The Stock-to-Flow model (S2F), invented and popularized in 2019 by PlanB in the piece “Modeling Bitcoin Value with Scarcity”, is one of the most popular price theories for bitcoin, suggesting that the S2F of bitcoin is what drives its price.
The popularity and credence of the model was earned mainly through three parts of supporting evidence:
- high R-squared between the log of S2F <> log of marketcap (~0.95)
- a cointegration test suggesting a more fundamental relationship between those same variables (Nick Emblow’s Aug 2019 study)
- the relationship being consistent also for other scarce assets, such as gold
List of counter-evidental discoveries and events
During the recent months, a series of interesting reveals have been made by various people, weakening the case for the S2F model and its supporting evidence. Each item in the list below addresses one supporting argument above. These are the recent highlights that I think have been most instrumental in tearing the S2F model apart, beyond the more fundamental criticisms that have been aired by many since the beginning.
- March 11: GeertJancap looks at 50 years of gold S2F data and finds no relationship between gold’s S2F variations and its value (marketcap)
- March 23: First sighting of Nick Emblow detecting a serious error with the cointegration test (“this is a problem” tweet) (screencap)
- March 27: Nick Emblow giving a detailed account of why the cointegration tests were invalid, switches to ARDL-based cointegration testing instead
- April 27: PlanB proposes “S2FX”, according to Nick Emblow as a means of escaping the cointegration deficiencies of the original S2F model (Nick’s comment (screencap))
- April 28: Sebastian Kripfganz (time series expert, University of Exter, author of the ARDL command Nick Emblow used) explains why the ARDL-based cointegration test isn’t applicable either
- April 29: (deleted tweet) Nick Emblow admits error, asks “Maybe S2F is bullshit after all?”
- May 6: Marcel Burger shows Saifedean that a simple counter keeping track of how many times he goes to the toilet (modeled as if he goes to the toilet 1–3 times a day with a uniform distribution) is just as highly correlated (R-squared value) with the bitcoin marketcap as S2F is
- May 12: Sebastian Kripfganz gives a presentation at Value of Bitcoin, achieving two things: 1) aggressively refuting cointegration, 2) finding no statistical evidence for a relationship between S2F and the bitcoin price
- May 20: Marcel Burger publishes a thorough “The Fall of Cointegration” walkthrough (Why S2F and bitcoin price can’t be cointegrated)
- June 11: Nick Emblow finds that the number of bitcoin in circulation is just as highly correlated (R-squared value) with the bitcoin marketcap as S2F is, and thus becomes completely convinced that the S2F correlation is entirely spurious (coincidental) (screencap) (image linked)
- June 30: Nico Cordeiro, Strix Leviathan LLC, looks at 115 years of gold S2F, still not finding any correlation between gold S2F and marketcap
- Update: Nick Emblow: “Bitcoin S2F model is fun, but basically wrong. After accounting for the autocorrelation in the residuals the coefficient for log s2f becomes almost zero (meaning: almost irrelevant)”
S2F model is fun, but basically wrong. After accounting for the autocorrelation in the residuals the coefficient for log s2f becomes almost zero (meaning: almost irrelevant).
It’s quite telling that even the main boosters of the S2F model (the ones applying the most sophisticated statistical analysis, on which the Bitcoin community has thus far relied) eventually turned on the model due to the lack of sound econometric assumptions.
Notably, Nick Emblow and Marcel Burger are now both vocal critics of the S2F model (an impressive testament to their intellectual honesty, which I’m very thankful for).