The Economics of Bitcoin: On Regression

In a storyline sounding all too familiar, economics circles have been up in arms with each other over the emergence of Bitcoin, the cryptocurrency and payment system that burst on the scene in 2009. Amongst the debate, two fundamental arguments exist: firstly, whether or not Bitcoin is, or can be a money, and secondly, whether or not Bitcoin is efficient in its use as a money. This article will look to establish the de facto Austrian position in regards to whether or not Bitcoin is a money. On that note, if you do not know much about Bitcoin, I direct you here in order to acquire base knowledge on the subject.

Though there have been a multitude of criticisms toward Bitcoin, it must be said that clearly the most important debate to the Austrian community is whether or not it “can” be a money; namely, whether or not it violates Mises’ regression theorem. Examples of arguments of this type include those by The Mises Institute’s Frank Shostak and blogger “Smiling Dave” among others. This topic is by far the most significant of the lot, as those libertarians who claim that Bitcoin does violate the regression theorem are directly attacking the character of the formation of money prices put forth by Austrians. But why does it follow that this is important? Well, those libertarians who reject Bitcoin on these grounds are not, and cannot be classified as, Austrian economists in this matter, as they are not working from a praxeological framework. The de facto Austrian position must be one in which Bitcoin does not violate the regression theorem, for reasons that will be explained later in the article. Thus, those posteriori arguments put forth by people claiming that Bitcoin violates the regression theorem, and will therein implode in some spectacular crash for this reason, must quickly and emphatically be separated from holding any “Austrian” position. It is not, and cannot be the Austrian position, and to associate such claims with the Austrian school is slanderous to a degree. One may make the argument that Bitcoin might potentially crash due to it being entirely based on the network effect and exchange value, but the classification of this argument must not be praxeological, rather one of a speculative nature.

The Economics of Regression

Before we examine any arguments against Bitcoin’s capability as a money, we must first explain the basics of the regression theorem. The theorem is based on Austrian price formation, applied to a system of indirect exchange. As a caveat here, it is necessary to define a medium of exchange as something that holds exchange value, and money as a “generally used” medium of exchange.

Under a system of direct exchange, or barter, prices are formed by the dynamics of market supply and demand schedules, which are made up of supply and demand schedules of individuals. These individual schedules consist of the ordinally ranked marginal utilities of two goods: thus, the crux of price formation in a system of barter is the weighing of individual marginal utilities of two goods against each other.

Under a system of indirect exchange, or one using money, the aforementioned price formation cannot occur at first glance. The price of good x against money is based on market supply and demand schedules, then individual schedules, and then the rankings of marginal utilities of good x against money. The issue arises when we realize that the marginal utility of money is based on existing prices of the array of all other goods in the economy, bringing us into circularity. In summation, the price of good x is based on the utility of money, which is based on the prices of all other goods, which is based on the utility of money.

Where do we escape this circularity? With the introduction of time. It is clear that the marginal utility of money today, and thus the money prices of goods today, are based on the money prices of goods yesterday. The money prices of goods yesterday are determined by the utility of money yesterday, which are based on the money prices of goods the day before that. We then see that, through the introduction of time, we will enter into an infinite regression.

And here, we enter the brilliance of Mises in establishing the regression theorem. As we regress further back in time, Mises claims, we eventually will reach the point at which the utility of money isn’t in determined by its exchange value, but rather its direct use value. The price for a certain money good is thus established through the ordinal rankings of direct use value, which provide the basis for utility of the money good, allowing future prices to be set when the good is eventually used as a medium of exchange. To put it a different way, a system of indirect exchange will always regress back to a system of barter. This process is perhaps best illustrated with a graphic provided in Rothbard’s “Man, Economy, and State”.


Here we can see the entire process as described above. Looking at time period 7, the price of gold is shown to be based on the weighing of the utility of all other goods against the utility of gold, which in turn based on the price of gold on day 6, and so on. The key stage for this graphic is time period 3, shown as establishing the price of gold through the rankings of marginal utilities of gold and all other goods in the economy. This is the point at which the price of the money good, in this case gold, regresses back to. At this moment, all utility derived from the good is for direct use, as there is no exchange value for gold established as of yet. So finally, we may conclude that any medium of exchange or money must eventually regress back to a point in which its utility was determined by direct use value, as this direct use value establishes the money prices and exchange value of the money good.

Bitcoin’s Regression

We may now apply our knowledge of the regression theorem to Bitcoin. The foremost issue that must be pointed out is that it is empirically quite apparent that Bitcoin is being used as a medium of exchange. This fact alone defeats any argument claiming that Bitcoin “cannot be money” based on a violation of the regression theorem. There are currently prices for goods in terms of Bitcoins. Using this fact and our knowledge of the regression theorem, we can deduce that because Bitcoin prices for goods exist, Bitcoin must eventually regress back to a point in which its utility was based on direct use value. Those arguing against Bitcoin fail to understand this fundamental point: for Bitcoin prices of other goods to currently exist, as a prerequisite of these prices, there must have been some direct use value for Bitcoin. These prices could not ever have conceivably existed today without Bitcoin regressing to direct use value. Those arguing against Bitcoin from the basis of violating the regression theorem have already lost their argument due to Bitcoin prices for goods existing today. This is a crucial point made by Bob Murphy:

“…the certain group of Misesians who keep deriding Bitcoin and saying it will eventually collapse, it’s a passing fad, it will never take off beyond internet geeks, etc. etc., because of Mises’ regression theorem, aren’t making any sense. Mises’ regression theorem wasn’t making an empirical prediction about a medium of exchange never attaining the status of money, unless it started out as a regular commodity. No, Mises is saying we can’t conceive of even a medium of exchange (which is a weaker condition than money) that didn’t start out as a regular commodity. Bitcoin is clearly, unequivocally a medium of exchange right now.”

