Harold Hotelling and Steve Landsburg vs Bob Murphy and George W. Bush

Just delicious! A great exercise in economics. Start out with a simple model with a lot of unrealistic assumptions and figure out how changing them matches the ‘real’ world and what else that might imply.

Sent to you by Bruce via Google Reader:

Harold Hotelling and Steve Landsburg vs Bob Murphy and George W. Bush

via Consulting by RPM || Free Advice Blog by Bob Murphy on 10/10/12

It doesn’t look good for me, does it? But give me a chance:

During his commentary on the first presidential debate, Steve Landsburg wrote:

6) Romney says “all of the increase in energy has been on private land, not govt land”. Very ignorant. If there were more drilling on govt land, there’d be less on private land (assuming there’s any truth at all to Hotelling style models and how can there not be?)

In case you want context for Romney’s claim, check out this IER blog post.

In the comments I said to Steve:

Steve, what’s your problem on #6? You don’t think it’s relevant that Obama is taking credit for a rise in domestic oil production, that occurred precisely on those areas where he doesn’t control? (I’m assuming Romney’s basic stat was right.)

Did Romney say, “Now if you had allowed for more drilling on federal land, Mr. President, then in the new general equilibrium, production on private land would have followed the same path”? Maybe he thinks that, but he didn’t say it, and total output would certainly be higher (and spot price of crude would currently be lower) if Obama gave green light to unrestricted drilling on federal land. So why was Romney’s response so ignorant?

Then Steve answered me in the comments by writing:

I don’t get [your claim about oil prices, Bob]. Oil is an exhaustible resource. Allowing drilling on federal land does not change the supply of oil and it does not change the demand for oil, so how can it change the price of oil?

Or to put this another way: Hotelling tells us that in the absence of supply and/or demand shocks, the price of oil has to rise at the rate of interest. The rate of interest is what it is, and doesn’t change just because part of the oil supply moves from below-ground to above-ground. So the path of oil prices is determined independent of whether you allow drilling on federal lands.

(The only exception would be if the President is capable of instituting a *permanent* ban on drilling, effectively taking the oil under that land out of the oil supply. But surely nobody believes that the current President can set drilling policy for 30 years in the future.)

Steve is referring to Harold Hotelling’s classic 1931 article on the economics of exhaustible resources (The Journal of Political Economy, Vol. 39, pp. 137-175). With your permission, I will quote from my EconLib article on oil prices to understand Hotelling’s framework:

Assume that every last drop of oil in the world is conveniently located at the surface of the earth, dispersed among thousands of small pools, each of which is owned by a different individual. Each of these owners—who controls a tiny fraction of the world’s total stockpile of oil—knows exactly how big his own pool is, and the pools of oil owned by his competitors. Further suppose that it costs each owner virtually nothing to extract a barrel of oil and sell it on the market. Assume also that the cost of storing the oil is zero, and further that each owner can predict with perfect foresight the demand for oil at every date into the future. There is no doubt that the known oil in the various pools is the only oil that will ever be available. Finally, suppose that each owner is also quite confident that there will always be people wishing to buy some barrels of oil, for virtually any price, into the foreseeable future. Under these very unrealistic yet convenient assumptions, what can we say about the price of oil?

Harold Hotelling provided the elegant answer back in 1931. On the margin, an owner of the oil must be indifferent between selling an extra barrel of oil today—and earning the spot price—versus holding it off the market and selling it in the future. Since we have assumed away storage and extraction costs, and any risk that the quantity demanded of oil will drop to zero if the price rises too far, we can conclude that the spot price of oil (the spot price is the current price at any given time) must rise over time with the interest rate. For example, if a barrel of oil sells today for $100, and the interest rate is 5%, the spot price of oil in twelve months’ time must be $105 in order to make it worthwhile for the owner to keep some oil off of the market today and carry it forward to next year. The idea is that the amount he earns by having the oil sit in the ground must equal the amount he would earn in interest on a portfolio of bonds.

