Introduction

Recently Plan B, an early Dutch bitcoin adopter who anonymously shares his insights via Twitter, came out with an article [1] that dives into the relation between bitcoin’s price (and market cap) and the stock-to-flow ratio. It has attracted a lot of attention and the crypto community really praises his analysis. People fell in love with the conclusions that followed from his analysis, which is easy to understand as it predicts future price levels of six figures and more. Even though the idea of investigating market capitalisation or price as a function of stock-to-flow ratio’s is very interesting, one should respect the underlying model assumptions that hold for ordinary least squares regression. In this article I’ll pinpoint the flaws of the analysis, and I’ll have a look at alternative methods to come up with an improved model in a follow up article. I can’t guarantee I can find a model that is statistically significant and respects all the imposed assumptions though.

Respecting the assumptions

Plan B attempted to fit a model that describes the relation between the natural logarithm of bitcoins market cap and the natural logarithm of the stock-to-flow ratio by means of ordinary least squares regression. The standard set of 4 (Gaus-Markov) assumptions that needs to be respected (see Verbeek, Modern Econometrics [2]) are as follows :

- (1) The expected value of the error term is zero (which means that on average the regression should be correct)

- (2) The error and the independent variables should be independent.

- (3) The error term should be homoskedastic (i.e. error terms have the same variance)

- (4) There should be zero correlation between different error terms (i.e. autocorrelation is excluded)

Together, (1), (3) and (4) imply that the error terms are uncorrelated drawings from a distribution with expectation zero and constant variance. If the above assumptions are not met, the standard errors of the coefficients might be biased and therefore the results of the significance tests don’t mean that much anymore. In order to draw conclusions based on the ANOVA results, we also have to check if the underlying model assumptions hold.

A review of plan B’s model

To make sure the review is appropriate, I have used Plan B’s dataset. In my own dataset I’ll introduce some improvements, but for now his dataset is used. After running the…