Wednesday, April 10, 2013

A wonkish look at bitcoin economics

Bitcoin is an increasingly popular electronic currency, used both for legitimate and illegal transactions. Economists haven’t taken a serious look at bitcoin yet, so I thought I’d take a stab at it. In particular, I’m going to look at the “intrinsic value” of bitcoin, answering the question whether the recent rapid rise in price (to $240 at the time of writing this) is justified.

The TL;DR version is this: bitcoins have real value (they are not a fantasy), and that value is between $0.01 and $15000.

Bitcoin vs. Money

There have been many un-serious looks at BitCoin. Take, for example, this 2011 blogpost by Nobel-prize winning economist Paul Krugman, where he compares bitcoin to the gold standard. He’s completely wrong.

The mistake economists make is assuming that bitcoin works like real money. It doesn’t. While bitcoin is designed as a “medium of exchange”, it doesn’t serve the other traditional functions of money, such as a “store of value”, “unit of account”, or “measure of value”.

In recent months, the price of bitcoins has skyrocketed. In classic economics, this means that the bitcoin economy has experienced massive “deflation”. Likewise, when the bitcoin bubble bursts and the price goes down, the bitcoin economy will experience hyper “inflation”.

But this inflation/deflation has no effect. Prices aren’t denominated in bitcoins, but in some hard currency like dollars or euros. Buyers exchange their dollars for bitcoins, give the bitcoins to the seller, who then immediately changes them back to euros. The entire process takes about 30 minutes. The only requirement is that the exchange rate for bitcoins not fluctuate wildly during this half-hour window. Since bitcoins are electronic, they can easily be subdivided, so "billionth of a bitcoin" is a workable value. When analyzing bitcoin, we have to toss out this idea that it is a “measure of value” and the related ideas of inflation/deflation.

Bitcoins are not legal tender. That’s entirely the point: it’s a rebel currency designed to evade normal government controls. But that means there is no government protection, either. This means that you cannot borrow bitcoins, because the government won’t force you to pay back the loan. While might be able to store bitcoins in a “bank”, rather than paying you interest on your deposit, the “bank” would charge you a fee. Thus, there is no bitcoin financial system. Our entire economic system isn't based on money but derivatives of money -- all that goes away leaving bitcoins by themselves.

Bitcoins are not a “store of value”. Sure, speculators are hoarding bitcoins, but that’s a different thing. You can’t safely store bitcoins on your computer, because they will be lost when your hard drive crashes or a hacker infects you with a virus. You can’t rely upon somebody else to store them for you, because as mentioned above, there’s no law forcing them to give them back. And, as recent hacks of bitcoin businesses have shown, it’s unlikely that an online site is safe enough. Only experts have enough skill to safely store their own bitcoins over long periods of time.

This is the failing of economists. They’ve built up a bunch of assumptions and rules-of-thumb about how “money” works, but bitcoins aren’t really money, and those assumptions break down. We have to go back to first principles.

Measuring the bitcoin money supply

Bitcoins are currently above $200/coin. Is this price justified? Or is this due to speculators? What’s the “true” value of bitcoin? To answer this question we have to first find out the “true value” of any currency, like the dollar or euro. Why is $1 worth $1? Or, better asked, why is $1 worth a quarter of a Big Mac hamburger? The answer is this: economists don’t really know. They have theories, and some evidence, but they aren’t certain.

The basic theory of money is simply “supply and demand”. People demand money both as a medium of exchange and store of value. People demand money because barter is inefficient. If you want your car fixed, you might try to offer the mechanic some chickens, a goat, or a year of free haircuts. But if your mechanic is a long haired hippie, they are not going to want any of these things in trade. What they want is something that they can easily exchange elsewhere. In other words, mechanics demand money.

The same goes with savings. Long term savings are in things like your house, but in an emergency, it’s hard to sell your house. Therefore, people want some savings in something more liquid, which is to say, money.

That’s where the value of $1 comes from: supply and demand. People demand a thing that can easily be exchanged, and that demand creates value. This value is as real as the value of anything.

That’s the theory, and there is evidence to back it up. For example, when governments print more money, the supply goes up, and as you would predict, the value of money goes down. That means it then takes more money in exchange for the same goods. In other words, prices go up, and inflation occurs. That’s what happened in pre-war Germany and Zimbabwe more recently: the governments printed more and more money, causing hyperinflation with prices doubling daily.

