Mises' Regression Theorem

I repeatedly find that much time can be saved, effort conserved, and wisdom gained by going straight to the source. The Internet has allowed for a great deal of information to be shared but it turns out, much of it is simply noise, or at best, a noisy rehash of what the great thinkers have produced.

Bitcoin, as it turns out, is no different. And for the source of Bitcoin, how much closer can we get to it than the words of its creator, Satoshi Nakamoto, and the discussions he had with curious observers in Bitcoin's earliest days?

In this blog post, I want to talk about "Mises' Regression Theorem", which provides a mathematical framework for understanding money and its origins. Seeing something so seemingly complex as money be so elegantly modeled in just a single mathematical abstraction made me truly admire the power of abstract logic and reasoning, of which math is simply a manifestation.

Mises' Regression Theorem original Bitcoin discussion thread

It all began with the earliest records of Satoshi's discussions, and eventually, this specific thread on Mises' Regression Theorem, and how Bitcoin does not violate it.

"...a money price at the end of day X is determined by the marginal utilities of money and the good as they existed at the beginning of day X. But the marginal utility of money is based, as we have seen above, on a previously existing array of money prices. Money is demanded and considered useful because of its already existing money prices. Therefore, the price of a good on day X is determined by the marginal utility of the good on day X and the marginal utility of money on day X, which last in turn depends on the prices of goods on day X \u0096 1. The economic analysis of money prices is therefore not circular. If prices today depend on the marginal utility of money today, the latter is dependent on money prices yesterday."

Very simple - the price of money on any given day is dependent on the price of money the day before.

"Rothbard then goes on to explain that in order for money to emerge from a barter economy, it must have a preexisting commodity value. This commodity value arises from barter demand for the potential money in direct consumption (i.e. ornamentation). This value seeds future estimations of the value of the money as a medium of exchange. The natural market emergence of money is thus fully explained."

A wonderful explanation for the natural market emergence of commodity-based money from a barter economy where one commodity eventually emerges as the dominant money.

"However, once an economy has been monetized and a memory of price ratios for goods and services has been established, a money may lose its direct commodity value and still be used as a money (medium of indirect exchange)."

"On the other hand, it does not follow from this analysis 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 \u0096 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, the author quoted in the thread, notes that a medium of exchange may lose its direct commodity value and still be used as a medium of exchange. Rothbard denotes such a money as a "medium of indirect exchange".

"This explains the history of fiat currencies. They originally started off as simple names for weights of commodity money (silver) that developed out of the pre-monetary barter economy. Despite later losing their ties to direct commodity value through state interference, paper currency retained status as money because of memory of previous money prices. This factor is so strong that the relationship between gold and the USD, for example, is somewhat inverted. Gold no longer circulates as a common medium of exchange. Prices are set in USD, not in gold. Most individuals wishing to trade in gold do so based on their knowledge of USD/gold price ratios. ("Hey, let me buy that $100 couch from you in gold?" "Ok, USD/gold is $1000/oz. Give me 1/10oz of gold.") Legal tender laws, state taxation, and the entire financial regulatory environment maintain this inertia of USD prices and make it challenging to return to gold money directly, despite the destructive inflationary nature of fiat currencies."

Continuity is powerful. Fiat currency is one of the best examples of this - people continue to use green pieces of paper as money even after it ceased to be backed by gold, which is the actual original money, simply out of custom, ease, and ignorance.

"The essential point is that once exchange can occur between a money (USD) and Bitcoins, providers of goods have a means by which to value Bitcoins as a potential medium of exchange. The money regression is satisfied, because taken back far enough we reach traditional commodity money: BITCOINS -> USD -> MONETIZED GOLD & SILVER [start monetary economy] -> [end barter economy] COMMODITY GOLD & SILVER."

The natural progression of money from:

would thus be the expected progression of money.

When I phrase it like that, it's truly incredible that people are using paper as money today. Historians will look back on this time period as a great anomaly in humanity's (temporary) departure from sound money.

Daniel Krawisz' Take - "The Original Value of Bitcoins"

Daniel Krawisz, an OG Bitcoin blogger, has a take on Mises' Regression Theorem that is worth reading.

"The regression theorem addresses two separate issues: the emergence of a medium of exchange, and the evolution of a medium of exchange into money. A medium of exchange is defined to be something that is bought for the purpose of trading it for something else later. Money is the medium of exchange which is pre-eminent among all others."

A succinct take on what a medium of exchange is, and that money is the most widely used medium of exchange.

"As to the first issue, the explanation depends upon the observation that in order for something to be sold it must be treated as an economic good by both buyer and seller—meaning that they both would want some of it, even if they each are willing to pay different prices. If the buyer did not treat it as a good, then he would not be willing to pay for it, and if the seller did not treat it as a good, then he would be willing to give it away, or even pay to have it taken away. Since a medium of exchange is something which is bought and then resold, it must be treated as an economic good by both parties in both transactions."

"Thus, the first person who is able to use a good as a medium of exchange must buy it from someone who also treats it as a good—yet who did not use it as a medium of exchange. Hence it follows that a thing becomes a medium of exchange on the basis of some other demand, and no other evolution is possible."

The birth of a medium of exchange based on market phenomena requires that someone else values the medium of exchange as an economic good (not solely as a medium of exchange) first.

"The correct approach should have been clear to any Austrian economist, but until recently, Austrian analyses of Bitcoin have been superficial. It is not yet generally understood among Austrians that Bitcoin is fundamentally different from both gold and fiat currencies, and therefore requires a fundamental analysis going back to first principles. This may have to be reiterated a few more times before the Austrian movement is convinced."

Going back to first principles is required to appreciate what Bitcoin is achieving and could potentially be. You cannot simply look at history and parrot that gold has always been used as sound money and thus always will be.

"The correct approach, I think, was hinted at by Šurda, who obliquely says, "According to my opinion, the rational expectations of the potential utility of Bitcoin for the potential buyers exceeded the price demanded by the producers, and trade emerged".10 Bitcoins would have had value to the person with the right entrepreneurial mindset."

The bootstrapping of Bitcoin's value as an economic good from 0, explained.

"Bitcoins are a puzzle to resolve, not an excuse to deny reality." - Daniel Krawisz.