Modeling Bitcoin Value with Abundance
Disclaimer: This is not financial advice and does not constitute a solicitation to buy or sell any financial instrument and/or virtual currency such as Bitcoin. You should always do your own research and consult a professional financial advisor before investing. The views herein represent the private views of the author only and not necessarily of his employer.
Scarcity and Abundance
As we all know, Bitcoin is a scarce asset. Bitcoin’s algorithm dictates a strict inflation rate that halves approximately every 4 years and which currently stands at around 1.7% per annum. Bitcoin’s Stock-to-Flow ratio, which measures the circulating supply of Bitcoins in relation to annual production, currently stands at around 60 years, meaning that it would take 60 years for Bitcoin’s supply to double if the current rate of production was maintained. However, the terminal amount of Bitcoin is ultimately capped at 21 million coins.
On the other hand, we also know that Fiat monies like the US Dollar are anything but scarce. The banking system (commercial & central banks) is capable of creating money ex nihilo (“out of nothing”) which is a well-documented fact. Theoretically, this credit and money creation has no limits except that commercial banks have to avoid non-performing loans and write-offs in order to comply with the equity requirements dictated by the Basel Accords.
Although some central banks like the ECB comply with accounting standards like the IFRS, central banks are essentially not obliged to follow standard accounting practices and can even run negative equity without legal consequences. As a matter of fact, central banks cannot become insolvent in their own currency (that they create ex nihilo) but only in foreign currency. An important aspect that goes a long way in explaining why governments and central banks sometimes resort to the practice of deficit financing via the central bank (aka “Overt Monetary Finance”).
The debate about monetary inflation has recently gathered pace with the extreme amount of money created due to the Covid-19 pandemic. In 2020 alone, the US liquid money supply (M1) has increased by 65%. Even the most-aggregated measure of US money supply (M3) has increased by 25% in 2020. In other words, from the amount of Dollars that are currently in existence, approximately 1/4 has been created in one year alone. The monetary base, which is the amount of money that the Fed credits financial institutions for its open market operations, has increased by 52% in 2020 alone. Thus, we can clearly say that money is being made abundant.
Plan B famously explored the valuation of Bitcoin via its scarcity based on the Stock-to-Flow Ratio. The model focused on the supply side of Bitcoin valuation. Recent econometric evidence suggests that the simple relationship between the log of Stock-to-Flow Ratio of Bitcoin and the log of Bitcoin price is most-likely spurious if one accounts for serial correlation of the residuals via a Prais-Winsten regression. 
Although I personally think that the supply side of Bitcoin could be sufficent to model Bitcoin’s price fluctuations based on the short-side principle (disequilibrium economics), this article rather tries to explore the demand side of Bitcoin valuation.
What can Weimar tell us about Bitcoin?
One of the poster childs for money creation gone bad is probably the so-called ‘Weimar Hyperinflation’ which took place from around 1921 to 1923 in Germany. Under the heavy burden of World War I reparation payments, the German government was eventually forced to pay its conquerors via the “printing press” which led to a strong depreciation of the German Mark and a simultaneous ballooning of consumer prices and the general cost of living in Germany.
To put things into perspective, in 1920 one US Dollar bought 73 paper Marks. In 1923, one US Dollar was exchanged for 4.2 trn paper Marks — a depreciation of 57 billion per cent. At the same time, the general cost of living increased by 107 billion per cent, the German stock index by 98 billion per cent and an ounce of Gold measured in German paper Marks increased by 57 billion per cent.
Price increases were so astronomical that there was even a novel mental illness detected where people suffered from the need to write down zeros. As real wages plummeted, a large proportion of the population plunged into poverty as well. The German Mark and the economy only stabilised when the government declared a range of measures including the return to a gold-backed currency and a promise to back the German Mark with tangible assets such as real estate in Germany.
“Inflation is always and everywhere a monetary phenomenon.”
— Milton Friedman
Famous economist Milton Friedman and the Monetarist school of thought were convinced that inflationary developments are ultimately related to money creation. Frenkel (1976) has analysed this notion with respect to the German Hyperinflation of the 1920s from a monetary perspective. As German money creation dynamics became significantly higher than in other countries, they became increasingly evident in the German Mark exchange rate and the general cost of living.
In fact, Frenkel (1976) found a significantly-positive relationship between German money supply growth and the depreciation of the German Mark vis-à-vis the British Pound Sterling (DM/£) during the Weimar Hyperinflation (from February 1921 until August 1923). Frenkel’s research has amongst others motivated a large amount of research on that subject that ultimately relate inflation to currency depreciations. For instance, The Troubled Currencies Project of the Cato Institute utilises currency depreciations to approximate the “true” inflation rate in any country.
Nowadays, the money creation dynamics of the United States have also become significantly different from the rate of money creation in the Bitcoin network (>50% US M1 growth vs. 1.7% Bitcoin growth). Based on the abovementioned reasoning, as the Bitcoin supply is basically inelastic with respect to changes in price, the US Dollar/Bitcoin exchange rate could also potentially be a yardstick for the “true” extent of inflationary developments in the United States and particularly the amount of money creation.
The Monetary Abundance Model of Bitcoin
In this article, I will use Frenkel’s monetary approach to analyse Bitcoin’s recent price developments vis-à-vis the US Dollar (USD per BTC).
