Strategic Reasoning

Senator Jay Rockefeller adds his voice to the chorus calling for the U.S. to deplete the strategic petroleum reserve in order to bring down oil prices.

Put aside the question of whether we should want to bring down oil prices. Put aside the question of whether this is a good use of the strategic reserve. Let’s just ask whether this idea would even work.

Simple economics certainly suggests that the answer is no. Oil, after all, is an exhaustible resource. This means that every barrel sold today is a barrel that can’t be sold tomorrow. Therefore profit-maximizing oil suppliers, of whom there are many, must constantly be asking themselves whether they’d prefer to sell another barrel now or leave it in the ground to sell later. And the key inputs to that decision are the current price and the expected future price.

If the government starts depleting the oil reserve now (with, presumably, the intent to replenish it in the future), they bid down current prices and bid up expected future prices — creating an incentive for all the other suppliers to sell less now and more in the future — pushing current prices right back up again. For a non-exhaustible resource, this would partially offset the government’s action, but for an exhaustible resource (like, for example, oil) there should be a 100% offset, at least on a naive application of Hotelling’s Rule.

Here (roughly) is the reasoning behind Hotelling’s Rule: The price of oil, in expectation, has to rise at the rate of interest. That’s because leaving oil in the ground is a form of investment, and therefore has to pay the same amount as any other investment (after adjustments for risk, etc.) That pretty much nails down the price path. If a current supplier (like the government) tries to change that price path by increasing current output and lowering the current price, then the expected growth rate (briefly) exceeds the interest rate, inducing everyone else to leave more oil in the ground. They increase this investment until it’s not a good investment anymore, which is to say until they’ve completely offset the effects of the government’s action.

If that’s wrong, it must be because Hotelling’s Rule doesn’t apply, in which case it must not apply for some reason. Has anyone even tried to offer a candidate for that reason?


23 Responses to “Strategic Reasoning”

  1. 1 1 Bennett Haselton

    I don’t have an answer, but it reminds me of a question that nagged at me ever since I first watched “Goldfinger”: James Bond discovers that Goldfinger has been amassing supplies of gold, and Goldfinger plans to detonate a nuclear bomb in Fort Knox to ensure that “the entire gold supply of the United States will be radioactive for 57 years… and the value of my gold stockpiles increases roughly 10 times”.

    Ever since hearing that, I wondered if that would work. It seems to me that gold that will be radioactive for 57 years and then go back to being normal gold, should be worth the same today as normal gold, for roughly the same reasons as Steve outlined above. (It’s like the opposite of releasing oil from the strategic reserve; you’re taking gold out of circulation and putting it *into* a reserve for 57 years. It seems that in theory, neither should affect the price of the good.)

  2. 2 2 Coupon_Clipper

    Funny. I had the same question as Bennett when I first saw the movie!

  3. 3 3 Mike H

    How ’bout this? “Hotelling’s rule is defining the net price path as a function of time while maximising rent”. If the holder of the reserves decides not to act in a way that maximises rent, doesn’t that violate the assumption of Hotelling’s rule ever so slightly? :-)

  4. 4 4 Harold

    People do not always react rationally. It sometimes seems that people behave as though oil were an inexhaustable resource, depite all evidence to the contrary. Maybe people behave as though oil were sufficiently inexhaustable within the timespan they care about.

    The sun is eventually an exhaustable resource, but we are justified as treating it as inexhaustable over human timescales.

    Many countries may wish to give the impression that they have greater reserves than they actually have. They must maintain the illusion that they could switch up and down producution at will for as long as they like, or they may wish to send other signals to the world. Political purposes may lead them to produce different amounts than would be required to maximise income.

    Countries also need to mauntain their income stream. If oil price falls, a country may decide to continue production to keep the money coming in. It may be economically better for them to borrow the money to keep up the revenue stream, and pay it back with the higher oil price later. However, this may not be politically possible.

