Considering Crypto-Currencies and Difficulties with NGDP Targeting

Today, in considering nominal GDP targeting under a non-legal tender, crypto-currency standard, I discovered that what seemed like an obvious solution to the problem of NGDP targeting is actually quite complicated. Justin Merill asked,

Theoretical question: if there were a digital currency, let's call it NGDP coin, that adjusted its supply to target NGDP, how do you imagine it happening or what is the ideal mechanism?

Let's take for granted that it is not a national currency and not intended to target the NGDP of a geographical region.

The good news is that the ledger makes it incredibly easy to calculate NGDP because you know both the size and quantity of transactions. But if the currency becomes more widely adopted, would it warrant a shrinking of the supply of currency? Financial transactions would be included in the calculus, is that problematic? This would be more like Fisher's version than Friedman's.

The other potential problem is what is the reaction function? Over what time period should it average the transactions and make adjustments? If volume cuts in half in one day, it would seem odd to double the currency.

Seems like a good idea right? All the data is there, so why not target actual changes in NGDP as defined by the crypto-currency? My study of the gold standard has taught me that the adoption of a standard is complicated and breeds unexpected difficulties. Increased use of the currency is the equivalent of an increase in demand assuming that the definition of the price level remains constant, and most importantly, does not include FX transactions.

Justin and I had a fruitful exchange in considering the problem.

Jim Caton: Wider adoption would be equivalent to a drop in V (a rise in k), thus meriting an increase in M if the goal is to target NGDP. Otherwise, P must drop as the money will be used in more transactions. If P is sticky downward, will lead to a drop in y.

Justin Merill: But FX transactions would be included as V, would they not?

Jim Caton: But then you are changing the definition of P to include FX transactions, which does not solve the problem. Depending on the index, we can target input goods or consumer goods or both.

Justin Merill: But then that becomes problematic for calculating since as stipulated, it isn't restricted to a geographic region. It has to be self-referential somehow.

Justin Merill: I guess you could survey participants at the time of transaction if this is a "real" transaction of goods/services or a financial transaction, but that seems tedious.

Jim Caton: Yes, so it appears that the problem is not as simple as it looks at first. It would as though we included all currency transactions as part of GDP if we were to use only the raw data. Since fx trading is recorded, you could take (total nominal expenditure) - (expenditures in exchanges that are not included in your index).

Justin Merill: That would be tricky if you have decentralized exchanges. Yeah, the whole thing is tricky.

The trick is that, even though the initial adoption of a currency by an individual requires a transaction, that transaction is not considered in the measure of the price level, and therefore velocity has not changed. The crypto-currency economy has experienced an increase in y according to the equation of exchange, MV = Py. This is not necessarily true for the economy as a whole, which includes exchanges that don't employ the crypto-currency. Changes in the crypto-currency money stock, M, should therefore target changes in y that do not represent actual changes in production - i.e., increases in y that result from the expansion of the crypto-currency economy - in addition to changes in V. If the whole economy has experienced growth, M should not be adjusted to match changes in y that represent real growth, only changes in y that represent increased adoption of the currency.