Oil - Is There a Bubble?

There is something puzzling about the price of oil. It is high and rising. I think there are a couple of good reasons why the price is high. First, demand is growing fast (in part because of growing demand from emerging markets), and new discoveries of oil have slowed down. Second, low real interest rates keep the price high. That is standard economic theory. An easy way to understand this is that when the real interest rate is low, producers have less incentive to take oil out of the ground. If they sell the oil today, what will they do with the money they earn? They’ll get a low rate of return, so they might as well keep the oil in the ground and sell it later. This restricts current supply and drives the price up today. Real interest rates have been low for a variety of reasons that have been widely discussed – U.S. monetary policy, a world saving glut, etc.

I can understand why market fundamentals make the price of oil high – but why is it rising? Let me explain this question. Oil is a durable, storable commodity. If the increase in excess demand is expected by the markets, it should be incorporated in the price immediately. That is, if the markets have understood for some time that rising demand from emerging markets was squeezing the market for oil, the price should have jumped immediately to reflect those expectations. If markets expected rising demand four years ago, and could calculate that the price would be $120 today, then the price should have been a lot higher than $40 back then. Anyone who bought a barrel of oil in 2004 would have made a 200% return over those four years. But in anticipation of $120 oil prices in 2008, markets should have bid up the price back in 2004.

Economics is an inexact enough science that we can’t know whether $125, or $60, or $200 is the right price based on fundamentals. I don’t know one way or the other what the right price of oil is, but what I don’t understand is the steady increase in the price of oil. How can an asset such as oil consistently pay such a high return?

Adding to the puzzle is the fact that the futures price has consistently underpredicted the rise in the price of oil over the past several years. If the futures price reflects mostly the market’s anticipation of the future spot price, how is it that the market has been fooled over and over for so many years?

One possible explanation is that the market has kept learning about the strength of demand and the weakness of supply over the years. It is consistently being surprised, in other words. That may be right, but it is a shaky argument: why is the market always being surprised in the same direction – that excess demand is greater than we thought?

Another story that I think makes some sense is the one that Jeffrey Frankel and Jim Hamilton have promoted – that Fed monetary policy has played a role. As I noted at the outset, a drop in real interest rates should cause commodity prices to rise. But here again, the decline would also have to be unanticipated to explain the continual increase in the price.

I think there is a lot of truth to the view that markets keep getting surprised in the direction that makes oil prices higher. We have been surprised at the growth in emerging markets, the shortfall in supply from some countries (such as Iraq), and the continuing low real interest rates. On the other hand, it seems to me that rising prices are also typical of frothy markets (like the housing market of late.) In fact, the steep rate of increase could even be a “rational bubble”. The rate of increase of the price is so high, perhaps, because the market is incorporating a probability of the bubble popping and prices falling back down to earth.

Let me back up and talk about the market for an exhaustible resource such as oil. The amount of oil pumped out of the ground doesn’t just depend on the current price. If I don’t pump the oil today, I can pump it tomorrow. Tomorrow’s price matters, bubble or no bubble.

Let’s start with the market when there is no bubble, and, as economists do, let me make this as simple as possible. Let’s assume there is no uncertainty about how much oil is in the ground, or how much people will want to buy at any price, and no cost of extraction. What should happen then is the expected rate of increase in the real price of oil should equal the real interest rate. Why? If I sell my oil today, I can take the proceeds and get the real interest rate. If I don’t sell my oil, its price goes up at the real interest rate. The incentive to “hoard” is exactly balanced by the incentive to sell, and any individual producer is indifferent between selling now or later.

In this case, there is no excess supply of oil. End users buy as much as they want at the market price, and producers pump out exactly that much. Ultimately the level of the price is determined by the condition that, as the price rises at the rate of interest forever, the sum of demand over the current year and all future years equals the amount in the ground.

Now let me turn the possibility of a “rational” bubble, and now I’m going to use some math. In a rational bubble, the oil price is rising, but there is some probability that the bubble will burst. Let r be the real interest rate. Let p(t) be the log of the real price of oil at year t, pfun(t) be the fundamental long-run price (after the bubble pops), and let k be the probability of the bubble popping. To keep it simple, I’ll assume r and k are constant. Then the expected rate of increase in the real price of oil should equal r:

r = (1-k)(p(t+1)-p(t)) -k(p(t)-pfun(t)).