    The scheme sounds like a non-starter really, but it could at least in the short term reduce the price a bit.

  5. 5 5 Doug

    Actually I heard a good candidate explanation (though I’m can’t remember where exactly).

    Hotelling’s rule assumes that the owner of the resource has 100% expected ownership and control over the resource extraction forever or until he sells it (recouping the expected net present value). This doesn’t necessarily describe the main player in the market who can shift production to the future, Saudi Arabia.

    Especially now with the revolutions in the Middle East, the Saudis have a less than 100% expected value for oil production shifted to the future (with p declining monotonically with time horizon). Therefore they have incentive to over-produce present supply compared to what Hoteling’s rule would suggest.

  6. 6 6 Alan Wexelblat

    My answer mirrors Doug’s – Hotelling’s rule assumes an invariance of conditions that doesn’t likely match the real world. In the US we don’t nationalize or seize resource industries, but that’s hardly true for the rest of the world (Arab countries, South American countries and African countries have all done this with startling frequency in our lifetimes). Even if you take the current turmoil in the Middle East/North Africa as a historical anomaly it would not be particularly rational to assume that the present owners of the oil supply will remain in that position.

    Even if you discount hostile action, there are a variety of natural events that may render your resource inextractable at the proper time. BP, for example, cannot now extract oil from the Gulf of Mexico. There’s a good chance in the next decade that melting ice in Alaska will render the trans-Alaska pipeline useless, which would make the oil owned up there either inaccessible or significantly more expensive to transport to refineries.

    And so on, and so on. The expected future price cannot be computed with a high degree of certainty as you move farther and farther into the future. This may make it rational to capture available profits now, at a low risk, rather than simply withdrawing from the market in anticipation of future higher profits due to the higher risk.

  7. 7 7 Rocky Humbert

    Steve: You touch on an interesting point here – but it also reminds me of the economics of hoarding more generally:

    A important point missing from the political analysis is that the spot price of crude is substantially below the one-year future price of oil. Could one argue that the only economically correct time to release oil from the SPR would be when the crude yield curve goes into severe backwardation?

    And more generally:

    What is the economic justification for the SPR or any hoard? And, even if you accept its rationale, when is the optimal time to sell/consume a hoard? Presumably, the SPR exists to provide some price inelastic amount of crude for the purposes of national security. Yet if one believes in efficient markets and Hotelling’s Rule, one might question the entire utility of any SPR… So should Hotelling be relevant for analyzing the right SPR decision?

    Free market theorists argue that after a hurricane, price gouging is a desirable market response because it brings new supply into a market and allocates limited existing supply. However, this presumes that the new supply will arrive in a useful timeframe. A speculator who buys, hoards and gouges the price of milk in the days following a hurricane produces a socially useful outcome only to the extent that more (lower cost) milk arrives in the market before children starve. Similarly, allowing the price of crude to spike (before the release of SPR oil) is socially useful only to the extent that the market responds to higher prices with incremental supply in a timeframe before lasting economic damage is caused.

  8. 8 8 nobody.really

    Bennett Haselton

    I don’t have an answer, but it reminds me of a question that nagged at me ever since I first watched “Goldfinger”


    Funny. I had the same question as Bennett when I first saw the movie!

    Uh, dudes? If I recall correctly – and I do — Goldfinger features Honor Blackman in the role of Pussy Galore. Pussy Galore. And you spent the movie pondering commodity prices? It’s a wonder the world has any econ-minded people at all, given their apparent indifference to the breeding reflex.

    (I only majored in economics because I saw the bumper sticker “Economists do it with models.” Talk about yer bait and switch….)

  9. 9 9 nobody.really

    What can we learn about Hotelling’s rule from the fact that commodity prices seem to go UP in response to the unrest in Libya? After all, the fact that the pumping stations are not currently functioning does not mean that the oil has been destroyed. If Landsburg’s hypothesis were accurate, then this (presumptively) temporary interruption in the flow of oil from Libya should have no bearing on the price of oil. Yet is seems to.

