December 7, 2021

Mises’s Regression Theorem, Bitcoin, and Subjective Value Theory

“If value is subjective, and if a medium of exchange is a good like any other, then how can we say that a good could not first be valued by some person somewhere as a medium of exchange rather than for some other purpose beforehand?” ~ Emile Phaneuf III

Mises’s regression theorem, first detailed in the original 1912 German version of his book The Theory of Money and Credit, sought to explain how the purchasing power of money is determined in the market. The regression theorem was an attempt to solve a problem which puzzled the economists of his day – something they saw as illogical: how to “explain the purchasing power of money by reference to the demand for money, and the demand for money by reference to its purchasing power.” Mises attempted to solve this by arguing that people make predictions about the purchasing power of money in the future by looking at the purchasing power of the money’s immediate past. And to explain the purchasing power of the immediate past – yesterday – they look to the purchasing power the day before yesterday, and so on. In short, he applied marginal utility theory to money, and was able to avoid a circular argument by introducing a time element.

One can see a problem, however, as it seems to spiral backwards in time into an infinite regression. But Mises doesn’t think so. He writes:


Explaining in a little more detail, Mises writes:

If in this way we continually go farther and farther back we must eventually arrive at a point where we no longer find any component in the objective exchange-value of money that arises from valuations based on the function of money as a common medium of exchange; where the value of money is nothing other than the value of an object that is useful in some other way than as money […] Before it was usual to acquire goods in the market, not for personal consumption, but simply in order to exchange them again for the goods that were really wanted, each individual commodity was only accredited with that value given by the subjective valuations based on its direct utility. [Emphasis mine.]

Up until this point, his theorem seems fairly non-controversial, but he also makes sweeping claims, which we will view through the lens of subjective value theory later on.

[W]henever a good which has not been demanded previously for the employment as a medium of exchange, begins to be demanded for this employment, the same effects must appear again; no good can be employed for the function of a medium of exchange which at the very beginning of its use for this purpose did not have exchange value on account of other employments […] Nobody can ever succeed in constructing a hypothetical case in which things were to occur in a different way. [Emphasis mine.]

And yet again:


But before we explore Bitcoin’s compatibility (or possible lack thereof) with the theorem, we must first address what the theorem does not say.

First, the theorem is not a warning from Mises that a medium of exchange not adhering to it cannot sustain itself. Rather, it is a bold statement asserting that a medium of exchange not adhering cannot come into existence in the first place. Second, the theorem does not say that the direct (non-monetary) use value must maintain itself in order for a medium of exchange to continue to have exchange value. In other words, as just an example, if gold-backed paper certificates are traded in the marketplace, the regression theorem does not claim that those certificates of deposit cannot retain their status as a medium of exchange if the gold custodian cancels redeemability. 

One interpretation highlighted by Laura Davidson and Walter Block proposes that Mises’s regression theorem “is relevant only when a new medium of exchange arises out of a pure barter economy.” As for a relevance to Bitcoin specifically, the authors assert that it “does not need to have a direct-use value in order to be a medium of exchange, because it did not emerge from a pure barter economy.” They argue that new media of exchange are able to come about with an already-existing money price structure (or memory of it), just as already happened with the German Rentenmark (1923), the Euro (1992), and the Argentine privately-issued “credito” (2002). Applying this to Bitcoin, these authors claim, as this new digital asset emerged in various countries within non-barter conditions and already-existing fiat money prices, Bitcoin need not be held up to scrutiny of the regression theorem.

However, despite the present author’s careful rereading through Mises’ss classic works The Theory of Money and Credit and Human Action for any statement from Mises’ss own words establishing this barter limitation for his regression theorem, it seems there is no evidence for it. Further, Davidson and Block both concede in a podcast that they are also unaware of any such limitation from Mises himself. What we do have from Mises are his sweeping claims, quoted above, which (in this author’s view) seem, if anything, to clearly apply broadly – with no such barter limitation of scope.

Bitcoin and the regression theorem

On the face of it, Bitcoin’s existence seems to violate Mises’s theorem, unless a preceding non-monetary use can be demonstrated. That is, Bitcoin would have to be first valued for its direct utility before it could hold indirect exchange value.

So have the criteria been met, or does Bitcoin violate the theorem? It isn’t that difficult to satisfy the theorem if we consider that Bitcoin isn’t just a monetary unit in isolation; it exists on top of a Blockchain with a sophisticated payment network, handles final settlement in a matter of minutes (if the seller is willing to pay a high enough mining fee), makes cross-border payments with ease and in a permissionless way, solves the double-spend problem without the use of a centralized third party, and so on. As such the non-monetary use cases of Bitcoin satisfy the theorem.

