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The Regression Theorem: Practical Applications

May 23, 2017

In my last post, I offered a brief summary of the regression theorem and provided some historical context to explain why it is an important idea.  In this post, I will trace some practical applications of the regression theorem.

Commodity monies can emerge naturally.

The first practical application of the regression theorem concerns commodity monies—that is, items that have some value apart from their role as a medium of exchange. Since commodity monies have some non-monetary use value, they command a positive price at the outset, before anyone accepts them as a medium of exchange. “When individuals began to acquire objects, not for consumption, but to be used as media of exchange,” Mises (1934, pp. 109-110) explains, “they valued them according to the objective exchange-value with which the market already credited them by reason of their ‘industrial’ usefulness, and only as an additional consideration on account of the possibility of using them as media of exchange.” In other words, commodity monies have no trouble getting off the ground because they have some initial positive value before they are employed as money. “The earliest value of money” need not be a question would-be users have to give much thought because it “links up with the commodity-value of the monetary material” (p. 110).

The practical relevance of the regression theorem, with respect to commodity monies, is that no special explanation is required. Commodity monies can emerge naturally—that is, in the absence of sovereign support—along the lines described by Menger. In other words, the regression theorem is consistent with the observed existence of traditional monies like gold, silver, copper, and salt. It is also consistent with the somewhat strange monies—like cigarettes—that sometimes emerge in more modern times when individuals find themselves in difficult situations without access to more familiar monies.

Fiat monies require sovereign support.

The second practical application of the regression theorem concerns fiat monies—that is, items that have no value apart from their role as a medium of exchange. Unlike commodity monies, which have some value at the outset, before they are employed as a medium of exchange, fiat monies have no such value. How does one assign a positive value to an item that she does not consume and that no one else consumes either? To say that the item is valuable because it might be useful as a medium of exchange merely begs the question since an item can only be useful as a medium of exchange if it has some positive value. Think about trying to spend a zero-dollar bill. Or, a 100-bancor bill that has a current value equal to $0. Why would anyone exchange valuable goods and services for an item that, at the outset, is worth nothing?

This logic led Mises to conclude that, although commodity monies can emerge naturally, fiat monies cannot. “This link with a pre-existing exchange-value is necessary not only for commodity money, but equally for credit money and fiat money.’ No fiat money could ever come into existence if it did not satisfy this condition.”

How, then, can we explain the existence of fiat monies? Mises (1934, p. 111) offers two explanations. “It may have come into existence because money-substitutes already in circulation, i.e., claims payable in money on demand, were deprived of their character as claims, and yet still used in commerce as media of exchange. In this case, the starting-point for their valuation lay in the objective exchange-value that they had at the moment when they were deprived of their character as claims. The other possible case is that in which coins that once circulated as commodity-money are transformed into fiat money by cessation of free coinage (either because there was no further minting at all, or because minting was continued only on behalf of the Treasury), no obligation of conversion being dejure or defacto assumed by anybody, and nobody having any grounds for hoping that such an obligation ever would be assumed by anybody. Here the starting-point for the valuation lies in the objective exchange-value of the coins at the time of the cessation of free coinage.” Notice that both explanations require sovereign power.

In the first case, a contractual obligation to redeem a note on demand for some underlying commodity is broken. Private actors do not have the authority to invalidate a contract. It is true, of course, that private note-issuing banks can (and historically did) include an option clause, whereby they could suspend redemption. But such suspensions are temporary (and, historically, required banks pay their customers a penalty rate of interest during the period of suspension). It is not clear why anyone would sign a contract that permitted permanent suspension since the bank would then be well within their rights to take your money and run. As such, we should expect suspensions—to the extent that they are contractually permissible—to be temporary; and—to the extent that they are permanent—to be precipitated by the legal invalidation of a contract, which private actors cannot accomplish without assistance from the legal authority.  Indeed, in many historical cases, governments first monopolized the note issue and then invalidated their own obligation to repay, transforming a redeemable claim to commodity money into an irredeemable paper, or fiat, money.

In the second case, there is a legal prohibition—in whole or in part—against the minting and melting of coins. In this scenario, the supply of coins is not permitted to fluctuate in response to changes in purchasing power of coins and, as such, its value becomes divorced from that of the underlying commodity. Again, such prohibitions cannot be orchestrated by private actors, who do not have the authority to prevent coins from being minted or melted. Government are required for such prohibitions.

What about modern fiat monies that were not once redeemable claims or coins? Does the existence of such monies disprove the regression theorem? George Selgin offers a third mechanism for creating an intrinsically worthless item. In brief, a government can introduce a new fiat money from scratch—but it must fix the value of the new money, at least provisionally, to some existing money. Consider, for example, the South Sudanese pound, which was introduced on July 18, 2011. It had not previously been a redeemable claim; nor was it a coin that users had been free to mint and melt. Indeed, it did not exist prior to 2011. But, when it was introduced, the Republic of South Sudan pegged its value to the Sudanese pound, which had circulated in South Sudan and would continue to circulate in Sudan. In such cases, the government can create some demand for the new fiat money via public receivability and legal tender laws; but it must also provide a synthetic connection to some historically accepted item by establishing a fixed exchange rate.

Aside from cryptocurrencies like bitcoin, which I will discuss in a future post, I am aware of no historically accepted fiat money that did not come about through one of these three mechanisms. (If you know of such of an example, please email me!)


The regression theory offers some clear predictions regarding what sorts of items can and cannot function as money and under what circumstances. Commodity money can emerge naturally. Fiat monies require some form of sovereign support to get off the ground (though, once they have gained circulation, the fixed exchange rate or sovereign backing can be removed). In my next two posts, I will consider how well these predictions stack up in a world with cryptocurrencies.