    Admittedly, I don’t have a data set with which to determine whether world events ACTUALLY cause changes in commodity prices, or whether I invent post-hoc rationalizations for what are actually random fluctuations in commodity prices. So perhaps Landsburg’s hypothesis is accurate and my belief that world events (unrelated to long-term supply) alter commodity prices is wrong. Or perhaps world events (unrelated to long-term supply) DO alter the price of fixed commodities, and Landsburg’s hypothesis is wrong. Or perhaps there’s some way to reconcile the idea that world events (unrelated to long-term supply) alter commodity prices with the idea that only long-term supply and demand alter commodity prices.

  10. 10 10 geoffrey

    Oil in the world is kind of like energy from the sun. It should be considered inexhaustible over any reasonable time horizon. Yes, there are different qualities from an economic perspective. The Saudi crude is really cheap to produce (practically just poke a hole and it pops up). But there may be more crude in North Dakota’s Bakken formation albeit more expensive to produce. Hoteling rule covers current reserves using current technology. Technology has and will cause major shifts in the market. It has for natural gas (getting the gas out of relatively nonpermeable shale though hydraulic fracking) has plummeted the price. Similar techniques may have downward price pressure on oil.


  11. 11 11 mobile

    The SPR does not exist to buffer the U.S. government and military from undesirable fluctuations in the oil spot and futures markets. It exists to buffer the U.S. from the massive disruptions to the market itself: to assure a supply when the whole Middle East catches on fire and stops producing oil, when an asteroid hits the Atlantic and rubs out every harbor and coastal city on four continents, when any one of a thousand black swans drops a giant turd on the underprepared, where a few precious million gallons of diesel fuel is what separates the continuation of your way of life with the ash heap of history.

  12. 12 12 ryan yin

    Suppose the reason why we don’t seem to see Hotelling’s rule applying in practice is that the owners of various exhaustible resources are deeply uncertain about their ability to extract (or transfer right to extract) in the future. Then they should extract much more today (since expected future profits are very low, and they want to extract now until current profits are the same in PDV terms). That means prices today should be lower relative to the permanent dictator world, and since future resources are lower, future prices should be higher. So it seems like this model predicts that prices should grow faster than Hotelling predicts. But that doesn’t seem to be what we see — we’re going in the wrong direction.

  13. 13 13 Craig Pirrong


    I accept your challenge. I’ve written a post at my Streetwise Professor blog that shows how various short run rigidities that Hotelling abstracted from can make it optimal to hold inventories of oil above ground, and to draw down on those inventories in response to adverse supply shocks like those in Libya at present.

    It is necessary to understand what the purpose of SPR is. I conjecture that it is a second best response to an anticipated government failure, e.g., that the government would control oil prices in the event of a war. If this is indeed the rationale, then SPR should not be operated on commercial principles. Said commercial principles would imply that in the presence of various rigidities, a supply shock like that experienced today would make it optimal to draw down on inventories, including SPR.

    The post is here.

  14. 14 14 blink

    Like ryan yin and others, I see insecure property rights as the most likely candidate for Hotelling rule violation. Of course, this suggests that the price today is too low. (Though unlikely) rapidly increasing prices could be mean property rights have become more secure.

    Selling oil from the strategic petroleum reserve could offset a temporary supply disruption. This assumes that oil production cannot be expanded rapidly by existing producers, though I have no idea whether this is the case.

  15. 15 15 ryan yin


    To be clear, I’m actually not saying insecure property rights are the most likely candidate (almost the opposite). The Hotelling price path generally fails empirically because prices rise too slowly or fall, whereas insecure property rights would predict they rise much faster than Hotelling predicts (so this issue exacerbates the puzzle instead of helping solve it)

  16. 16 16 Steve Landsburg

    Craig Pirrong: Nicely done. Thanks.