(For those who aren’t familiar with logs, p(t+1)-p(t) is approximately the percentage increase in the price of oil, and p(t)-pfun(t) is approximately the amount by which oil is “over-priced” in percentage terms. The “expected rate of growth” of the oil price is simply the weighted average of the growth rate of the price if the bubble persists and the percentage decline expected if the bubble bursts. The weights are given by the probability of the bubble persisting or popping.)

So, as long as the bubble has not popped, you will see

p(t+1)-p(t) = [r+k(p(t)-pfun(t))]/(1-k).

The percentage rate of increase in the price exceeds the real interest rate. Indeed, you can see that the growth rate in oil prices would have to rise as the price rose (as p(t)-pfun(t) gets larger.) That is, the price would accelerate until the bubble burst.

In this type of rational bubble, the futures price would indicate an “expected” increase in the price equal to r, the real interest rate. But until the bubble burst, the actual increase in the price would always exceed the real interest rate. So the futures price would always underpredict the actual increase in the price of oil, much like it has in fact over the past four or five years. The payback to speculators betting against oil only comes when the bubble finally bursts.

From the perspective of producers, there is no difference between this and the no-bubble case (assuming that the producers care only about their expected return.) If they “hoard”, they expect the price to rise at the rate r, and if they sell now they can take the proceeds and earn r. They are indifferent between selling now and hoarding. There is no excess supply. Producers pump out of the ground exactly what people will buy at price p(t). The level of the price in this case is determined just as in the no bubble case – the sum of the expected demands in every period equals the amount of oil in the ground.

A bubble in asset prices need not be “rational”. But if the run-up in prices were too rapid, so that the “expected” growth rate of the price exceeded the interest rate, there would be a strong disincentive to sell any oil. Producers would want to keep the oil in the ground, and, as Paul Krugman has argued, speculators would have an incentive to hoard oil. We see very little of that type of behavior going on, as Krugman has noted.

You could make this more complicated by adding uncertainty, risk aversion, cost of pumping, etc., but it wouldn’t change the basic story. Let me note that producers may face some constraints to pumping out as much oil as they would like to at the current high price. But if so, that only means that the current price is temporarily higher than it will be once capacity is increased. That is, it is a reason to think oil prices may fall.

There is some question in the academic economics literature about whether such a bubble as I describe is really rational. This revolves around some esoteric questions of whether there is a “transversality condition” that applies or not. There has been some very complicated modeling of this under different assumptions, but I think in practice it is at least possible that a bubble could exist in a market for an exhaustible resource. There is something of a consensus that we have seen bubbles in other asset prices in the recent past – the dollar in1985, Japanese property prices in the late 1980s, the dot com bubble in the late 1990s, and, perhaps, some U.S. residential real estate markets in the past few years.

The problem for economists is that the market for oil is so complicated that we cannot very accurately calculate what the price of oil “should be” if there is no bubble. We have to read the entrails to figure out whether the price is really reflecting market fundamentals – demand, supply, real interest rates – or has a bubble component. As I look at the rising price, I wonder which story is most plausible: (1) the markets have been surprised over and over about demand by end users and production capabilities; (2) markets have been surprised over and over about how low real interest rates are; (3) there is a bubble. These stories may go together, in fact. Indeed, it is hard to see how a bubble could get started all by itself, or how it could go on for a long time before it popped. In the previous asset price bubbles I mentioned above, it seems as though fundamental economic causes set off the rise in asset prices. But it looks like the bubble traders were inspired by the price increases to bet on further increases in prices, even when there was little evidence that the price needed to rise more based on fundamentals. It’s as if the fundamental traders normally keep the bubble traders at bay. But a series of shocks to the fundamentals in the same direction seem to undermine the confidence of the fundamental traders and give the bubble traders the upper hand. In any case, if either (2) or (3) are true, we might see oil prices coming down in the future, as real interest rates return to more historic levels, or as the bubble bursts.