Now we must distinguish between (little-b) bitcoin, the monetary units, and (big-B) Bitcoin, the underlying payment network and technology. This isn’t just because old school bitcoiners like to see the proper capitalization of the word. More specifically for Mises’s theorem, if early adopter bitcoiners valued the Bitcoin trust-minimizing payment network and technology before they valued the bitcoin monetary units (which is exactly what happened as far as I can tell), then Mises’s regression requirement of having “exchange value on account of other employments” before it was used as a medium of exchange has been met, and thus, the digital asset does not violate the theorem. Indeed Bitcoin (the payment network) and bitcoin (the monetary unit) are inseparable in a way that PayPal (the payment network) and the USD (the monetary unit) are not. If we try to strip away Bitcoin’s payment network from the monetary unit, we really have no bitcoin monetary unit either.

To elaborate, Bitcoin (the payment network) has a single, native digital currency: bitcoin. PayPal has no such single, native currency. It is true that PayPal benefits from tapping into the USD’s large network of users and vice-versa, but this doesn’t change the main point: that the payment network (PayPal) still needs to tap into a digital currency that is not its own in order to work. Nobody sends anybody else “paypals” as the medium of exchange. PayPal—without use of a non-native, fiat digital currency—is a bow with no arrows. (I have Peter St. Onge to thank for this bow-arrow metaphor).

Konrad Graf provides a useful example:

What if we demanded of telephones that they must have some value all by themselves – even when disconnected from the telephone network? […] A telephone is a kind of good that is only valuable within the context in which it is valuable. […] Arguing that Bitcoin ought to have some value outside of the precise context in which it is meaningful seems similar to requiring that telephones also be useful when disconnected.

But if value is subjective (a central tenet of the Austrian economic way of thinking), then it is difficult to state that a new medium of exchange could not be first valued as a medium of exchange rather than for some other purpose beforehand. Peter St. Onge (2014) makes this point:

Among Menger’s greatest contributions in his Principles is the realization that money is fundamentally a good like any other — demanded for its usefulness in enabling transactions and store of value — with an actual price dictated by its scarcity. […] If money, like any other good, derives its value from the benefits it offers, it’s hard to see why the money, even those benefits, require an antecedent. Just as the internet can be valuable without a ‘pre-internet,’ a cryptocurrency enabling anonymous, irreversible, low-regulation transactions and saving can be valuable without a precursor. If there is no regression requirement for value in any other good, why does money alone bear this burden?

Further, despite the present author’s disagreement with Davidson and Block’s assertion that Mises’s regression theorem is limited to situations of barter, these authors do make a very important observation: that it is easier for a new medium of exchange (“Medium A”) to get going when there is already another medium of exchange (“Medium B”) in widespread use for which we have prices to look to. So, for example, if potatoes have a chance at becoming a secondary medium of exchange (“Medium A”), it is easier for this to come about in a non-barter society in which all goods and services are already priced in US dollars (“Medium B”). In other words, goods and services already being priced in dollars allows us to know long before we even begin to try to use potatoes as a medium of exchange what the price ratio is, for example, between a particular car and a particular house. So, thanks to dollar prices, we can know that the market value of one unit of a particular house is roughly fifteen units of a particular car. As such, we can know that we should have to pay roughly fifteen times as many potatoes for the house as we would have to pay for the car. Now, we still have the difficult process of price discovery ahead of us because we still don’t know the market value (in potatoes) of cars or houses. So again, Davidson and Block are still correct that an already-existing (non-barter) price structure can play a crucial role in aiding new media of exchange to get off the ground in the first place.

As for the process of price discovery, how would it be possible for individuals to infer a subjective value on a good that has no history of exchange value? As Robert Murphy points out, Mises may not have imagined a situation in which a new medium of exchange could come about, beginning at first with zero market value, then (in dollar terms) worth just a few cents, then increasing over time to be worth thousands of dollars. Applying this to Bitcoin, it is at least possible that Bitcoin was valued by some person somewhere first as a medium of exchange and then for some other purpose. This is the topic of our next section.

How the regression theorem violates the subjective theory of value

Despite Bitcoin easily having been able to satisfy the theorem in a variety of ways (signaling one’s values, speculation, etc.), we needn’t forget about Mises’s sweeping statements about the impossibility of a medium of exchange first being valued for non-monetary uses. (Konrad Graf argues that it is a logical impossibility). But is value subjective, or is it not? Why would the subjective theory of value apply to all other goods except for money? If value is indeed subjective, then there is no particular reason why someone couldn’t first value something for its indirect use. This also, by the way, need not refute the core of Mises’s regression theorem: that individuals make calculations (at least in most cases, although Mises’s statements imply his belief that it applies in all cases) by looking to the prices of the immediate past, and that if you follow the trail of a medium of exchange back far enough, that it will lead you to something valued for reasons other than its use as a medium of exchange. But, as William J. Luther has argued, rather than considering this a “necessary condition” as Mises believes it to be, it might be more appropriately considered a “contributing factor.” Put another way, “All else equal, an item possessing non-monetary value is more likely to get off the ground than an item that does not.”

