He has a back test, which looks plausibleBefore I get to my model, I want to take a step back for a moment and discuss a strange paradox in economics known as Gibson’s Paradox. This is one the most puzzling topics in economics. Gibson’s Paradox is the observation that interest rates tend to follow the general price level and not the rate of inflation. That’s very strange because it seems obvious that as inflation rises, interest rates ought to keep up. And as inflation falls back, rates should move back as well. But historically, that wasn’t the case.
Instead, interest rates rose as prices rose, and rates only fell when there was deflation. This paradox has totally baffled economists for years. Yet it really does exist. John Maynard Keynes called it “one of the most completely established empirical facts in the whole field of quantitative economics.”? Milton Friedman and Anna Schwartz said that “the Gibsonian Paradox remains an empirical phenomenon without a theoretical explanation.”?
Even many of today’s prominent economists have tried to tackle Gibson’s Paradox. In 1977, Robert Shiller and Jeremy Siegel wrote a paper on the topic. In 1988 Robert Barsky and none other than Larry Summers took on the paradox in their paper “Gibson’s Paradox and the Gold Standard,”? and it’s this paper that I want to focus on. (By the way, in this paper the authors thank future econobloggers Greg Mankiw and Brad DeLong.)
It’s my hypothesis that Summers and Barsky are on to something and that we can use their insight to build a model for the price of gold. The key is that gold is tied to real interest rates. Where I differ from them is that I use real short-term interest rates whereas they focused on long-term rates.
Here’s how it works. I’ve done some back-testing and found that the magic number is 2% (I’m dumbing this down for ease of explanation). Whenever the dollar’s real short-term interest rate is below 2%, gold rallies. Whenever the real short-term rate is above 2%, the price of gold falls. Gold holds steady at the equilibrium rate of 2%. It’s my contention that this was what the Gibson Paradox was all about since the price of gold was tied to the general price level.
Now here’s the kicker: there’s a lot of volatility in this relationship. According to my backtest, for every one percentage point real rates differ from 2%, gold moves by eight times that amount per year. So if the real rates are at 1%, gold will move up at an 8% annualized rate. If real rates are at 0%, then gold will move up at a 16% rate (that’s been about the story for the past decade). Conversely, if the real rate jumps to 3%, then gold will drop at an 8% rate.