The regression theorem isn’t a normative claim saying that for money to be “sound” it must have direct use value of some kind. It is an apodictic statement, established through a priori reasoning. In order for people to argue against Bitcoin, they must refute the chain of logic that brought Mises to the conclusion about regression that he came to. Any argument stating something akin to “the medium of exchange that is Bitcoin violates the regression theorem” is akin to saying “a circle is square”. The fact that Bitcoin currently is a medium of exchange implies that it doesn’t violate the regression theorem, as defined by the regression theorem. Austrian economists are certainly open to criticisms of the theorem itself; however, self-refuting arguments against Bitcoin such as the example given above need to be dismissed as a misunderstanding of both the basis of the regression theorem, and what Mises was trying to communicate. Until any such criticisms of the a priori logic are brought forth, we can establish that the de facto Austrian position on Bitcoin must be that it doesn’t violate the regression theorem.

With this being said, it seems apparent that the part that troubles people in understanding this debate is what direct use value a good like Bitcoin could possibly have. As a caveat, it should be known that the character of Bitcoin’s direct use value is irrelevant to any discussion involving the regression theorem, which merely says that Bitcoin must have had direct use value at some point. However, it would not be totally useless to elaborate on this topic if it visualizes what the direct use value may have been, and for this visualization, I once again turn to Bob Murphy’s speculation of what may have happened at its inception:

“…when Bitcoin was first introduced and no one had any idea of its purchasing power, the very first people to trade for it did so because it provided them with direct utility because they knew there was at least a chance that it would serve to chafe the governments of the world with their printing presses.”

Bitcoin’s utility, Murphy argues, might have derived from Bitcoin being capable of slaying the current government fiat system, which seems to be a very logical possibility. Utility from seemingly non-material uses like this may be hard for those against Bitcoin to grasp, as it is abstract, but this by no means is a negation of this point. It must be stressed once again that, material or non, Bitcoin must have had a direct use value of some kind.

One last item that must be addressed is the notion that, because people buy and sell Bitcoin in terms of fiat money, and only then use Bitcoin to buy other goods, in truth they are not using it as a medium of exchange. Blogger “Smiling Dave” puts forth this argument in a post claiming that people do not actually use Bitcoin as a medium of exchange:

“All the buying and selling of bitcoins for dollars or pesos or other currencies over at and other places are not, repeat not, transactions where bitcoins are media of exchange. Only instances where a person sells his apples in exchange for a bitcoin, and then buys oranges with the bitcoins, count as bitcoin being a medium of exchange.”

The fatal mistake in this logic is that he is not viewing the fiat dollar as a good in itself. A transaction in which an actor buys Bitcoin, paying with fiat dollars, and then uses Bitcoin in buying say, an apple, is by definition using Bitcoin as a medium of exchange. The fiat dollars as a good are not being used to buy the apple, and thus, in this transaction, cannot be called the medium of exchange. It is the marginal utility of the purchased Bitcoin, not the fiat dollars, that are being weighed against the marginal utility of the then purchased apple.

Arguments of this type can be contrasted to that of gold and fiat money. If I sell my fiat dollars to buy a bar of gold, and then use my bar of gold to buy an apple, what is the medium of exchange being used? Dave would claim that it is the fiat dollars, and not the gold, but this is incorrect. The dollars are not being valued for their exchange value in the transaction, rather the gold is. We could use Dave’s logic to similarly say that if I sold my apple to buy a bar of gold, then used my bar of gold to buy fiat money, that it is the apple that is used as the medium of exchange in this transaction. Once again, this is patently untrue, as the apple’s utility was not being weighed against the fiat money in any way. In application to other examples as well, we find this conception of what a medium of exchange is to become progressively nonsensical. If I sell my house to buy fiat money, then sell my fiat money to buy an apple, we do not say that the house is the medium of exchange, but clearly the fiat money. Or in another case, if I sell my labour to buy a bar of gold, then use that bar of gold to buy a house, the medium of exchange in this transaction isn’t my labour, but the bar of gold. Needless to say, once given a thorough analysis, we find this claim to be palpably illogical.