There are other theories about where the value of money comes from. Some people believe that the value of currency comes from the government who prints it. The evidence for this theory is not good. Saddam-era Iraq is a good example. The 1991 Guld War cut off Iraq from the outside world. Instead of using high-quality “Swiss” printing presses, Iraq printed new money on low-quality presses. They also printed more of it, causing devaluation and inflation. The old currency continued to be used in the semi-autonomous Kurdish region, even though it was no longer officially recognized by the government. Moreover, when Saddam’s regime fell, both forms of Iraqi currency continued to be used, even though no government existed to set its value. Even bad money is better than bartering three chickens and a goat -- the value comes from the demand, not from the government.

Yet another theory about the value of money is that it's due to irrational "faith" or "perception" of value.  Economists disagree. A fundamental axiom of economics is that people are rational. When they value gold, dollars, or bitcoin, the assumption of economists is that people have a rational reason for doing so. Bubbles may seem irrational, but it's from people rationally betting. Some will be winners, some will be losers. It's like betting on who wins the superbowl: just because they lost the bet doesn't mean the losers were irrational choosing that team. All evidence suggests that valuing money is the "rational" thing to do, and trying to setup a barter system is less rational.

So if the “true” value of bitcoin is set by supply and demand, what are the "suppy" and "demand" for bitcoin?

The entire premise of bitcoin is that it can be used in the underground economy. This includes illegal activity, such as buying drugs, but also a lot of legal-but-shady activity, like buying porn or transferring money to your cousin overseas. The IRS estimates that the unreported underground economy is about $2-trillion per year (out of a total GDP of $14-trillion). So let’s use that number as our “demand” part of the equation.

What is the “supply” of bitcoin? That’s determined by mathematics of the bitcoin algorithm. There are about 10-million bitcoins now, which will rise to a maximum of 20-million bitcoins over the next decade. So that’s 20-million bitcoins chasing $2-trillion in transactions.

Compare this to the official economy, with $2.4 trillion in money (M1) chasing $14-trillion in transactions, or a 6.553 ratio. Simply divide $2-trillion by 6.553 by 20-million and poof, you get the precise value of bitcoin: $15,260 per coin (fifteen thousand dollars).

That seems like a lot, much more than today's $240 price, but it's based on an enormous number of probably invalid assumptions. Changing the assumptions changes the valuation. For example, if we assume bitcoin is only used for 10% of the underground economy rather than 100%, then the value is 10% that number, or $1,526.

Put another way, with bitcoins approaching $300, that means punters are assuming bitcoins are going to take over 2% of the underground economy. If you think bitcoins will take over more of that, then you should be buying bitcoin. Likewise, if you think bitcoin will take over less, then you should be selling bitcoin.

Note that I use the M1 measure of the money supply in this calculation. Let’s talk about money supply for a moment.

There are three good measures of the money supply: M0, M1, and M2.
  • M0 is just the amount of physical money, which is about $800-billion in bills (mostly $100 and $20 bills). The 20-million possible bitcoin is the M0 of bitcoin.
  • M1 includes M0, plus checking accounts. When you deposit money, your bank immediately lends out most of it. The borrower spends that money, which gets deposited in a bank, which likewise lends out most of it. This “fractional reserve banking” multiplies the effective amount of money available to about $2.4 trillion.
  • M2 includes M1 and M0, plus liquid savings like money market funds. This is money that households can easily spend, but which they generally choose not to. This is roughly $10 trillion.

If you think bitcoins will be used primarily for transactions and not for savings, then M1 is the more appropriate measure. If you think there will be more saving of bitcoins, then M2 is likely a better measure, so increase your estimate of bitcoin value by four times.

Since there is no banking in bitcoins, that makes M0 and M1 equivalent. If you think banking services like “fractional reserve lending” are likely to appear, then reduce your estimate of the value of bitcoin by three times.

The value of protocol

The above discussion is a top-down analysis from the “economics” perspective, comparing bitcoin to money. Let’s also do a bottom-up analysis looking at bitcoins as a “network protocol”, as a means of exchanging money -- but not being money itself. That last bit is important: we call bitcoins money, but technically, it's just a protocol for exchanging dollars into other dollars.

