A more modest role for Scarcity on bitcoin?
PlanB claims that Scarcity drives MarketCap. But is it really?
Introduction
Bitcoin papers built upon power-law relationships have gained some traction recently. The straight line in a log-log chart or the curved, gradually less steep line on a lin-log scale are appealing, and suggest that a simple mathematical formula describes the bulk of bitcoin properties quite well.
I have contributed to this, with three papers. One of these caught the most attention, likely because I reproduced the results by PlanB, who made quite an impact on the bitcoin community with his stock-to-flow paper.
Sometimes a power-law relationship is hugely informative. If we know the distance of a planet to its sun, the power-law allows us to calculate its orbital time. This is Keppler’s third law and seems to be valid across the universe.
At other times, the power-law is less informative. Even if the suggestion of a strong relationship is there, it may only reflect that there are other common factors co-driving the two variables.
PlanB tries to get the point across that Scarcity drives MarketCap. But is it really?
Analysis
Starting with the data on a high time resolution, as I have shown in my previous paper, there are three variables:
- Time, the number of days from 3 jan 2009 = Genesis of bitcoin
- Scarcity, the stock-to-flow ratio
- MarketCap, (Price of bitcoin) x (number of bitcoin in circulation)
Power-law analysis typically starts by plotting one variable against another on a logarithmic scale. A regression line is then computed with a Slope, an Intercept and a R² value. The square root of the R² value is R, the correlation between the two variables.
Correlation is a form of bi-variate analysis, where we look at pairs of observations. Essentially we study each pair in isolation. Multivariate methods analyse three or more variables simultaneously. Partial correlation is such multivariate method. Like normal correlation, partial correlation also expresses the strength of a linear relationship between two variables, but after removing the influence of a third variable (and a fourth, fifth etc.). It is the first step towards translating correlation into causality. If a high correlation between two variables collapses when partialized to a third variable, the correlation is caused by the third variable driving the two. The mathematical symbol for correlation is the greek letter ρ (rho). Correlation between two variables X and Y is written as ρ(X,Y). Partial correlation is written as ρ(X,Y·Z). Often R is used instead of ρ, and its squared value R².
Partial correlation with three variables can be computed from the three normal correlations:
Applied to the trio Time, Scarcity and MarketCap this results in the following correlation and partial correlation values, on all data until today:
- ρ (Time, MarketCap) = 0.969
- ρ (Time, Scarcity) = 0.978
- ρ (Scarcity, MarketCap) = 0.949
- ρ (Time, MarketCap · Scarcity) = 0.621
- ρ (Time, Scarcity · MarketCap) = 0.748
- ρ (Scarcity, MarketCap · Time) = 0.043
A graphical representation of these results is:
Conclusion
From the current data available for bitcoin, it appears that Time drives both Scarcity and MarketCap to a large extent. That’s the reason for the high correlation between Scarcity and MarketCap. There doesn’t seem to be an additional driving force by Scarcity on MarketCap.
In a next article I will apply a multiple linear regression model on Time, Scarcity and MarketCap, to elaborate the relationship between the three variables in linear formulas. The conclusion is identical: Time drives Scarcity and MarketCap, and Scarcity doesn’t drive MarketCap.
All of this does not mean that Scarcity is not an important characteristic of bitcoin, it’s only saying that for MarketCap modeling and forecasting via extrapolation we can do without.
Thank you for reading!
