It’s relatively common to see the regression theorem being mentioned in economic discussion, especially when it comes to whether or not something is money. This is surprising because the regression theorem has absolutely nothing to do with money or the definition of money. Regression theorem only involves prices and is really more a direct restatement of common sense.
To understand the regression theorem, we must understand the Austrian description of the establishment of prices – where does price come from? How do we know how much to sell good X for? The quick answer is the current price comes from past prices. The current price of an item comes from the price that it was yesterday, a week ago, a month, or a year ago. The price of a good comes from what the good was worth in the past, the price evolves and changes through the countless interactions in the market and originates from previous prices. By the same token, the value of money must too evolve from the past.
Here an objection was raised: “Monies have not always been in existence, they rise and fall. If price comes from the past and at some point in the past this money was not in existence, then where did the price come from in the first place? That certainly sounds like circular logic to me? In order to respond to this criticism, the regression theorem arose.
To quote Rothbard from Man, Economy, and State (source):
“To determine the price of a good, we analyze the market demand schedule for the good;…