A Critique Of The Bitcoin Stock-To-Flow Model – Analysis

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 dubs the “stock-to-flow” (S2F) model of bitcoin pricing. Influenced by Nick Szabo on “unforgeable costliness” and Saifedean Ammous on S2F, PlanB’s initial post described a statistical relationship between the market value of bitcoin and its stock-to-flow ratio.1

PlanB later presented a different model, dubbed 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 has helped PlanB garner 1.8 million Twitter followers as of September 2022, as well as a number of appearances on the podcasts of promoters of Austrian economists in the bitcoin space, such as Stephan Livera and Saifedean Ammous, some as recently as November 2021.

Put briefly, the S2F model claims that the market capitalization (total stock times price) of bitcoin and any other monetary commodity is determined by its S2F ratio—the stock in existence divided by the rate of production. Our pseudonymous modeler then produces charts depicting an extremely tight fit between market capitalization and the S2F ratio.

Technical criticisms have been levied at the different versions of the S2F model since their inceptions, and the models have come under increasing scrutiny in the current cryptocurrency bear market. Our purpose in this article is to focus narrowly on some of the fundamental conceptual errors 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 stock in any S2F model of asset pricing.

Value, Scarcity, and Price

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

According to the great Austrian economists, all economic goods are scarce by definition. Scarcity is a general condition under which 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, “goods-character.” This is not simply a terminological quibble, as PlanB’s definition of scarcity as a physical relationship between the existing stock and the current production (the “flow”) of a resource ignores the subjective element of valuation that ultimately underlies economic demand and goods-character.

In the Austrian understanding of scarcity and value, scarce goods always fetch some price. However, what specific price someone is willing to pay for some quantity of a good has no necessary relationship with a physical measure of it such as the stock-to-flow ratio. Therefore, the “hypothesis” of the S2F model is fundamentally misconceived, and no further exercise in data gathering or reparameterization will salvage its theoretical coherence.

S2F and the Law of Demand

Readers may question our claim that there is no necessary relationship between price paid and physical supply measures by appealing to the law of demand. Is it not true that if supply decreases, then price will rise? 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 were higher (lower), then the quantity demanded would be lower (higher), or at the very least would not be higher (lower), than it otherwise would be.

Furthermore, the law of demand has nothing to say about the specific prices which individuals are willing to pay for various quantities of a good. Demand and supply curves are simply conceptual tools for an economist to visually depict such a counterfactual relationship. The specific shapes 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 of the law of demand, but merely collects historical data concerning the valuations of the individuals taking part in various exchanges at various times.

As readers of the Austrian treatises or attendees of Mises University will know, prices form as a result of the subjective valuations of the individuals taking part in an exchange. All prices involve the demonstration of inverse preference rankings by the parties taking part in an exchange, meaning the buyer of bitcoin prefers the quantity of bitcoin bought to the number of fiat money units given up and the seller of bitcoin prefers the opposite.

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

Thus, the relationship PlanB posits between stock-to-flow and market price is economically meaningless. To suggest that “scarcity, as measured by [stock-to-flow], directly drives value” is to entirely spurn distinctive Austrian insights concerning value theory and price formation in favor of a mechanistic notion of price determination. Lest readers think we may be tilting at a strawman, PlanB has directly stated his 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 wish to give the impression that the stock-to-flow ratio of a good is entirely meaningless, as it can be an important factor in determining the quality of a monetary commodity. When individuals evaluate a given quantity of money, various qualities of the money commodity influence its valuation, but only those qualities that the acting individuals consider important. A high stock-to-flow ratio may in fact be deemed important, as it indicates that the purchasing power of the individual’s cash holding is not expected to fall due to increases in the supply of money.

However, this doesn’t mean that a higher ratio is always better, as a higher stock-to-flow ratio might be irrelevant from the point of view of market actors during certain periods of time. Thus, gold and silver do not make worse money commodities than bitcoin or other cryptocurrencies with fixed supply simply because their stock is likely to increase over time or because production schedules may fluctuate. The key consideration 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 in money, standard market forces will integrate the demand for money and the cost of producing money (say through gold mining) such that no problem in supply arises. In fact, the fixed supply cap of bitcoin will inevitably result in a decreasing supply, as private keys to certain balances are forgotten, which is also fine from the Austrian point-of-view. Individuals will simply choose to use the kind of medium of exchange they prefer based on the qualities they consider important.

Final Thoughts

We have avoided delving into the technical problems with PlanB’s S2F models in order to isolate the fundamental error in economic theory that renders any apparent correlation between the price of bitcoin and its temporary stock-to-flow ratio incidental at best. Nevertheless, grave statistical issues inherent to 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 resulted in PlanB’s work being described by one critic as “math-laden marketing.” Ultimately, in light of the fundamental conceptual errors of PlanB’s “hypothesis,” we must concur.

Supporters of predictive financial models such as the S2F model may fall back on the idea expressed in following quote, which PlanB attributes to George Box on his website: “All models are wrong, some are useful.” However, this attitude betrays a fundamentally positivist inclination completely at odds with the epistemological and methodological tenets of Menger, Mises, and Rothbard, who as a rule recognize incorrect models to be useless for comprehending 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 metrics without ever gathering data and running regressions. Positivist critics may consider our position “intolerant” and extreme, but truth itself can 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 as far as money is concerned.

About the authors: 

• Kristoffer Mousten Hansen is a research assistant at the Institute for Economic Policy at Leipzig University. He received his PhD from the University of Angers and is a former Mises Institute research fellow. 
• Karras J. Lambert is a PhD student in economics at George Mason University and a 2021 Mises Institute Summer Research Fellow. He previously earned a Masters degree in finance from Peking University HSBC Business School and a B.S. 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