Treasuries, TIPS, and Gold (Wonkish)/September 6, 2011, 9:18 PM

Treasuries, TIPS, and Gold (Wonkish) 財務省証券、物価連動債、そして金(オタク風)

(Yes, it’s 4:30 AM where I am. I found myself wide awake, thinking about gold prices. You got a problem with that?)

In assessing economic prospects since the financial crisis of 2008, there have been two kinds of people: people who divide people into two kinds and people who don’t inflationistas and deflationistas. The inflationistas look at budget deficits and monetary base, and see severe inflation and soaring interest rates as the obvious outcome; the deflationistas say, hey, we’re in a liquidity trap, so monetary base is sterile and budget deficits are just soaking up some but not all of the world’s excess saving.

I am, of course, a big deflationista, and as I see it record low interest rates strongly vindicate my position. As I like to point out, if you’d believed the inflationistas at the Wall Street Journal and elsewhere, you would have lost a lot of money.

But what about gold? As some readers and correspondents love to point out, you would have made a lot of money if you’d bought gold early in this mess. So doesn’t that vindicate the inflationistas, to some extent?
でも、金に関しては? 読者やメル友の中にそのことを指摘したがる人がいるんだが、もしあなたがこの混乱の初期に金を買っていたら、お金をがっぽり稼げただろう。それなら、これはある程度までインフレ論者の立場を証明することになるのか?

My usual response has been that I have no idea what drives the price of gold, to say that it’s a market driven by hoarding in Asia, Glenn Beck followers, whatever. But maybe I’ve been too flip here. Why not think about what actually should be driving gold prices? And I mean think about it, rather than going for slogans about inflation, debased currencies, and all that.
僕のいつもの返答は何が金の価格を押し上げているのかは分からないというもので、それはアジアでの買いだめやグレン・ベックの支持者その他のことによって左右される市場であると言ってきた。でも、たぶん僕はこのことを軽く考えすぎだった。なぜ、実際に金の価格を押し上げているはずのものが何かを考えないのか? そして、僕はインフレや通貨の堕落、その他のスローガンへ向かうよりも、そのことについて思案している。

Well, I’ve been thinking about it ― and the answer surprised me: soaring gold prices may be quite consistent with a deflationista story about the economy.

OK, how do we think about gold prices? Well, my starting point is the old but very fine analysis by Henderson and Salant (pdf), which was actually the inspiration for my first good paper, on currency crises. H-S suggested that we start by modeling gold as an exhaustible resource subject to Hotelling pricing.
オッケー、僕が金価格についてどう考えているのか? 僕の出発点はヘンダーソンとサラント(pdf)による古くはあるが、すごく見事な分析であり、それは実際に通貨危機に関して、僕が始めていい仕事ができた論文にインスピレーションを与えた。ヘンダーソンとサラントは金をホテリング・プライシング(Hotteling pricing)に従う枯渇資源としてモデル化することから始めることを提示した。

Here’s how it works. Imagine that there’s a fixed stock of gold available right now, and that over time this stock gradually disappears into real-world uses like dentistry. (Yes, gold gets mined, and there’s a more or less perpetual demand for gold that just sits there; never mind for now). The rate at which gold disappears into teeth ― the flow demand for gold, in tons per year ― depends on its real price:


Crucially, at least for tractability, there is a “choke price” ― a price at which flow demand goes to zero. As we’ll see next, this price helps tie down the price path.
本質的に、少なくとも取り扱いやすくするためには、「チョーク価格(choke price)」―フローの需要がゼロになる価格―が存在する。次に見るように、この価格により、価格の軌道は拘束される。

So what determines the price of gold at any given point in time? Hotelling models say that people are willing to hold onto an exhaustible resources because they are rewarded with a rising price. Abstracting from storage costs, this says that the real price must rise at a rate equal to the real rate of interest, so you get a price path that looks like this:
それなら、ある一定の時点において、金の価格を決めているものは何か? ホテリング・モデルが示すところによると、人々が喜んで枯渇資源を持とうとするのは、その価格が上昇することにより報われるからであるという。これは、貯蔵費を無視すれば、金の実質価格は実質利子率と等しい率で上昇する必要があるということになり、その時、価格の経路はこんな感じになる:


Obviously there are many such paths. Which one is correct? Given rational expectations (I know, I know) the answer is, the path under which cumulative flow demand on that path, up to the point at which you hit the choke price, is just equal to the initial stock of gold.
明らかに、そのような経路は多数存在する。どの経路が正しいのか? 合理的期待を想定すれば(分かってる、分かってる)、その答えは、ある経路でフローの需要がチョーク・プライスに達する時点までの集計が、初期の金のストックとちょうど等しくなるような経路だ。

Now ask the question, what has changed recently that should affect this equilibrium path? And the answer is obvious: there has been a dramatic plunge in real interest rates, as investors have come to perceive that the Lesser Depression will depress returns on investment for a long time to come:
今、あの疑問を考えてみよう、最近、この均衡の経路に影響を与えることができる何が変わったのか? そして、その答えは明らかだ:投資家が、小恐慌は長期的に投資の収益性を圧迫すると捉えるようになってしまったために、実質利子率が劇的に低下した。


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.
利子率が低くなることはホテリング・パスにどんな影響を与えるのか? それを平坦にさせるというのがその答えだ:投資家に金を保有するインセンティブを持たせるため必要な価格上昇は少なくなる。

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.

But suppose this is the right story, or at least a good part of the story, of gold prices. If so, just about everything you read about what gold prices mean is wrong.

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. Not only are surging gold prices not a sign of severe inflation just around the corner, they’re actually the result of a persistently depressed economy stuck in a liquidity trap ― an economy that basically faces the threat of Japanese-style deflation, not Weimar-style inflation. So people who bought gold because they believed that inflation was around the corner were right for the wrong reasons.

And if you view the gold story as being basically about real interest rates, something else follows ― namely, that having a gold standard right now would be deeply deflationary. The real price of gold “wants” to rise; if you try to peg the nominal price level to gold, that can only happen through severe deflation.

OK, none of this necessarily rejects other hypotheses about gold; in particular, there could be a bubble over and above the Hotelling aspect. But the crucial message is, I think, right: If you believe that gold prices are signaling an inflationary threat, I have to tell you, I do not think that price means what you think it means.

Update:Larry Summers directs me to a 1988 paper he wrote with Robert Barsky (pdf) with a similar theme, although applied to the gold standard era rather than recent events.