goods and services. However, this figure includes a handful of users who reported spending in excess of $10,000 U.S. Nearly half of users surveyed had actually spent less than or equal to $100 on goods and services.  The median amount spent was $175.

N = 70 (users who reported $0 in spending were dropped)

 We can actually take this information and make a very rough estimate of how much stuff in U.S. dollars has been bought with Bitcoin. According to the MtGox overview, there were 22,855 active users in January. Given that MtGox services about 93 per cent of all volume, we can estimate that the total number of users currently using Bitcoin is about 25,000 (22,855/93%). This assumes that users of other exchanges have about the same transaction volume. This figure is conservative because there may be a few users who mine Bitcoin and buy goods without ever using an exchange at all, and it may be that some users of Bitcoin are inactive for more than 30 days.

So, the estimate of total goods and service bought by the currently active users is about 25,000*72%*$1,594, or about $28.3 million U.S. Each user surveyed has been active for about a year, so $28.3 million U.S. is a very, very rough estimate for the value of goods and services sold over the past year to the currently active user base.

Although the number of active users is probably an underestimate, the amount spent per user is probably an overestimate. The survey was posted on two popular Bitcoin forums, which could include users who are more likely to buy goods and services than average. It may also include more ‘power users’ – those who have bought a significant amount of goods and services – than those who exist in the general population of Bitcoin users.

Along with goods and services, 57 per cent of users said that they had made donations to non-profit groups or causes.

Has the Relative Anonymity of Bitcoin Been a Driving Factor of its Adoption?

Of the users who purchased some goods or services, 67 per cent admitted that they did so to hide their identity. This is really not surprising given the popularity of sites like Silkroad. Of course, this does not mean that users who wished to remain anonymous bought illicit goods and services – they may also just have a preference for remaining anonymous.

N= 89

Have Users Purchased Bitcoin as an Investment?

 It is abundantly clear, that most users have been buying at least a small amount of goods and services with Bitcoin or making significant donations to non-profit causes. So, how bullish is the sentiment on the price of Bitcoin? Are users buying Bitcoin because they expect the market for Bitcoin transactions to increase relative to the number of Bitcoins in existence?

Current Bitcoin users are overwhelmingly positive on the price of Bitcoin. A full 84% of those surveyed believe that the value of Bitcoin will rise in the future and nearly half are expecting a large increase in value. Because of the extremely positive sentiment on the price, two-thirds of users have purchased Bitcoin as an investment. On top of that, 27% are currently mining Bitcoin for profit.

N = 89

What’s Next?

In the next post, I am going to use this data to look at some of the economics behind Bitcoin, including the velocity of money and whether there is evidence of users hoarding.

To support my efforts to increase knowledge about the Bitcoin market for goods and services, user sentiment, etc, please make donations to 1EySGJWKjN5U4gQwkvPjNApKxL1KwpCZ9L