An essential part of bitcoin is that it takes 10 minutes for a transaction to complete. That number is baked into the protocol. Your transaction gets added to a blockchain, and that chain gets computed and rebroadcast out to the rest of the network. There is a new blockchain every 10 minutes. A typical transaction will therefore take 30 minutes: 10 minutes for the buyer to convert hard currency to bitcoins, 10 minutes to exchange the bitcoins, then 10 more minutes for the seller to change those coins back to hard currency.

Let’s assume a $2-trillion economy where bitcoins are converted back to hard currency as fast as possible, where nobody holds onto the coins longer than they have to. Running these numbers ($2-trillion divided by (365*24*60*2) divided by 20 million) comes out to 10 cents per bitcoin. Assuming a smaller economy, such as bitcoins handling 2% of the underground economy, and you get 0.2 cents per bitcoin. Since there’s a little slack in the system, let’s call this 1 cent.

This assumption that people get rid of bitcoins as fast as possible won’t be true, of course. Take a hypothetical gambling site that deals only in bitcoins. It'll take bets over the season on which baseball team will win the superbowl, and only then paying the winners at the end of the season. The value of 10 minutes is only the minimum, the average will be larger.

Your belief in how long a bitcoin will be held (on average) therefore changes the equation. If the average coin is held for a day rather than 30 minutes, the value of a bitcoin goes up 50 times. Conversely, the time between block chain confirmations can do down (it's actually 7 minutes now instead of 10), reducing the value of bitcoins. Today's value of $240/bitcoin implies the average length of  time somebody holds onto a bitcoin is 7 years (assuming bitcoins handle 2% of the underground economy).

The value of politics

Can the government outlaw bitcoin, driving its value to zero?

The government has an excellent track record in this respect. They’ve bankrupted other popular electronic currencies, like “e-gold”. Americans can no longer obtain Swiss bank accounts, because the Swiss are tired of the U.S. government harassing them all the time. This means there is a serious risk that the government can either shut down bitcoin completely, or drive it underground severely reducing it’s usefulness and value.

But here’s the thing about bitcoin: it’s based on math, no organization controls it. Even if the government bankrupts public facing sites like Mt. Gox and throws its owners into jail, bitcoin transactions will continue.

Indeed, you could have the reverse effect: the more government shuts down competing currencies, the more valuable bitcoin becomes as the one currency the government cannot shut down. There will always be a huge demand for an underground, non-governmental currency that government will never successfully squash.

Conclusion: is this a bubble?

I've laid out arguments why bitcoins are worth as low as 1 cent and as high as 15 thousand dollars ($0.01 to $15000). So, should you be buying or selling right now with the value around $200?

Let’s say you bought at the height of the dot-com bubble. How much money would you have lost? At the height of the bubble, their stock price was $100 a share. Now it is near $300. You wouldn't have lost money, you would have instead tripled your investment. Of course, the other 99% of dot-com companies either went out of business or lost most of their value. Amazon is one of only a few companies that have held onto their value.

The point is this: just because it's a bubble doesn't mean it's a bad time to invest. Given certain assumptions, I've laid out a good argument why bitcoins could be worth thousands of dollars, much higher than the current price of $240. If you agree with those assumptions, you should be buying bitcoins.

The point is also this: the Internet did take off, exceeding the wildest dreams of even the most optimistic visionary. But this didn't mean that early dot-com investors made any money; most lost their shirts in the dot-com crash. Bitcoin could become wildly successful, accounting for a trillion dollars a year in transactions, all with a valuation of pennies-per-bitcoin. That means you can still lose a lot of money while being "right".

Full disclosure: I own 4 bitcoins (that I got from mining), and I have no plans to sell them. Neither do I have plans to buy any.

Update: since starting this post and completing it, the bitcoin bubble appears to have burst:


Anonymous said...

Looks like a DDOS attack or technical site issue then a true bubble bursting- price is at 198/BTC as of 2:23PT

Anonymous said...

It would seem that at those rates, mining is a profitable enterprise?

Craig Wright said...

Please read Have a look at Ch 6.

This is just the tip of the iceberg, but really, the analysis of this using armchair economics...

Craig Wright said...

And as for NO serious analysis... Please read some of the academic journals in finance, monetary theory, etc.

You have missed so much!

Craig Wright said...

Lastly. "The mistake economists make is assuming that bitcoin works like real money."

Really? You think money is money as a government prints it? Have a look at the history of currency. Where money started.

