[UPDATE: In the analysis below, I neglected nominal interest rates, which would allow the spot price of gold to rise over time. In my examples it wouldn't change too much, since short-term nominal rates were so low this year. But I think this might thwart Rothbard's general critique of Fisher, returning it to the familiar issue of the 0% floor on nominal interest rates--which isn't where Rothbard felt the action was.]

At the Rothbard Graduate Seminar today we went over Murray Rothbard's argument in Man Economy & State that the "Fisher relation" is bogus. Rothbard argues that it's wrong when people say, "If lenders desire a 2% real return, and they expect 5% price inflation, then the nominal interest rate must be 7%."

Rothbard argues that this is nuts, because the prices of inputs (raw materials, capital goods) would change almost instantly to eliminate any expected future price move. I don't think Rothbard developed the insight enough, and as it stands I think he is skipping way too many steps to reach his conclusion. However, it inspired the following train of thought:

* Gold is extremely well-suited for long-term storage and has a high market value per unit of weight and volume. Therefore, it can't possibly be the case that most investors expect the spot price of gold to rise by, say, more than 10% over the next twelve months. If they really believed that, they would stockpile gold now, pushing up its price to the expected future level. With a liquid futures market, the speculators would even more easily eliminate large expected price swings.

* Under this framework, the fact that gold has risen 9% year-to-date does not mean that past injections of money are finally "having an impact." No, what it means is that the market's estimate of the spot price of gold on (say) July 1, 2009 increased by 9% from January 2 to June 10. The Fed presumably had a lot to do with the increase of gold's spot price, but if so it was because of what the Fed did (including their public statements) from January 2 to June 10. How could the market possibly be reacting in February 2009 to things the Fed did in the fall of 2008?

* Obviously the above, breezy analysis is abstracting away from many serious real-world complications. Perhaps one of the biggest is that speculators don't simply have "an expected spot price of gold" for July 1, 2009. Rather, it would be much more accurate to say that they have a range of possible spot prices, the different partitions of which they assign more or less likelihood.

* I think part of what may be happening in the current environment is not so much that speculators revised their estimate of July 2009 spot prices up by 9% from January to June. Rather, they may have gone from thinking "99.9% chance gold will be $870 and 0.1% chance it will be $2000 on July 1" on January 2, to thinking "99.5% chance gold will be $870 and 0.5% chance it will be $2000 on July 1" on June 15. (Note that there's nothing special about those numbers; I am just trying to get my point across, not trying to come up with realistic distributions to yield the actual gold spot prices.)

* If the above is what's going on (perhaps over a longer time frame than simply year-to-date), then this would surely show up in the spreads between call options with various strike prices, right? (Sometimes my intuition leads me astray in derivatives pricing.) If so, does anyone know where to grab this data? If I still had access to a Bloomberg terminal, I think it would be simple to find.