  17. 17 17 Tom

    Notional value is not the only thing that affects price. Supply and demand from people who actually use the commodity (or actually need cash) can intervene. For example, some people burn oil to stay warm. You can look this up.

    The strategic petroleum reserve has no direct effect on prices because it is too tiny in size to matter, not because supply and demand are irrelevant to price.

  18. 18 18 Scott H.

    I read Pirrog’s post, and have one other element to add to it — OPEC. The organization seeks to maintain its monopoly over oil prices. In order to do this all members must be kept happy by adhering to their “fair share” of the production quota. Deviating from this quota would bring repercussions far beyond the current interest rate and its considerations. Even “independent” producers must (would?) operate in such a way as to not break the monopoly pricing.

    On that note, it should be noted that Hugo Chavez – the would-be dictator of Venezuela — is the scourge of the oil consuming world. For it is none other than he that restored OPEC’s oil monopoly. Prior to Chavez taking the Presidency in 1998, Venezuela was a nation seeking to extract as much oil as possible using largely the best technology available – its own PDVSA in league with US oil companies. Venezuela regularly cheated on it quota by overproducing. The effect was that all OPEC countries subsequently began to overproduce. The Saudis would then flood the market with oil every so often in an attempt to punish cheating producers. Anyone remember how cheap gas was in the 90s? OPEC was a laughing stock. Once Chavez took office he immediately fell in line with OPEC requirements. He also has taken tremendous steps to cut Venezuela’s production. Not only did he fire most of the oil producing expertise in his own country during a political fight with the national oil company (he fired them all), he also threw out most all American producers. As a result Venezuela’s production has gone steadily down from that time – even though its proven reserves have risen substantially. In 1998 average crude price per barrel was $11.91. In 2008 it was $91.48.

  19. 19 19 awp

    It seems to me that insecure property rights should already be accounted for in the decision to produce today or not. So that companies are producing more today than they would if their property rights were secure, but still not necessarily max capacity. A fall in price tomorrow with an expected increase the day after would still have the same effect on the margin: decreased production tomorrow and increased production the day after.

    “The price of oil, in expectation, has to rise at the rate of interest.”

    I would say that the most likely reason Hotelling would fail empirically is unpredicted, or the variance of, changes in Supply and Demand. Say all of a sudden and apparently completely unexpectedly, 2 mil Chinese and Indians a year are moving from bicycles to motercycles, .5 mil are moving from motorcycles to econoboxes, and .05 mil a year are moving from econoboxes to Range Rovers.*

    *Numbers are completely pulled out of my @_$, but I expect that the scale is not really that far off for the last ten years.

  20. 20 20 Mike H

    In any case, isn’t Libya now doing precisely the opposite of what Jay Rockefeller called for? They are withholding their oil, causing buyers to bid the price up, creating an incentive for holders of oil to sell now, are they not? Perhaps those in charge of the reserve just see an opportunity to make a quick buck while the price of oil is high, and the waffle about ‘let’s do this to keep the price low’ is just waffle.

  21. 21 21 Richard

    There’s something I don’t get. I’ve always learned that, theoretically, the price of oil and the interest rate have an inverse relationship. This is because if the interest rate is low then the markup for producing is low and thus the an increase in demand for consuming oil drives up prices. If it is high, the markup is high and therefore a decrease in demand will lower the price. How does this fit in with the idea of oil as an investment that must rise with the rate of interest?

  22. 22 22 vic

    Hotelling’s rule can’t be relevant to an entity that itself can arbitrarily determine the interest rate.

  23. 23 23 Coupon_Clipper


    Nobody.really: Your whole post was hilarious!

  1. 1 Streetwise Professor » SPR: Where Hotelling Doesn’t Rule
  2. 2 Ending Permitorium Could Lower Oil Prices More Than Reducing SPR | Institute for Energy Research
Comments are currently closed.