Robert Graham said...


I have looked at the history of money, and where money started. I have read a lot about finance, monetary theory, etc. You've got this weird "Appeal to Authority" critical thinking fallacy going on, claiming on I'm wrong, but not being able to form your own words as to what, specifically, is wrong. Please learn to speak in your own words, not somebody elses.

Modelling bitcoins-as-currency fails. For one thing, you can't create loans, charge interest, etc. Everything that we've learned about money in the last couple thousand years fails.

Modelling bitcoins-as-protocol is really what we should be considering. It's a way of exchanging currency online rather than a way of being a currency.

chris said...

I think you're mistaken about the effect of bitcoin not being legal tender.

All that means is that when settling payment due as a result of a contract, you can't foist bitcoins on the other party in lieu of payment. But the payment is still outstanding, can be enforced, and can be repayed in a legal tender.

You can still draw up contracts involving bitcoins and then settle in dollars -- as you say a hard currency.

I think people could lend and borrow bitcoins just like they lend and borrow cars and lawn mowers. In the event of a dispute, the courts can and probably will treat bitcoin like an ordinary good -- either return the bitcoins or compensate the lender with a suitable payment in dollars.

h16 said...


I have found your post quite interesting and I would like to know if you would be ok if I (or somebody) would translate it into french for publication on a french web newspaper ( ?

Robert Graham said...

Yes, you can translate. Post a link so I can read it, s'il vous plait.

gruvr said...

Nice thinking and exposition.

I've made the argument that bitcoin DOES have an innate value similar to that of a coupon, in saving transfer costs normally required by banks etc.

That is, bitcoin provides functionality of reliable token transfer which normally requires an intermediary like a bank. If you transfer $100K of bitcoins you pay almost nothing, compared to the fees and other overhead costs of using the current financial system.

Here's (draft) blog post I'm writing I'd love some feedback on it from others trying to reason about value.

Anonymous said...

You are incorrect that the government will not force you to pay back a bitcoin loan, or that the government will not enforce theft of bitcoins.

Just because bitcoins aren't "money" doesn't mean they're exempt from all laws. People can make a contract about any item, money or not, and the government will enforce that contract. There's an exception for contracts to do illegal things, but in general if I loan you 1000 bitcoins for a week at a non-usurious rate of interest, a court will force you to pay me what we agreed if you breach the contract.

Indeed, whatever valid contract we make, the government will enforce the breach of it, whether the subject of our transaction is money, bitcoins, gold bars, real estate, or candy bars.

Similarly, stealing bitcoins is a crime in every jurisdiction I'm aware of, and is civilly compensable even without a contract (e.g., pursuant to the tort of conversion).

Bitcoins are sometimes used for illegal purposes. So is money. Doesn't mean bitcoins exist in a special lawless universe. They are part of our world, just like everything else.

h16 said...

@Robert Graham
I will, thanks.

Anonymous said...

So why can't you use loans etc? It's all based on trust etc...and I get that. Sometimes trust is based in a specific authority (as in the US government laws) or a distributed authority (such as a reputation system as in Daemon by Daniel Suarez).


h16 said...

@Robert Graham : the link to the french translation is this one :

Enjoy :)

sunny kumar said...
This comment has been removed by the author.
Luke Clifford said...

I think a lot of the points covered in this are correct enough. But for actual indepth understanding of the BitCoin market, I think some actual sourced books might be worth a read.

I've actually posted a few links to some of the books i've been reading on my own site:

Feel free to take a look and leave any feedback. :)

Anonymous said...

First bad post in a long time.

Your rational looks like this: if it's a not a FIAT currency backed by a government it's not _REAL_ money.

That, sir, it's just bullshit.

Living Waters said...

Really, we all need to think about the bigger picture of this. Anyone can barter and trade for a bitcoin, nickel, Deutschmark, or whatever. But, I know people who are trading good dollars for bitcoins in anticipation that the price will keep going up. iTechCentral has posted a writeup in comparing bitcoins with wooden nickels, it's a good read for anyone looking to grasp the bigger picture of bitcoin economics.

Ken Shirriff said...

You have an extra factor of 60 when you compute $2-trillion divided by (365*24*60*2), so you're assuming a 30-second bitcoin holding time, not 30 minutes. Fixing this makes your minimum bitcoin value about 11 cents.