### Grant McDermott

Data. Economics. Environment.

# Krugman, Hotelling and gold

... and negative (short-run) supply curves.

Paul Krugman's recent column, which links the high price of gold to a disinflationary environment, has generated a lot of discussion in the blogosphere. In essence, he references the Hotelling Rule to show that a high gold price is perfectly consistent with the rock-bottom treasury yields... despite the fact that these two extremes seem to simultaneously imply contradictory expectations of 1) hyperinflation and 2) deflation/very low inflation.
What effect should a lower real interest rate have on the Hotelling path? The answer is that it should get flatter: investors need less price appreciation to have an incentive to hold gold. But if the price path is going to be flatter while still leading to consumption of the existing stock — and no more — by the time it hits the choke price, it’s going to have to start from a higher initial level. So the change in the path should look like this:

And this says that the price of gold should jump in the short run.

The logic, if you think about it, is pretty intuitive: with lower interest rates, it makes more sense to hoard gold now and push its actual use further into the future, which means higher prices in the short run and the near future.

[...]For this is essentially a “real” story about gold, in which the price has risen because expected returns on other investments have fallen; it is not, repeat not, a story about inflation expectations. [...]So people who bought gold because they believed that inflation was around the corner were right for the wrong reasons.
Krugman's invocation of the Hotelling Rule here is pretty neat. I certainly count myself as someone in the non-inflationista camp and have been using the "right for the wrong reasons" line on gold bugs for a while. At least those claiming the high gold prices reflects an impending surge in (hyper)inflation, while the actual numbers themselves $$-$$ CPIX, BPP and bond rates $$-$$ show anything but. It's like an overweight person looking into a fairground mirror and congratulating themselves on their successful diet... all the while losing weight for unrelated reasons. Perhaps they've become enamoured with their reflection and forgotten to eat?

Tortured metaphors aside, I do, however, have two problems with Krugman's analysis:
1. Bond rates certainly aren't low everywhere (Greece, Portugal, etc), and US consumers certainly aren't the only ones buying gold.
2. The Hotelling Rule has, historically, been a poor guide to the price path of gold (and, indeed, other metals). There's nothing wrong with the reasoning behind the H-R in of itself; indeed, it conveys an elegant truth that is almost impossible to refute, ceteris paribus. However, abstracting to a pure interest rate effect hasn't proven empirically successful. In short, it has been overwhelmed by technological shocks on the supply side, as well as other demand-related factors.
That's not to say that there isn't merit in Krugman's argument, because it certainly serves a purpose in trying to reconcile high gold prices and low interest rates. At least, in the US. My own opinion differs, to be sure, but is not entirely incompatible. I see the high gold price is primarily a function of fears of insolvent governments being unable to repay their debts, and the simple dearth of alternative investment opportunities out there. As long as equities are yielding negative returns and bonds yields are low and/or risky, even modest rises in gold prices suddenly become very attractive. <Insert jokes about beauty contests here.>

===

There is a quasi-related factor to all this is that I want to finish today's post with:

The supply elasticity of gold production in certain countries $$-$$ most notably South Africa $$-$$ is negative. That is, gold miners actually cut back on production following an appreciation in the price of gold rise. Just as high gold prices and low interest rates seem incompatible (at least at first blush), the idea that producers should reduce production in the face of rising prices appears to contradict common sense. Until you understand a bit more about the circumstances under which gold miners operate.

Gold mines in South Africa are incredibly deep, making them complex and expensive operations to run. When the price of gold suddenly rises, producers are afforded the opportunity to prolong the life expectancy of a mine. They do this by mining the poorer quality veins of gold first, since it is now profitable to do so. When the price falls again, whether that be in absolute terms or relative to costs, they switch back to mining the richer deposits and thereby maintain projected cash flows. Gold producers are thus trading off short-term profitability against the expected lifetime value of their mines.

Rather presciently, John Maynard Keynes hypothesised the backward-bending supply curve for South African gold production for these reasons back in 1936.

THOUGHT FOR THE DAY: There are many factors pushing up the price of gold to extreme highs. Personally, I don't think that inflationary fears can justifiably be cited as the key driver. At the same time, there are reasons to be sceptical that high gold prices necessarily follow low interest rates (as per the Hotelling Rule). Nevertheless, there are certainly strange forces at play in determining the gold price right now. Some of the most important ones would, at first glance, even appear to contradict common sense. It may be convenient to be right for the wrong reasons for a while, but you wouldn't want to stake your career (or your house) on it any longer than is necessary.