Thursday, September 8, 2011

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.


  1. "I also count myself as someone in the non-inflationista camp that has been using the "you've been right for the wrong reasons" line on gold bugs for a while. (Well, at least those that claimed the a high gold price was indicative of inflation, while the actual numbers themselves and bond rates showed anything but."

    I think you need to distinguish between monetary inflation and price inflation in your analysis.

    Monetary inflation in the US is reaching extreme levels at the moment. The correlation between US M2 and the gold price since May/June to present is close to 1, go check it on Fed website.

    Also, 1) actual CPI numbers are a poor reflection of price inflation, eg. ignores quality deterioration of product and price increases of many asset classes, and 2) the bond market is completely manipulated by the Fed and other central banks (it's the point of monetary policy) and not reflective of underlying market rates of interest.

    Therefore, using these metrics in your analysis will be misleading...

  2. How about a forecast of where you see the gold price heading over the next 5-10 years, apply your analysis and give a view of where the price is headed. $500 or $5000?

  3. Hey Stickers

    Long time no chat. When I read articles like Krugman's I get that butterfly feeling in my stomach that tells me to go loooooooong gold. This is intellectual pretzel twisting of the highest order from Krugman.

    This is from the man who missed the bubble, missed the bust, hated gold all the way up its 650% rally this past decade, and advocates more debt and money printing to fix a problem caused by debt and money printing.

    I bet if gold sold off back to $1000/oz Krugman would waste no time donning his I-told-you-so-badge, but he would still have to explain how it got from $250 to $1000 without him predicting it.

    I just can't take the man seriously anymore.

    I can't wait to keep being right for the wrong reasons all the way up to $5000/oz...

    C'mon Twig, take a couple oz punt!!

  4. Hello lads, I thought that this one might draw you out of the woodwork! Okay, some quick replies:


    "I think you need to distinguish between monetary inflation and price inflation in your analysis."

    Jokes, bud... but I know, that you know, that I know the difference between monetary inflation and price inflation. I've read my Milton Friedman for one thing... We can get pedantic about semantics, but of course "inflation" is just a convenient way to parse the ultimate effects of an increase in prices. (If monetary inflation didn't have any real impacts on prices, then I'm not sure what all the fuss would be about?) Ofc, if you are just spelling things out for other commentators, then that's also perfectly fine.

    "actual CPI numbers are a poor reflection of price inflation, eg. ignores quality deterioration of product and price increases of many asset classes"

    Okay, you start saying things like this and I start seeing epicycles. This is not a satisfactory counterargument and measurement errors -- to the extent that they exist -- could not mask severe (price) inflationary effects.

    "the bond market is completely manipulated by the Fed and other central banks (it's the point of monetary policy)"
    Absolutely correct. In this case, I wonder how many people missed the fact that the Fed would be powerless to intervene against rising (price) inflation. Of course, among other things we have to distinguish between countries that issue their own currency (cf. spreads on the Club Meds), but I imagine that you are on board as far as that goes.

  5. "How about a forecast of where you see the gold price heading over the next 5-10 years, apply your analysis and give a view of where the price is headed. $500 or $5000?"

    Without trying to sound like I'm just sitting on the fence, I honestly think somewhere in the middle. My entire point is that a high gold price is consistent with anaemic economic growth, insolvent Govts AND weak inflation. (E.g. FWIW I thought Roubini was crazy to call a $2,000 cap on the gold price when his own stag-deflationary analysis would support it going that high. Mind you, I suppose his broader argument is about the extent that gold investors are over-leveraged .)

    In short, barring a near miraculous economic recovery (don't hold your breathe), people will still be holding onto gold as tail risk hedge. I told my family to buy gold as soon as the crisis hit in late '08 and was recommending silver early afterwards as well. However, that certainly doesn't make me a gold bug -- for reasons that are best left to another time, I think that the gold standard is a bad idea. (Although, if you're interested, this article hits most of the key points from my perspective.)

    I have a counter question though, what do you think CPI will look like in 5-10 years time?

  6. @Russel

    Okay, beyond the above... Some additional comments on yours! (Which I'd like to preface by saying that I have no vested interest in defending Krugman... I certainly think that he is brilliant, but just as certainly does make him right. Because he isn't and neither is anyone else.)

    "This is intellectual pretzel twisting of the highest order from Krugman."

    I'm not sure about that. I've expressed my doubts about the extent to which the argument holds in my post here, but there's no debating the fact that he has presented a widely-accepted theory that consistently fits with his worldview. Likewise, I'd like to see Peter Schiff and co. explain the persistence of rock-bottom interest rates and failure of hyperinflation to materialise alongside their (correct) calls of a high gold price in a similarly consistent manner. I suppose that the point, again, is that so many people were arguing as if these things were mutually exclusive when they really weren't. If someone needs to explain certain elements "retroactively", then so be it... As long as it fits consistently with their original theory.

    Most importantly though, read the final paragraph of Krugman's that I quoted above. I don't believe that his primary concern has never been gold, it has always been inflation and interest rates. Gold has just been a sideshow for him and... If he has been correct about the latter two, then I'm not sure how much point scoring for the former -- which supposedly just a reflection of these real variables -- anyone deserves to get. (Much as your bank balance is better for it.)

    "... advocates more debt and money printing to fix a problem caused by debt and money printing."

    Again, I don't think that I've ever explicitly labelled myself a red-blooded "Keynesian", so I don't wish to appear as if I'm arguing blindly for team Krugman.[*] However, I find his arguments of liquidity trap economics very compelling. Indeed, I've yet to see a proper refutation of it.

    [*]If you are interested in that debate and are willing to do so in a constructive way, then might I suggest starting here?


No anonymous comments please. (Pseudonyms are fine.)