Eddy Elfenbein recently put forward a simple model relating gold prices and interest rates:

The key insight is that Gibson’s Paradox never went away. It still exists, just in a different form. I got this idea from a 1988 paper by Larry Summers and Robert Barsky, “Gibson’s Paradox and the Gold Standard.”

Where I differ from Summers and Barsky is that I focused on short-term interest rates while they focused on long-term rates. Well, with Operation Twist we got a perfect test of who’s right.

The Fed’s new plan is to sell short-term Treasury bills and buy long-term Treasury bonds. This means that long-rates will be pushed down and short-rates will be pushed up. If gold rises, then Barsky and Summers are right; if gold falls, then I’m right.

At this point Elfenbein is only talking about correlations. But as he continues to discusses his model, he seems to take a causal stance:

I said in my original post that the price of gold is basically a political decision. The Fed can change the game anytime they want to. I can’t say whether this will lead to a long-term decline in gold. That will depend on inflation and interest rates. But for now, the gold market is clearly observing the short end of the yield curve.

I don’t want to presume too much about Elfenbein’s belief about any potential causation. But it’s still an interesting question: is there any evidence of causation? If so, in which direction does it run?

Looking at the chart in Elfenbein’s post, I can see a few places were gold clearly seems to lead the model. Visual inspection may be good for forming an initial hypothesis, but I wanted something less prone to human error. There are several statistical tools that test for causality in time series. A popular one (making it readily available in software packages) is the Granger causality test.

Here are the results of running Elfenbein’s data* through the test:

Granger causality test

Model 1: Model ~ Lags(Model, 1:5) + Lags(Gold, 1:5)
Model 2: Model ~ Lags(Model, 1:5)
  Res.Df Df      F   Pr(>F)
1    221
2    226 -5 3.4034 0.005543 **
Model 1: Gold ~ Lags(Gold, 1:5) + Lags(Model, 1:5)
Model 2: Gold ~ Lags(Gold, 1:5)
  Res.Df Df      F Pr(>F)
1    221
2    226 -5 1.0924 0.3654
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

From this, I can conclude that gold Granger-causes the model but not the other way around. Gold returns provide statistically significant information about future values of the model, and thus short-term real interest rates’ movement around 2%. I used a lag of 5 months here (where the relationship was strongest), but it holds for many other lags.

We would not expect this result if “the gold market is clearly observing the short end of the yield curve.” It’s important to note that “Granger causality is not sufficient to imply true causality. If both X and Y are driven by a common third process with different lags, one might still accept the alternative hypothesis of Granger causality. Yet, manipulation of one of the variables would not change the other.”

So does “The Fed can change the game anytime they want to”? Maybe. But this test casts doubt on the idea that they do so by changing interest rates to affect the price of gold or that we can look at something like Operation Twist and expect that a fall in gold prices is the likely result.

Interestingly, Jehu Eaves, a Marxian blogger responding to my results on Twitter, thinks these results fit with Marx’s theories, placing The Fed in the laggard position:

This would be logical. Marx’s observations was that as prices denominated in gold increase so do interest rates. This would mean, fundamentally, gold lease rates are driven by the inverse of gold dollar price. Dollar interest rates then react to gold lease rates as the absolutely riskless form of saving over treasuries. Essentially, gold prices is driving Fed policy, not the other way around. It also means the real economy is reflected in the price of gold: as gold price increases, the economy contracts.

* I used normalized monthly returns of gold and the model.