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.

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[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.

Bitcoin Commerce Market Size: How much are Bitcoin users spending?

As I reported previously, the average Bitcoin user reported purchasing about $2,180 of goods and services in the past year. Users were primarily buying internet services, electronics, or illegal goods (probably on SilkRoad).

To estimate the amount of commerce, one needs an estimate of the number of active users. Unfortunately, Mt. Gox hasn’t reported the number of active users in a while. The last time I estimated the sales for the number of ‘active users’ – the number of users who had made an exchange in the last 30 days. I may have underestimated the number of actual users buying/selling stuff with Bitcoins since some users may have been inactive on exchanges but buying goods and services.

Based on the number of unique addresses since April 2012 to just before Easter of this year, about 3.4 times more unique addresses are used every day (46,000/13,000) now. The number of transactions excluding popular addresses shows a similar tripling from just over 6,000 to just over 18,000 daily transactions (I’m ignoring the meteoric increase over the last couple of week).

As of August 2012, Mt. Gox had over 190,000 accounts but only 8% (about 15,000) had actually been active in the past month. In January 2012, Mt. Gox reported just under 23,000 active accounts based on 122,500 accounts (18.7%). Last year,

A Reddit user, John Vandivier, posted a good analysis of the number of Bitcoin users (, but I believe this counts the number of users ever rather than number currently active. He estimated in February 2012 that there are about 450K accounts. As noted above, the number of active users actually dropped on Mt. Gox between January and August 2012, despite the rise in the number of accounts.

So, now here is the very, very, rough math (please feel free to provide suggestions to improve this estimate). Last year in April there were 25,000 active users multiply by 3.4 gives 85,000 active users. This is similar to taking John’s 450k estimate, adjusting for the increase in unique Bitcoin addresses in the past month (about 10%, so we’ll say 50K) and assuming about 15% of accounts are active. This estimate gives right around 80,000 active accounts.

So, if the average user spends around $2,180 on goods and services with Bitcoin about 82,500 accounts are active, and 64.4% have purchased something.

Total Bitcoin commerce in the last year was about $116 million – quadruple the amount from last April.

Similarly, the total average donated per user ($183) multiplied by 82,500 active users and 40% of users who have actually made a donation, creates a total Bitcoin donated estimate of $6.1 million.

A number of things could affect these estimates:

Reddit/Bitcointalk users make more and/or higher valued purchases than average. In particular, the number of very active users who have spent thousands of dollars on goods and services is probably higher on Reddit/Bitcointalk than in the general Bitcoin user population. It’s also possible that many speculators who don’t purchase anything with Bitcoin don’t participate in these forums – Reddit and Bitcoin users are probably more likely to make purchases than average.

The assumption of 82,500 active accounts does not take into consideration users who may only be active less than once a month. It could also be quite conservative given that there are reportedly now millions of wallets.

Last, and least likely, substantial market manipulation could make the market appear more active than it actually is, completely ruining the number of active user estimates.

I think the first is particularly important. The users who reported over $10,000 pretty significantly skew the average and I suspect Reddit and Bitcointalk have the most active users in the entire community. Dropping the users who reported over $10,000 in spending, the average spending per Bitcoin user is a much more conservative $1,200.

At a much more conservative estimate, the total amount of Bitcoin e-commerce in the past year was just over $64 million U.S.

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Bitcoin Survey Results – 2013


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.

In last year’s survey, Bitcoin users reported spending an average of about $1,550 U.S. each. Given the estimated number of active users, about 25,000, I estimated that the total commerce of Bitcoin in the past year was around $28 million.

In addition to last year’s survey, researcher, Nicholas Christin, estimated that  public Silk Road transactions alone accounted for about $22 million U.S in spending, although he later reduced this estimate to $15 million. His estimate matches quite well with my previous survey, given that I found that about 70% of users admitted that they had used Bitcoin to remain anonymous while making a purchase. A quick and dirty calculation of 70% of $28 million gives $19.6 million. It makes some sense that my estimate is a bit higher given that he only measured public sales.