Concerning Fallacious Economic Arguments

At this point, it seems necessary to refute a few of the many fallacious arguments floating around the Austrian community in regards to Bitcoin and the regression theorem. The first is an incorrect interpretation of the theorem in regards to Bitcoin put forth by the blogger “XC”. He/she asserts that the regression theorem is not violated because Bitcoin regresses back to fiat money, then to commodity (gold) money. This proposition entirely confuses the theorem, as it fails to ascribe any direct use value to Bitcoin; it doesn’t explain in any way why an actor would exchange his fiat money for an amount of Bitcoins in the first place. To establish a price for a Bitcoin, actors must weigh the utilities of a Bitcoin and a certain amount of fiat money. The regression theorem requires the utility of Bitcoin to regress to direct use value, and XC’s claim that Bitcoin regresses to fiat, then to commodity money fails to ascribe any direct use value to Bitcoin, and therefore misses the point.

The second argument currently being debated in Austrian circles comes from a post by blogger “Michael Suede”. In a marginal improvement upon other criticisms of Bitcoin, Suede attempts to refute the regression theorem itself, claiming that it is irrelevant in the face of a market demanding some form of money:

“So, once we have a perceived need in a free market for a trade facilitator and a store of wealth, what should we expect the market to do?  We can expect it to try and find a solution to this problem! Mises attempts to argue that the market solved this problem because people valued gold for its own sake before it became a money, and it was this value they had for gold in ornamental use that allowed it to become a money.

This is patently wrong.  Consider that as soon as the market perceives a need for money, it wouldn’t matter if gold had a pre-existing value in ornamental use or not, because it would suddenly have value as a trade intermediary as soon as the need for a trade intermediary entered the public consciousness.”

Ironically, Suede’s interpretation of what Mises was claiming in the regression theorem is “patently wrong” in itself. Mises’ theorem does not say that the market solved the problem of trade facilitation and wealth storing through introducing money, despite the fact that Mises would certainly agree that introducing money into an economy would solve these issues. Indeed, these demands may well be the cause for the introduction of money. However, this in no way explains the origination of money, which is fundamentally the purpose of the regression theorem. Though the words “cause” and “origination” may seem similar, in this case they do not have identical meaning. The cause of money would be the reasons for demand, such as store of value, trade facilitator, etc., examples that Suede provides above. Separately, the origination of money asks how prices for money today were constructed, specifically how the infinite regress of price formation is broken. Understanding this, we see Suede’s statement that “it wouldn’t matter if gold had a pre-existing value in ornamental use or not” is illogical in that if gold had no pre-existing direct use value, prices could not regress to anything. He offers no explanation of how prices for the medium of exchange could conceivably form without ever having a direct use value in the past, showing an inadequate understanding of what the regression theorem is, and making his refutation of it fruitless.

The last important fallacy worth refuting is the notion that because a money or medium of exchange currently has no direct use value, or its direct use value is practically negligible in the face of its exchange value (such as Bitcoin), that it must therefore be a pyramid scheme based economic principle. On the surface, this claim appears to be in accordance with the regression theorem. This, however, isn’t the case, and a quote from Murray Rothbard shows us why:

“…it does not follow that if an extant money were to lose its direct uses, it could no longer be used as money. Thus, if gold, after being established as money, were suddenly to lose its value in ornaments or industrial uses, it would not necessarily lose its character as a money. Once a medium of exchange has been established as a money, money prices continue to be set. If on day X gold loses its direct uses, there will still be previously existing money prices that had been established on day X – 1, and these prices form the basis for the marginal utility of gold on day X. Similarly, the money prices thereby determined on day X form the basis for the marginal utility of money on day X + 1. From X on, gold could be de­manded for its exchange value alone, and not at all for its direct use. Therefore, while it is absolutely necessary that a money originate as a commodity with direct uses, it is not absolutely necessary that the direct uses continue after the money has been established.”

Rothbard makes the obvious point that if money prices have already been set by direct use value in the past, there is no requirement that the money good continue to have its direct use value in regards to the regression theorem. Similarly, it does not follow that it is necessarily a “pyramid scheme” because it has no direct use value. A pyramid scheme is defined as “an unsustainable business model that involves promising participants payment or services, primarily for enrolling other people into the scheme, rather than supplying any real investment or sale of products or services”. However, Bitcoin clearly does not fall under this definition, as it is potentially sustainable (as shown by Rothbard), and provides a service in the sense that it holds exchange value. Purveyors of this argument fail to understand that simply because Bitcoin doesn’t hold direct use value, or material uses, it does not imply that there are no “real services” provided. The exchange value it holds is the real service, and with this understanding, it is apparent that the “pyramid scheme” claim collapses under economic analysis.

In summation, with sufficient understanding of the regression theorem, we may conclude that, until Mises’ praxeological chain of logic is articulately challenged, the de facto Austrian position must be one in which Bitcoin does not violate the regression theorem, and thus may function as a medium of exchange or money. People may argue against Bitcoin on the basis of its merits as a money, in that it can’t be the most saleable good, or isn’t a reliable store of value, but these are not praxeological arguments against whether Bitcoin can be a money. They are arguments against whether Bitcoin is efficient as a money from a posteriori basis. As a community, we must stress the dissociating of Austrians with those who argue that Bitcoin cannot be a money; most people will associate these claims as being Austrian, whereas it has been made clear beyond reasonable doubt that they cannot possibly be so.



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