Modeling previous century’s US Industrial Production Index with the Scarcity of bitcoin. Not joking.

Source data

A proxy for bitcoin’s Scarcity is the Stock-to-Flow ratio, which can be obtained from the bitcoin blockchain as the number of newly mined bitcoin on a given day divided by the total number of bitcoin in circulation on that day. Data can also be found here.

The MarketCap of bitcoin is found here.

These two data sets both have 1112 data points.

The US industrial production index is found here, from Jan 1919 to Aug 2019, as monthly data. This data set has 1208 data points. We truncate it arbitrarily by using the data from the last 1112 months only, meaning we only use the data from Jan 1927 to Aug 2019.

We now have three time series: Scarcity, MarketCap and Production, all with 1112 data points. These can be stored as three columns in Excel, of which figure 1 shows the top and the bottom parts.

Figure 1: Scarcity and MarketCap of bitcoin at the specified day, and the US Production Index in the specified month

Next we take the natural logarithm of Scarcity, MarketCap and Production (the underlying reason is that we are looking for a power-law relationship, see here):

Figure 2: The natural logarithms of columns B, C and E in figure 1

Results

Now we are ready to make some scatter-plots in Excel. The chart of Scarcity vs. MarketCap, with the best fitting regression line is:

Figure 3: Bitcoin Scarcity — MarketCap plot

This is almost identical to the main plot in PlanB’s paper and to my reproduction of that.

The chart of Scarcity vs. Production, with the best fitting regression line is:

Figure 4: Bitcoin Scarcity — US Production Index plot

Overall correlation is high, and zoomed in on the part of the chart where ln(Scarcity) is between 1.5 and 3.0 there is a high tendency for the scatter points to follow the regression line, more so than in the Scarcity-MarketCap plot. Are we up to something here?

Discussion

Daily bitcoin scarcity measured from 2010 until 2019 is highly correlated with monthly US production levels from 1919 to 2017, even higher correlated than than bitcoin’s market capitalization measured on the same dates as bitcoin’s scarcity.

Isn’t that amazing? No. It’s not. Bitcoin scarcity is programmed to go up with time and so it does. Production levels in the US did go up over time as well. Any two mainly growing time series are correlated. Without any causality, or even a remote connection between the sources that generate the data.

Correlation plots are highly suggestive. They can make complex processes look extremely simple, just by probing two phenomena from such process, plotting them against each other in a scatter plot, and fitting a straight line through the data pairs.

Demonstrating a high squared correlation coefficient R² between two variables is insufficient to conclude that these two variables are related in the non-mathematical sense of the word, and even concluding that the two variables were sampled from the same process might be wrong.

There is another argument against a direct relation: Ethereum, the second longest existing cryptocurrency platform, doesn’t have halvings, and therefore StockToFlow is growing way slower. Still, Ether’s value has just as spectacularly grown over time as bitcoin, by a very similar population of traders, hodlers and speculators.

The conclusion that bitcoin’s market capitalization is related to bitcoin’s scarcity on the basis of a straight line and a high correlation value is at the least ‘questionable’. I don’t (dare to) say that it’s not there, but more work needs to be done.

My suggestion is to throw so-called co-integration tests at these two data sets. Claims are being made that co-integration is different than correlation, and more powerful. This made Nick write the magnificent sentence: Bitcoin is the drunk and Stock-to-Flow is the road home, on the basis that co-integration tests on Scarcity-MarketCap data could not falsify PlanB’s relationship. It would be great to see if these same tests applied to my deliberately spurious correlated Scarcity-Production data would falsify. If they do that would be terrific. If they don’t, we would not have learned much, only demonstrated how easy it is to be fooled and impressed by nice looking charts and methods. Because we do have a drunk and a road home here, but the drunk is not on the road!

Thank you for reading!