A Critique of the Bitcoin Stock-To-Flow Model – Analysis – Eurasia Review

By Kristoffer Mousten Hansen and Karras Lambert*

In March 2019, the pseudonymous “PlanB”, who describes himself as a “former institutional investor with 25 years of experience in financial markets”, published a short article describing what he calls the “stock-to-flow” (S2F) model. bitcoin pricing. Influenced by Nick Szabo on “unforgeable costliness” and Saifedean Ammous at S2F, PlanB’s first post described a statistical correlation between the market value of bitcoin and the stock-to-flow ratio.1

PlanB later presented another model, called the “bitcoin S2F cross asset” (S2FX) model, in April 2020, which also incorporated gold and silver. The S2F models’ predictions of an ever-rising bitcoin price matched the optimism of bitcoin enthusiasts and have helped PlanB gather 1.8 million Twitter followers from September 2022, as well as a series of appearances on the podcasts of promoters of Austrian economists in the bitcoin space, such as Stephan Livera and Saifedean Ammous, some as late as November 2021.

In short, the S2F model claims that the market value (total stock times price) of bitcoin and any other monetary commodity is determined by the S2F ratio – the stock in existence divided by the rate of production. Our pseudonymous modeler then produces charts that show an extremely close fit between market value and S2F ratios.

Technical criticism has been leveled at the various versions of the S2F model since their inception, and the models have come under increasing scrutiny in the current cryptocurrency bear market. Our purpose in this paper is to focus narrowly on some of the fundamental conceptual flaws of the S2F models from the point of view of Misesian economics. Our thesis is that one cannot simultaneously be a Misesian Austrian and put shares in any S2F model for asset pricing.

Value, scarcity and price

According to PlanB in its first post, the “hypothesis” of the S2F model is “that scarcity, as measured by [stock-to-flow], drives value directly.” We recently described the problems with assigning a “store of value” function to money, but PlanB takes this error a step further by conflating “value” with “price.” Terminological quibbles aside, PlanB’s definition of “scarcity” as stock-to-flow is simply wrong in terms of economics, as it only deals in physical quantities and never touches on the real economic facts.

According to the great Austrian economists, all economic goods are by definition scarce. Scarcity is a general condition where the existing stock of an object is insufficient to meet all demands. Having a price is a sign that an object is scarce and therefore has, in Menger’s terminology, “commodity character”. This is not just a terminological disagreement, as PlanB’s definition of scarcity as a physical relationship between the existing stock and the current production (“flow”) of a resource ignores the subjective element of valuation that ultimately underlies economic demand and product nature.

In the Austrian understanding of scarcity and value, one always gets scarce goods some price. But what specific the price someone is willing to pay for a certain quantity of a commodity bears no necessary relationship to a physical measure of it such as the stock-to-flow ratio. Therefore, the “hypothesis” of the S2F model is fundamentally misunderstood, and no further exercise in data collection or reparameterization will save its theoretical coherence.

S2F and the law of demand

Readers can question our claim that there is no necessary relationship between price paid and physical supply measures by appealing to the law of demand. Isn’t it true that if the supply decreases, the price will increase? This line of thinking fails to understand the counterfactual nature of economic laws. The law of demand, properly understood, describes an inverse relationship between the price of a good and the quantity demanded at a moment of choice. If the price was higher (lower), thereafter quantity demanded would have been lower (higher), or at least would not be higher (lower), than otherwise it would be.

Furthermore, the law of demand has nothing to say about specific prices that individuals are willing to pay for different quantities of a good. Demand and supply curves are simply conceptual tools for an economist to visually depict such a counterfactual relationship. The specific forms of the curves, except as understood in the narrow counterfactual sense just described, cannot be demonstrated by action. Therefore, measuring changes in price and quantity purchased over time does not test the law of demand, but only collects historical data on the valuation of individuals participating in different exchanges at different times.

As readers of the Austrian theses or attendees of Mises University will know, prices are formed as a result of subjective value judgments by the individuals participating in an exchange. All prices involve the demonstration of inverse preference rankings by the parties participating in an exchange, meaning that the buyer of bitcoin prefers the amount of bitcoin purchased over the number of fiat monetary units given up and the seller of bitcoin prefers the opposite.

