The Regression Theorem: Misconceptions

In two previous posts, I described the regression theorem and discussed its practical applications. In this post, I will discuss some misconceptions.

Misconception 1. The regression theorem only applies to a barter economy.

In a recent article, Laura Davidson and Walter Block argue that the regression theorem is only applicable in a barter economy.

It explicates how a barter economy—where all economic calculation is conducted ordinally—becomes a monetary economy in which calculation is performed cardinally. It should not be interpreted to mean that once a calculational framework in terms of money prices is established, that all future media of exchange (or monies) within that economy must arise from having a prior non-monetary use. The theory therefore is not an explanation for the origin of all monies or all media of exchange.

Of course, such a view would eliminate the practical applications I highlighted in an earlier post. I think Davidson and Block are wrong. Mises is quite clear that the regression theorem applies more broadly.

To explain an event historically means to show how it was produced by forces and factors operating at a definite date and a definite place. These individual forces and factors are the ultimate elements of the interpretation. They are ultimate data and as such not open to any further analysis and reduction. To explain a phenomenon theoretically means to trace back its appearance to the operation of general rules which are already comprised in the theoretical system. The regression theorem complies with this requirement. It traces the specific ex-change value of a medium of exchange back to its function as such a medium and to the theorems concerning the process of valuing and pricing as developed by the general catallactic theory. It deduces a more special case from the rules of a more universal theory. It shows how the special phenomenon necessarily emerges out of the operation of the rules generally valid for all phenomena. It does not say: This happened at that time and at that place. It says: This always happens when the conditions appear; whenever 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. And all these statements implied in the regression theorem are enounced apodictically as implied in the apriorism of praxeology. It must happen this way.

Misconception 2. The regression theorem says that, since a particular item lacked some non-monetary use at the outset, that item is not a money.

Some people claim that, if an item lacks a non-monetary use at the outset, it is not a money. Such claims are all too common in the context of bitcoin (which I will turn to in my next post!). However, the statement confuses a definition with a theoretical prediction. Money is defined as a commonly accepted medium of exchange. Any item that is a commonly accepted medium of exchange is money. Any item that is not a commonly accepted medium of exchange is not money. It is as simple as that.

Notice that we need not make any reference to the regression theorem in order to determine whether something is (or is not) money today. We need only consider whether it satisfies the definition of money—that is, whether it is a commonly accepted medium of exchange. To be sure, Mises claimed that “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.” But that is a theoretical argument, not a definition. It is to say that the item cannot become a money. It does not say that that the item is not a money by definition. Moreover, we should at least consider the prospect that Mises was wrong. Ruling such questions out by employing a non-standard definition of money gets us nowhere.

Misconception 3. The regression theorem cannot be empirically refuted.

Ok. This is a tricky one. There is a grain of truth here. It is true that a logically valid theory cannot be refuted empirically. But this creates some confusion so let’s break it down a bit. Suppose we have a theory that says “If A, then B.” One common approach is to go out into the world and see whether or not we observe B. If we don’t, some will mistakenly say: “See, that theory is wrong! We don’t observe B in the real world.” Usually, though, the real world does not satisfy all of the requirements in A. (It would be amazing if it did. When generating theories, we typically make some simplifications to keep the model tractable. The real world is a complex place.) In other words, what has been shown is not that the theory is invalid, but rather that it is not empirically relevant for the world we happen to live in where the conditions of the theory are not met.

What if one demonstrates both that (i) all the conditions in A are met and (ii) we do not observe B? In that case, we have shown that the theory is invalid. (And we have done so without overturning the philosophy of science!) Now, in practice, it can be very difficult to demonstrate (i) and (ii) conclusively. Suppose we observe an item functioning as a medium of exchange that appears to have lacked a non-monetary use at the outset. Can we state that the regression theorem is invalid?

Not so fast! As Graf explains, all that we have shown is that we have not found a non-monetary use. That is not quite the same as showing a non-monetary use did not exist. Perhaps some non-monetary use existed and will be discovered in the future. Perhaps some non-monetary use existed but will never be discovered. We cannot rule either of these cases out with the evidence at hand. In other words, our empirical evidence—that we have not found a non-monetary use—is insufficient to rule the regression theorem invalid.

Misconception 4. The regression theorem is valid.

That’s right: I am claiming that the regression theorem, as usually interpreted, is invalid. You might be surprised, given the difficulty of ruling out the regression theorem empirically. But we need not rely on an empirical refutation. We can refute it theoretically. My reasoning is pretty straightforward. There is no denying that Mises offers a valid explanation for how an item might become a medium of exchange. But others offer valid explanations that do not require some non-monetary use at the outset. Therefore, the strong version of the regression theorem—which states that an item must have some non-monetary use—cannot be valid. QED.

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