The Ammousian Stock-to-Flow model
Abstract: Employing the Stock-to-Flow definition of Saifedean Ammous, we get better cointegration results than with the classical (PlanB) definition. Switching to this definition doesn’t solve all problems around the SF models but is well worth investigating. The problems relating to the determinism-debate however are persistent.
Introduction
In SLP 171 PlanB and Saifedean Ammous discussed an SF model based on (what I call) the a priori definition of SF, i.e. SF as it would be if from Jan 9th 2009 every day there would have been 144 new blocks. In an OLS regression, that random variable performs amazingly well giving an R² near 1. But why wouldn’t agents update their beliefs about future flow with newly available information? This article explores the properties of an SF model in which agents take the current blockheight into account to update their beliefs about future flow.
It is organized as follows: ‘Definitions’ differenciates the classical, from the a priori and the Ammousian SF. It briefly comments on their theoretical significance. ‘Results’ presents the results of the statistical analysis of the ‘Ammousian’ SF model. ‘Discussion’ I raise some concerns as to the validity of the model and possible routes of argument that preserve the tight relationship between BTC-price and SF. ‘Conclusion’ recapitulates all very briefly.
Definitions
The a priori definition of SF looks at the SF ratio that would prevail if every day miners found exactly 144 blocks. Note, that one can think of different flavours of this definition: it could be backwards-looking dividing a priori stock by the a priori flow of the previous month or forward-looking, taking the relevant flow to be the a priori flow of the coming year. Put into Math the a priori stock (from a priori stock, every flavour of a priori flow and thus SF is derivable) is:
The classical definition: PlanB in “Modelling Bitcoin’s value with scarcity” used a definition of SF that was backwards-looking. It takes the flow of the past month, and extrapolates it to one year before dividing stock by it. Thus, classical SF is defined as:
What I call the Ammousian definition of SF is taken from “The Bitcoin Standard”. There, Saifedean Ammous defined SF this way: “We can understand money’s hardness through understanding two distinct quantities related to the supply of a good: (1) the stock, which is the existing supply, consisting of everything that has been produced in the past, minus everything that has been consumed or destroyed; and (2) the flow, which is extra production that will be made in the next time period.” (page 5) Thus, I take Ammousian flow to be the a priori flow of next year updated by considering the current blockheight. Thus, Ammousian SF right now (last update before publication was around blockheight 630500) is approximately 18,378,000/(144*365*6.25) ≈ 56.
While the Ammousian definition is still somewhat naïve, assuming that in the next year exactly 144*365 blocks are going to be found, that is even more so for the other definitions, but this depends on what argument one is trying to make. If one wants to argue, that SF itself is a target, which might actually be the case, now, that the model has gained so much popularity, then we would prefer a forward-looking SF variable. For that the classical view is not very well suited because the halving only fades in after the fact, while e.g. the Ammousian flow would start ‘preparing’ the halving one year in advance. On the other hand if one argues that SF merely captures underlying processes, the classical definition shines. An example of such an underlying-procecess-explanation might be that miners need to increase their price post-halving in order to cover their expenses and the price-rise triggers a bull run. During the bull-run Bitcoin’s supply might be inelastic, prolonging the run but also attracting more miners such that hash-rate increases and ‘locks miners’ in the higher prices.
Thus, which definition is best, depends on what you are trying to argue. Or the other way around, if the model with one definition clearly outperforms the others, that is a hint at what the causal mechansisms at play might be.
Results
The Ammousian SF model really does fare better in a Johansen cointegration test:
But cannot convince any Engle-Granger test with up to 30 lags:
Those are generally not good results. They are problably driven by the fact that cointegration is not the right thing to look at. As Sebastian Kripfganz pointed out, SF might not be stochastic (enough) to be able to cointegrate with a true I(1) series. This is what I call the determisism-debate.
Conclusion
Even though both tests should at some point reject the null of no cointegration, not even datamining/p-hacking can get the EG-tests to do that. But possibly even more serious is the issue of determinism. I wrote a whole article about that issue, so I will not repeat myself here. In light of these issues, however, it seems more and more unlikely that the halvings directly translate into Bitcoin value growth. We still have to live by the motto “Did I do anything today, so Bitcoin is more valuable in the future?” and keep improving Bitcoin piece by piece. Hyperbitcoinization will not happen due to SF-magic but only as a result of us having the best money available. Let’s not indulge in price achievements, even Silver was dear at some point. It is we, who make Bitcoin more valuable. Elf out.
Resources:
Reproduction-Package (at GitHub)