In a money economy, concrete quantities of the monetary goods change hands in return for concrete quantities of non-monetary goods, regardless of the total existing stock of goods throughout the world. A “market price” is the price arising from the exchanges during a market period; it is set between the valuation of the marginal buyer and the marginal seller so that no person is willing to sell below or buy above the market price.

Thus, the ratio PlanB establishes between share-to-flow and market price is economically meaningless. To suggest that “scarcity, as measured by [stock-to-flow], directly drives value’ is to completely discard distinctive Austrian insights regarding value theory and price formation in favor of a mechanistic notion of price determination. Lest readers think we’re tilting at a straw man, PlanB has bluntly stated its view that “even demand … is noise, … stock-to-flow is the real signal.”

Stock-to-Flow and the quality of money

With all that said, we do not want to give the impression that the stock-to-flow ratio of an item is completely meaningless, as it can be an important factor in determining the quality of a monetary item. When individuals evaluate a given amount of money, various qualities of the money commodity affect the valuation, but only those qualities that the acting individuals consider important. A high stock-to-flow ratio can actually be considered important, as it indicates that the purchasing power of the individual’s cash holdings is not expected to fall due to increases in money supply.

However, this does not mean that a higher ratio is always better, as a higher stock-to-flow ratio may be irrelevant from the market participants’ point of view during certain time periods. Thus, gold and silver do not perform worse as monetary goods than bitcoin or other fixed-supply cryptocurrencies simply because their holdings are likely to increase over time or because production schedules may fluctuate. The key issue is whether these increases and fluctuations are subject to arbitrary bureaucratic decisions or left to voluntary individual decision-making.

As long as there is a free market for money, standard market forces will integrate the demand for money and the costs of producing money (for example, through gold mining) so that no problems arise with the supply. In fact, the fixed supply limit of bitcoin will inevitably result in a decreasing supply, as private keys for certain balances are forgotten, which is also fine from the Austrian point of view. Individuals will simply choose to use the type of exchange medium they prefer based on the characteristics they consider important.

Final thoughts

We have avoided delving into the technical issues of PlanB’s S2F models in order to isolate the fundamental flaw in economic theory that makes any apparent correlation between the price of bitcoin and its temporary stock-to-flow ratio coincidental at best. However, serious statistical problems associated with the specifications of the S2F model, such as the fact that “stock-to-flow” regressions based on “market value” (price times existing stock) involve regressing “stock” on itself, have led to that PlanB’s work is described by one critic as “math-laden marketing.” Ultimately, given the fundamental conceptual flaws in PlanB’s “hypothesis,” we have to agree.

Proponents of predictive economic models such as the S2F model may fall back on the idea expressed in the following quote, which PlanB attributes to George Box on his website: “All models are wrong, some are useful.” However, this attitude reveals a fundamentally positivist bent completely at odds with the epistemological and methodological principles of Menger, Mises, and Rothbard, who generally recognize incorrect models as useless for understanding meaningful causal relationships in the real world. We can know that prices are not and never will be caused by changes in physical stock-to-flow measurements without ever collecting data and running regressions. Positivist critics may regard our position as “intolerant” and extreme, but the truth itself may seem intolerant to those who insist on denying it.

• 1. In a review of Ammous’s The Bitcoin Standard, Kristoffer Hansen has already described some theoretical and historical problems with the “stock-to-flow” metric when it comes to money.

About the authors:

• Kristoffer Mousten Hansen is a research assistant at the Department of Economic Policy at the University of Leipzig. He received his PhD from the University of Angers and is a former fellow at the Mises Institute.
• Karras J. Lambert is a graduate student in economics at George Mason University and a 2021 Mises Institute Summer Research Fellow. He previously earned a Masters in Finance from Peking University HSBC Business School and a BS in Economics from Drexel University. Karras specializes in economic theory in the tradition of Carl Menger and Ludwig von Mises.

Source: This article was published by the MISES Institute