Mises’ most notable accomplishment was his regression theorem, which traces the value of money back day by day to the time when it was valued only for its use.24 This author is mostly in agreement:
Let us say that the value of a unit of commodity money was V0 when it was still valued primarily for its use value. After the jth day, the change in value is a proportion of the day before's value. Thus, with ej the change in value on the jth day relative to its value on the day before. If ej were the same every day, the value of commodity money would be growing exponentially with a common ratio of 1+e. ej is not the same every day, however, because each day has its own particular effect on the value of commodity money. In the long run, the ej's may be considered random as they are not directly related to each other nor are they uniquely a function of Vj. Furthermore, it is assumed that they are taken from an unspecified distribution, but one with a finite mean and a non-zero, finite [variance].25 Phenomena that change in this way every day conform to the characteristics of proportionate effect (1999, p. 83).
But Mises stopped short of seeing the true significance of his regression theorem. This author’s first theorem (1999, p. 102), The Law of Proportionate Effect, asserts that phenomena which conforms to the characteristics of proportionate effect26 are lognormally distributed. And this is the foundation for the whole of the theory, right up to theorems 12 and 13 (1999, pp. 137-141), the Law of Price Adjustment, which claims that the price at saturation increases exponentially and the stock remains constant in response to an increase in the importance of a phenomenon relative to money.
24 It is a sad fact that there are many people with only a superficial knowledge of economics: They have heard of the Austrians and have recently learned that the dollar is not backed up by gold. Frequently dropping Mises’ and Hayek’s names, they will breathlessly tell one about this “conspiracy,” concluding that the currency will collapse at any moment and, hence, we should all buy commodities which, they say, have “intrinsic” value and are thus stable. It is unfortunate that such people associate themselves with the Austrians because, in fact, it was Menger who replaced intrinsic value with subjective value, disentangled use and exchange value and disassociated the origin of money from the decrees of the church or state; it was Mises’ regression theorem which explained the “psychological marvel” of how a fiat currency can retain value; and it was Hayek who explained why mining, being the highest of his five stages, is the most volatile. To counter such sophistry, this author recommends a more widespread distribution of Menger’s Principles (1981). Ever since Smith’s 500-page tome (1976) got itself attached to America’s Bicentennial celebration, popular bookstores have stocked multiple editions of it to the exclusion of all other economic treatises. Apparently people buy them to decorate their offices, since almost nobody has read past the pin factory story. Smith’s reputation has outlived his contributions while Menger dashes popular misconceptions that are as prevalent today as they were a century ago. If the Mises Institute offered bookstores a clothbound edition below cost, they would do more for the cause of sound economics than all their proselytizing. 25 There is a typographical error in my book on page 83: I wrote “average” but meant “variance.” 26 “That first-unit demand conforms to the characteristics of proportionate effect must be regarded as an axiom. A plausibility argument is provided here. Let mj = φ(mj-1) with mj the number of monetary units to which one is indifferent relative to the first unit of a phenomenon on the j'th day of that person's life. We want to show that φ(mj-1) = (1+εj)mj-1. Consider a man who wants to take out a loan at interest. He must think he will have more money in the future than he does now. (More money holdings, not necessarily more wealth.) If he does, the value of individual monetary units will tend to decrease over time relative to other phenomena; that is, φ is a positive function when averaged over all phenomena. To determine how much interest he is willing to pay, the man must specify this average φ. For him to calculate the interest owed per unit of time as a percentage of the principle is equivalent to specifying φ(mj-1) = (1+ε)mj-1 with ε > 0 fixed. Fixing ε is a special case of εj being a random variable. Here, the probability density function is unity at ε and zero elsewhere. Thus, the axiom that first-unit demand conforms to the characteristics of proportionate effect is a generalization of calculating interest as a percentage of the amount owed” (Aguilar 1999, p. 103).