It is important to distinguish between descriptive accounts of what we see people do (or expect them to do as boundedly rational actors) from what is logically possible for them to do. Thus, the main point we wish to argue here is that the certainty that Mises unnecessarily adds to his theorem (regarding the impossibility of any hypothetical different way) puts his theorem on shaky ground once we view it through the lens of subjectivity.

In Principles of Economics, Carl Menger lays out the subjective theory of value and writes that “value does not exist outside the consciousness of men.” Explained more elaborately, “Value is therefore nothing inherent in goods, no property of them, but merely the importance that we first attribute to the satisfaction of our needs, that is, to our lives and well-being, and in consequence carry over to economic goods as the exclusive causes of the satisfaction of our needs.”

Menger even put the concept of subjective value right into the criteria he gave for a good to be a good (referring to economic goods). He wrote that in order for a good to be a good, it must satisfy all four of the following criteria: There must be a human need for it; the thing must be capable of satisfying the human need; there must be human knowledge of the thing’s ability to satisfy the need; and there must be a “[c]ommand of the thing sufficient to direct it to the satisfaction of the need.” We need not necessarily fully accept all of Menger’s criteria: only to recognize his emphasis on subjectivity.

In Human Action, Mises explains the subjective theory of value, arguing that the role of the economist is to take “the value judgments of acting man as ultimate data not open to any further critical examination.” But, without realizing it, Mises’s subjectivism works against his claim that no medium of exchange could come about without prior direct-use value.

As for Bitcoin as a unique digital asset, Mises understood well that economic goods do not “have to be embodied in a tangible thing”, but in not having lived through the digital age, he could only categorize all non-tangible economic goods as “services.” Thus, being a man of his time (and of no fault of his own), he had no proper framework to categorize something like Bitcoin. Konrad Graf (who lived through the emergence of Bitcoin, along with the rest of us), appropriately calls Bitcoin a “‘scarce, intangible, digital’ good.”

Menger refers to money as “the most saleable of commodities” and shows how cattle served this purpose in the ancient world, and as time passed, a metallic standard based on gold, silver and copper took its place – especially as civilization progressed, and people moved from rural to urban environments. This “most saleable of all commodities” emphasizes the point of money being a good like all others. (We can use the terms ‘commodity’ and ‘good’ interchangeably).

Rothbard makes the argument even more explicitly:

A most important truth about money now emerges from our discussion: money is a commodity. Learning this simple lesson is one of the world’s most important tasks. So often have people talked about money as something much more or less than this. Money is not an abstract unit of account, divorceable from a concrete good; it is not a useless token only good for exchanging; it is not a “claim on society”; it is not a guarantee of a fixed price level. It is simply a commodity. It differs from other commodities in being demanded mainly as a medium of exchange. But aside from this, it is a commodity—and, like all commodities, it has an existing stock, it faces demands by people to buy and hold it, etc. Like all commodities, its “price”—in terms of other goods—is determined by the interaction of its total supply, or stock, and the total demand by people to buy and hold it.

And thus, the question must be asked: If value is subjective (a central pillar of the Austrian economic way of thinking), and if a medium of exchange (or money) is a good like any other, then how can we say that a good could not first be valued by some person somewhere as a medium of exchange rather than for some other purpose beforehand? Mises’s claim that “Nobody can ever succeed in constructing a hypothetical case in which things were to occur in a different way” runs head on against subjectivity.


To emphasize the central point to this article’s thesis, we can still consider the regression theorem useful without accepting the logical contradiction that, on one hand, a good can be subjectively valued for any reason, and on the other hand, that a good could not possibly be valued for a specific purpose (as a medium of exchange) unless it was first valued for some purpose other than that purpose. Empirical evidence that bitcoins were first valued for direct use value does not refute this. Bitcoin may indeed have emerged with perfect accordance to the theorem. There are, as of the time of this writing, roughly 12,000 digital assets listed on Do we really cling tightly to subjective value theory (as we should) whilst simultaneously clinging to a belief that not one of these could have been valued as a medium of exchange before some other purpose? Value is either subjective, or it is not.

This article, Mises’s Regression Theorem, Bitcoin, and Subjective Value Theory, was originally published by the American Institute for Economic Research and appears here with permission. Please support their efforts.