Of course, Hotelling’s Rule doesn’t tell us what the actual spot price is at any time; it merely tells us how quickly it must rise. To come up with the specific numbers, we would need to know the demand for oil over time. In a general equilibrium, the spot price would rise with the interest rate (Hotelling’s Rule) and consumers of oil would purchase their optimal number of barrels per day (depending on the price at the time), such that the total consumption into the future would just equal the original size of the pool.

I know there were some scoffers in the comments–both at Steve’s blog and here at Free Advice–who thought Steve was nuts for not seeing how a federal quasi-ban on oil development in certain areas is a leftward shift of the supply curve. But let’s be fair to Steve: What I think he’s arguing is that Obama can only postpone the development of oil in ANWR, offshore, etc. So in the new equilibrium, oil producers in Saudi Arabia, Venezuela, Canada, and even in the US on private or state-controlled lands will just ramp up their production rate accordingly. Rather than oil flowing evenly from ANWR, Venezuela, and Canada in 2012 and also in 2042, instead we draw more quickly from Venezuela and Canada and not at all from ANWR in 2012, and then we draw less from Venezuela and Canada but more from ANWR in 2042. (That is an awful sentence but if you read it twice you will get what I’m saying.)

Needless to say, I think Steve is wrong on this. Let me give some quick reasons:

First, I defy Steve to dot the i’s and cross the t’s on the framework at which he is hinting in his remarks. He’s perfectly right, Obama can’t tie policymakers’ hands for the next 30 years. So let’s set up a general equilibrium model in which there is a fixed pool of oil (much much larger than the current “known reserves” value because oil companies only go out and look for more known reserves when it is profitable to do so) as well as a known demand schedule for oil, and where the spot price is set in a Hotelling framework.

However, let’s make a few tweaks for the sake of realism. Assume there is a random variable to determine whether ANWR and other federal lands are off- or on-limits for development in the ensuing decade. Furthermore, assume that the (known) planetary demand curve for oil starts shifting left in the year 2150, because other technologies have more than offset the growth in population and per capita energy consumption. By 2200 the global demand for oil is zero.

I think if you put in reasonable assumptions about the lag between getting the green-light and then the actual pumping of oil from ANWR etc., and further you make reasonable assumptions about the maximum rate of extraction (or if you want to get fancier, you have a rising marginal cost of extraction based on the extraction rate per well), then you would find in the general equilibrium, spot oil prices would fall (meaning current global oil extraction would increase) whenever the random variable had a “green light” realization. This would be true immediately, even during the start-up lag, because the other producers would forecast lower (future) spot prices and would ramp up their current production rates accordingly to maximize the present-discounted value of their operation in light of the new information.

Second, in addition to the above Ivory Tower deep thoughts, we have this chart showing what happened to near-term oil futures prices when President George W. Bush in July 2008 removed just the Executive Branch moratorium on offshore drilling (which by itself had zero marginal effect) and then the Pelosi Congress allowed the Congressional moratorium on drilling in the Outer Continental Shelf (OCS) to expire a few months later:

(This article gives the full context for the above chart.) As the chart above suggests, we economists need to start out with the Efficient Markets Hypothesis and Hotelling’s Rule on our blackboards, but I think we also need to realize that the real world apparently doesn’t work that way. So our job is to figure out exactly what is wrong with those elegant, baseline constructions, since the average Joe will say something like, “Well people aren’t rational.” I agree that that’s not a satisfactory refutation of the EMH, but something is sure screwy with it–or at least, with the conclusions that prominent economists draw from it.

Finally, a question for Steve: Suppose that the US government dropped a nuclear bomb on Iran, and that all politicians from both parties said they would continue this policy for years to come. If I understand your position, you would say that this could raise world oil prices temporarily, but only until (say) other, existing well operators could expand output? So maybe by 2016 you think that world oil prices would be back to what they otherwise would have been, even if–in 2016–the US is still periodically nuking the Middle East, and at that time there is no likely presidential candidate who pledges to stop?

Things you can do from here:


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