Then there's the problem that bitcoin is an international currency and GDP is a measure of national economies. As far as I know, Sumner does not have a theory for optimal monetary policy for a currency shared by a coalition of nations (i.e. the EU). The management of the Euro roughly stabilizes NGDP in Germany, but not in Italy and Spain which is the source of the current crisis in Europe.

On the other hand, an old-fashioned monetarist coin (constant rate of increase - "Friedman Coin") would be easy to implement and a lot better than a fixed supply coin. I'll leave others to figure out the "Sumner Coin".

Who gets the extra Friedman coins? Also if you don't have a central bank stabilizing the supply of money via interest rates in response to velocity changes things can go to crap very quickly a la the Great Depression.

The problem with NGDP is the D. As far as I know, there is nobody (including Sumner) that believes the total nominal transaction volume of an arbitrary subgroup of international users should grow at some low constant rate over time.

Remember that MV = PY, Money Supply times Velocity equals Price Level times Real GDP. PY is nominal GDP, Y is real GDP. AFAIK, Sumner's followers argue that M should grow so that PY grows at some constant rate. V is assumed to be endogenous.

Now think of two countries with similar sized economies that share a currency. Imagine country 1 had Y growth of 3% and country 2 had Y growth of -1%. How should M change? As far as I know, this is virgin territory. Also, country 1 and 2 are basically Germany and Greece.

NGDP is easy to calculate for the users of bitcoin as every transaction is encoded in the blockchain. Of course, you are right that there is a difficulty because of a rapid unstable increase in V due to adoption, the NGDP of the Coin economy is measuring the economic activity of its users + some amount of canibalization of the legacy dollar economy. If you are looking for the "right" answer, I think it will elude you. But I have a "good enough" proposal for a Sumner Coin - start with the BTC reward scheme, and after PY stabilizes (i.e. changes less than 10% per month), use that as the base for PY and then set block rewards to grow PY by a constant amount. V is public so it is easy to calculate the appropriate M.

The Friedman coin is much simpler, since you are pegging M to a growth rate and not PY. Of course, the miners get the extra coins.

Both models decrease first mover advantage and relieve the need for transaction fees for stability of long-term mining. And for both models I would recommend an initial deflationary period to sweeten the pot for early adopters.

But it's more interesting how the Bitcoin monetary policy compares to the current real-world human-controlled monetary policies of government money - which in the cases of most countries is definitely pure instability and filled with error.

The Bitcoin monetary policy doesn't have to be perfect to be an improvement, because the status quo is very imperfect.

I'll give you 1 BTC on April 1st, 2013. You can repay me 1.5 BTC on April 1st, 2014, adjusted for deflation or inflation according to mtgoxUSD × CPI, as the case may be.

Problem solved. I give you spending power today, you give me more spending power later on, and we conduct the transaction in Bitcoins.

In the future, we will have our choice of price indexes that are denominated in Bitcoins directly.

On a planet with a growing economy and a growing population, Bitcoins will always be appreciating faster than material investments can grow. If you can plant 100 seeds to get back 103 seeds (3% material interest) and also the planetary population is growing at 2%, that's 5% interest on Bitcoins. Except then people try to hold more Bitcoins since they grow faster than seeds, which makes Bitcoins appreciate even faster... but even before taking that into account, you still wouldn't be able to grow enough seeds fast enough to pay back a loan in BTC, if the planetary economy used Bitcoin.

The deflationary process makes things much worse; the more people try to hold Bitcoins, the fewer circulate and the lower the velocity, increasing the apparent price of Bitcoins. This process continues until instability in the price of Bitcoins as people occasionally dump their hoards is so great that Bitcoins stop appreciating. Then fewer people want to hold Bitcoins and they dump their Bitcoins and the velocity goes up and the price goes down and the bubble pops.

(The reason this doesn't happen with existing central bank currencies is that central banks regulate interest rates to stabilize the supply of money and hence its price in response to velocity changes, or at least they're supposed to. The reason this doesn't happen with equities is that they have an intrinsic rate of return due to dividends or stock buybacks; real estate has intrinsic rent; bonds have returns denominated in stabilized money.)

So like I said, Bitcoin is a horrible crackpot theory of money as a store of value, married to a beautiful transaction settlement mechanism.

I am happy to offer you the loan, because Bitcoin prices are volatile and there is no guarantee if I keep my Bitcoin in storage that it will still be worth much one year from now. There have been many crashes. But if you agree to repay me an amount equivalent to 1.05x my current spending power then I know whatever you pay me I'll be in a better position than I am today in terms of my ability to pay my rent.

Such a loan offers me a drastically different risk profile than holding Bitcoins. If BTC were as guaranteed to increase as you say then they would cost more.

This is a loan denominated in dollars, it's just being transaction-settled via Bitcoin. The medium of account is dollars and the medium of exchange is Bitcoin. This is pretty much exactly the original point I was talking about. :)

People earn to consume. The bitcoin rich, if they apply the Kelly criterion to their own portfolios, will diversify into whatever assets will provide them a regular real dividend. That is, farms yielding grain, orchard yielding fruit, NG wells yielding NG, wind farms yielding electricity. They will not be buying any investment for the purpose of money, but for the purpose of CONSUMPTION.

There lies the negative feedback that will stabilize any new currency as it conquers the world.

I'm actually not totally sure if NGDP-LT is optimal in a free-banking scenario though. But certainly some sort of value stabilization is.

Is it implausible that these two forces would reach a relatively stable equilibrium, like stocks?

What ultimately sets the price of stocks (and prevents undue speculation) is the profit earned by a company.

This mechanism doesn't exist in currencies, where the value comes only from what people think it's worth.

Nobody does. Now why is that?

Friedman understood perfectly well that failure to increase the money supply in response to decreasing velocity was responsible for the Great Depression. He's sort of famous for that part, if I understand economic history correctly, it's why Bernanke apologized to Friedman's memory on behalf of the Fed. It seems odd to call them 'Friedman coins' when they depreciate automatically, but don't adjust to velocity and especially to changes in fractional reserve lending.

Probably executive order 6102 in 1933. By the time the government allowed private ownership of monetary gold again, it had fallen out of use as currency.