Returning to Gibson’s Paradox

The orthodox description of the mechanism of changes in the price of gold was written by Robert Barsky and Larry Summers in their famous 1988 paper, “Gibson’s Paradox and the Gold Standard“. I lack the intellectual standing to refute it, but I would like to suggest that this description may now be insufficient in light of price action over the last 40 years.

Gibson observed that, historically and rather counter-intuitively, interest rates were strongly correlated with general price levels rather than the rate of change in price levels. In a more simplified form, if interest rates were, over a given year, at 2%, common sense tells us the general price level should go from 100 to 102. And, if the following year, interest rates were to go to 0%, one would expect the price level to remain at 102. But, common sense is often wrong. The price level is more likely to ‘follow’ interest rates back down and return to 100. That is the paradox of “Gibson’s Paradox”.

This generally held true until the years approaching the Nixon Shock, when the pretense of a gold standard was finally abandoned.

After that, Gibson’s Paradox seemed to vanish, according to Barsky and Summers. Roughly half a century ago, prices began to move how common sense suggests they should. Interest rates now tend to approximate the rate of change of prices rather than absolute price levels. Therefore, prices over the last thirty years have continued to rise while interest rates have continued to fall.

The Barsky/Summers paper, however, argues that Gibson’s Paradox is still in action and that we can observe this in the price of gold (which is the focus of the paper), as well as other metals, but that we have to use real interest rates, rather than nominal interest rates. When we turn to real interest rates, Gibson’s Paradox jumps out again. Specifically, gold and other metals have a strongly negative correlation with real interest rates. So, for example, when the rate of inflation rises above the nominal yield of treasuries, gold goes higher.

Below is the Gold Standard, or classical, version of Gibson’s paradox. You can see that it looks okay during the 1970s but then begins to disintegrate over time, and by the 2000s, it is obvious that it doesn’t function the way it used to.


And, here is the Barsky-Summers model:


It is definitely more satisfying than the classical version, but I have to say that I find the chart unappealing, although I am certainly biased. Depending on whether or not you use “real” metals prices or use 10-year yields instead of 3-month yields or use the non-log values, the correlation comes back somewhere between 0 and -0.5. The adjusted price of gold (i.e, the real price) fairs better than adjusted copper, with the former correlation coming in a little over -0.4 and the latter at -0.1 to -0.2.

However, when nominal prices are used, both revert to an average, with gold coming in about -0.23 and copper at -0.30.

I have kind of slipped copper in here, because Barsky and Summers use a comparison of non-ferrous metals to back up their argument about gold. Copper is the king of non-ferrous metals, at least in economic terms, so I have used that as a proxy for their “non-ferrous metals” category.

And, this is where things get interesting. When commenting on the comparison between the non-ferrous metals/cpi ratio (i.e., real metals prices) and real interest rates, they say, “The results are, if anything, even more striking than those for gold…”. As for gold, they comment on it’s lack of correlation (relative to the non-ferrous correlation) with real interest rates in the following terms: “Also, it is clear that, from 1980 onward, the relative price of gold is higher for any given real interest rate than it was during the 1970s. Real interest rates are not the only determinant of the price of gold. [emphasis mine] Yet the impression that real rates were high after 1981and that these rates were associated with a low relative price of gold vis-a-vis the 1980 level is unmistakable”.

This is a rather innocuous distinction–metal prices seem to be a function of real interest rates but gold is to a lesser degree than non-ferrous metals–but I think that the distinction is actually far more meaningful than it appears.

The reason I came back to the Barsky and Summers paper is because over the last decade or so, gold has effectively been a function of the copper price divided by the ten-year yield. This is something of a reversion to the classical version of Gibson’s paradox. In this scenario, when the yield rises, the price of copper in terms of gold (i.e., the copper/gold ratio) rises along with it.


It is curious to me that Barsky and Summers did not examine this angle, although it is possible that I have so misunderstood their paper that this question was simply unnecessary. But, my reading of their paper suggests that prior to the collapse of the gold standard, the price of something like copper in gold rose and fell with interest rates.

Here is a comparison of the copper/yield ratio to gold prices over the longer term.


I am not overly impressed by this relationship. The correlation is strong (0.9), but both of these levels are rising, so a strong correlation doesn’t seem overly significant.

What is more, if my perhaps foolhardy attempt to reapply the classical version of Gibson’s Paradox to current conditions were correct, then the copper/gold ratio would approximate yields.

But, this is simply and perfectly wrong. In fact, it is the gold/copper ratio that is appears to be strongly correlated with yields.


The correlation here is 0.36. And, you can see why on a short-term basis it is the copper/gold ratio that appears to be correlated with yields. (As an aside, it is interesting to note that the big gaps in the relationship between copper/gold and yields generally occur in troughs in 5-year interest rate cycles).

I have argued before that one way to mitigate these warring correlations is to shift the gold/copper ratio forward sixteen months, so that it ‘predicts’ yields, but even if that were a perfect fit (actually, only 0.4), it still does not save us from the fundamental problem: that nominal interest rates are still relevant to price levels but Gibson’s Paradox has been turned inside out in the process.

Another way to think about this is to consider the phenomena from a dollar perspective: the 1970s were marked by severe inflation, while from a gold perspective, they were marked by severe deflation.

In other words, Barsky and Summers argued that the move away from the gold standard effectively shifted Gibson’s Paradox from nominal interest rates to real interest rates. Fair enough, but why is it that nominal rates are now performing an inverted function of Gibson’s Paradox by reducing the price of things like copper in terms of gold?

I cannot answer that, but I can, to a certain degree, reconcile the classical, Gold Standard version of Gibson’s paradox with the Barsky-Summers model.

This is the gold/copper ratio versus real 10-year rates.


And, here is the gold/copper ratio forwarded sixteen months versus real rates.


The correlation here is 0.6.

This would seem to conform with both the classical Gold Standard version of Gibson’s Paradox, which says that absolute price levels should strongly correlate with yields and with the Barsky-Summers version of Gibson’s Paradox, which tells us to look to real interest rates rather than nominal yields.

That is the gist of my argument: that Gibson’s Paradox is to be found in the correlation between the gold/copper ratio and real interest rates. Or, that the price of copper (in gold) still conforms to (real) interest rates and that Gibson’s Paradox still functions much as it always has.

As an interesting aside, if the gold/copper ratio serves as the market’s estimate of where real interest rates will stand, that is effectively saying that gold/copper = (future) interest rates/(future) cpi. And, I believe that the gold/(future)yield ratio correlates fairly well with copper/(future) cpi historically. But, it is rather strange that both gold and copper should seem to be signalling rising interest rates and inflation while both of the latter have continued to be very low. Is this a meaningful tension or merely a speculative one? Does this mean that commodities will have to come back to earth or that bonds will? We will have to reflect on that later.


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