Frenkel (1976) has stated the following relationship:
log (S) = α + β1*log(M) + β2*log(π) + ε
with S as the spot exchange rate; M as the money supply and π as the inflation expectations inherent in the forward exchange rate premium/discount, i.e. the forward exchange rate “basis”. Frenkel has defined π = 1 + π* in order to avoid unreal numbers with π* being the forward exchange rate basis which can also be negative.
I will use Frenkel’s approach here in order to estimate the following relationship (“Monetary Abundance Model of Bitcoin”):
log(USD/BTC) = α + β1*log(US M2 Money Supply) + β2*log(1+ USD/BTC Forward Basis) + ε
The relevant data are taken from the following sources:
- US M2 money supply (FRED): https://fred.stlouisfed.org/series/M2
- USD/BTC spot exchange rate (Coinmetrics): https://coinmetrics.io/newdata/btc.csv
- USD/BTC forward basis (Bitmex): https://s3-eu-west-1.amazonaws.com/public.bitmex.com/data/trade/
The data sample ranges from November 2014 until January 2021 and is dictated by the fact that earlier data on Bitmex forward exchange rates or other forward exchange rates are not available. I will use monthly data in this analysis. The Forward Basis is implied from the respective traded Bitmex contracts. I take daily averages of the respective forward basis, that I annualise based on the act/365 convention. Thereafter, the annualised forward basis is smoothed with a Hodrick-Prescott Filter in order to smooth the extreme variations around contract maturity dates.
Before estimating the abovementioned model, let’s take a look at the simple relationship between US M2 money supply coincident and lagged with respect to the USD/BTC exchange rate in logarithms. I will utilise a Prais-Winsten regression in order to account for the serial correlation in the residuals.
Apparently, only Log(M2) lagged by one month appears to significantly correlate with the log of the USD/BTC exchange rate. This implies that US money creation influences Bitcoin with a lag of one month. I will use this finding in the subsequent estimation of the “Monetary Abundance Model”.
If we estimate the second abovementioned equation (‘Monetary Abundance Model’) with US M2 money supply lagged by one month and the Bitcoin forward basis, we get the following result (Prais-Winsten regression again):
Accounting for potential inflation expectations inherent in the Bitcoin forward basis, the coefficient for the US M2 money supply is still significantly different from zero with respect to the USD/BTC spot exchange rate.
The coefficient is close to 6, implying that an increase of the US M2 money supply by one unit increases the USD/BTC spot exchange rate approximately by the order of 6 one month afterwards.
Although the magnitude differs from the findings by Frenkel (1976), who found a coefficient close to 1 with respect to the German Hyperinflation period, these results support findings by other analysts such as Willy Woo who found that a Dollar invested increases Bitcoin market cap by approximately 3.30 Dollars. Thus, these findings also imply that US money creation is currently magnified in the BTC/USD exchange rate.
Unfortunately, the “Monetary Abundance Model” appears to explain only a minority of variations of the USD/BTC exchange rate judging by the low R² statistic of only 28%. This implies that other factors that have not been incorporated into the model such as scarcity could be important.
However, if we incorporate the simple Stock-to-Flow Ratio into the abovementioned model as a robustness check, the Prais-Winsten regression implies that the log of the Stock-to-Flow Ratio is not significant at the 5% significance level and even exhibits a negative(!) coefficient. The Bitcoin forward basis has also been rendered insignificant by the inclusion of the Stock-to-Flow Ratio. However, US M2 money supply remains highly-significant.
We leave the exploration of other variables in the “Monetary Abundance Model” for future research.
All in all, the findings imply that “Weimar” could tell us a lot about the recent price developments in the USD/BTC exchange rate and that Bitcoin could potentially be a superior hedge against monetary debasement as US money creation empirically appears to be magnified in the USD/BTC exchange rate.
The “Monetary Abundance Model” also implies that the workings of the Frenkel (1976) approach to Hyperinflation already appear to be evident in the current USD/BTC exchange rate and that excessive money growth is likely to be a major support for Bitcoin going forward.
Thanks for reading!
 Plan B on Medium: Modeling Bitcoin Value with Scarcity
 Btconometrics on Twitter: https://twitter.com/btconometrics/status/1358361736303177728
 Cato Institute, The Troubled Currencies Project; Link: https://www.cato.org/research/troubled-currencies
 Willy Woo on Twitter: https://twitter.com/woonomic/status/1314600000286982144
Frenkel, J. A. (1976), “A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence”, The Scandinavian Journal of Economics, Vol. 78, №2, Proceedings of a Conference on Flexible Exchange Rates and Stabilization Policy (Jun., 1976), pp. 200–224
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About the author of Avantgarde Digital Research Blog:
André Dragosch has been working for almost 10 years in the German financial industry, mostly in Portfoliomanagement and Investment Research. He is currently working as a cross asset analyst and investment strategist at one of the largest German asset managers in Frankfurt where he is also responsible for digital asset research and in particular Bitcoin. He is currently doing a PhD as well in financial history at the University of Southampton, UK, where amongst others Prof. Richard Werner has supervised his work. He is been a private crypto investor since 2014. He is a married father who loves playing drums, running and travelling.