This Year’s Survey

For this year’s survey, I used GoogleDrive so I could collect a broader range of data. In addition to spending, donation, and mining habits of users, I also collected some baseline demographic data. I had nearly double the number of respondents this year (n =182). A big thanks to everyone who responded!

Bitcoin User Demographics

Survey respondents were from 22 different countries, although over half were from the United States. Europe was also fairly well represented – about 30% of all respondents were European. Despite the recent articles on Spaniards and Cypriots jumping on Bitcoin, less than 2% of respondents were from either country.

Respondents were overwhelmingly male – a full 97% of those who provided their gender chose male.

Most respondents – 61% – had been using Bitcoin for more than 6 months. About 20% of respondents were new to Bitcoin, which is quite a bit higher than last year. I did this survey during a huge price run-up, so that probably explains the jump.

Sixty-five percent were employed, 35% unemployed. However, many of the unemployed were students. Only 15% were both unemployed and not in school.

Nearly half of Bitcoin users have completed a university degree.

Bitcoin User Spending Habits

The spending habits of Bitcoin users were very similar to those from last year. Just under two-thirds of all respondents had purchased something with their Bitcoin in the past year, slightly lower than the 72% of last year. However, the amount spent per user was up a lot from last year. Bitcoin users who had spent any Bitcoin spent an average of $2,180 each on goods and services in the past year compared to $1,550 the year before. The drop in the percent of users who have spent Bitcoin may be related to the recent influx of new users – 58% of new users had not purchased anything with Bitcoin yet.

Some users reported spending well over $10,000 U.S. in goods and services, although the median amount spent per user was $200 U.S.

Many users – about 40% – have made donations in the past year. On average, each Bitcoin user who made a donation had spent about $180 U.S. A few respondents answered that they had donated over $1,000.

Users primarily bought internet services and electronics. However, about 25% of all respondents admitted they used Bitcoin to purchase illegal goods or services in the past year. Obviously, one would expect that this is underreporting the actual number of Bitcoin users who buy illegal goods and services since survey respondents normally underreport illegal activity. However, I think that the share of illegal goods in Bitcoin e-commerce has almost certainly fallen for the following reason.

Anonymity and Bitcoin

What I think is probability the greatest reversal since last year’s survey is that Bitcoin users are no longer as concerned about anonymity. This year, only 31% of respondents said that they had used Bitcoin for purchases to maintain their anonymity. Last year, exactly double – 62% – responded that they had used Bitcoin to help maintain their anonimity.

The drop might be explained by the much broader range of merchants and websites that now accept Bitcoin payment. WordPress, 4chan and Reddit, which have millions of users, have adopted Bitcoin as a payment method. On top of that a number of retailers, especially electronic retailers like BitcoinStore, have opened shop and deal exclusively in Bitcoin.

Are Bitcoin Users Gamblers?

Early adopters of a new technology are generally risk-takers, and it certainly shows. Forty-five percent of users reported gambling at some point with their Bitcoins and nearly one in five had gambled with Bitcoins in the last week.


Although 43% of users reported mining Bitcoins in the last year, over half of Bitcoin miners reported mining less than one Bitcoin. Six users reported mining 100 Bitcoins or more, all of whom had made significant investments – generally, thousands of dollars – in mining technology. The top six miners had mined over 90% of the total Bitcoins.

Bitcoin User Outlook

Like last year, Bitcoin users have a positive outlook on the price of Bitcoin. Despite the recent stratospheric rise in price, 85% of Bitcoin users believe that the price will rise in the next 12 months. Users are even more optimistic about the next five years – 90% believe the price will rise in the next 5 years.

Along with their optimism, 9 out of 10 Bitcoin users also plan on increasing their use of Bitcoins in the next year.

In the next post, I use this data to estimate the amount of Bitcoin e-commerce.

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

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