Streetwise Professor

March 21, 2011

SPR: Where Hotelling Doesn’t Rule

Filed under: Commodities — The Professor @ 1:45 pm

Steve Landsburg is a marvelous economist.  He has written several things on the Strategic Petroleum Reserve.  Today he invokes the Hotelling Rule to argue that the government should not tap SPR:

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?

Let me give that a try, Steve.  Hotelling essentially abstracts from short run rigidities/constraints and stochastic demand and supply.  The only economic decision in the Hotelling world is the rate of extraction.  This was–is–a reasonable abstraction to make in order to understand some crucial issues.  But it is an abstraction.

The more complex reality is that in the short run productive capacity is essentially fixed by the stock of capital–the number of wells, the capacity of the wells, the fields they are in, and so on.  Moreover, output is somewhat inflexible downwards: wells tend to produce at a given rate, unless they are capped.  Capping and uncapping involve fixed costs.  Thus, it is typically inefficient to cap wells in response to a demand decline, especially if that decline is anticipated to be transitory.

Furthermore, both supply and demand are subject to random shocks, and due to the fixed capacity (which limits the ability to expand output, especially in the very short run) and the downward rigidity in output, these shocks cannot be accommodated by adjusting output.  Under these circumstances, it is efficient to hold inventories of oil “above ground” (i.e., oil that has been produced from a well and then stored, as opposed to oil that is “stored” in the oil-bearing formation*).  Like other commodity inventories, these oil inventories can be used to dampen the price impacts of demand and supply shocks.  It is optimal to add to these inventories in response to short run declines in demand or increases in supply, and to draw down on these inventories when the reverse is true.

This is done with commercial inventories of oil.  During the financial crisis and recession, for instance, stocks of oil rose dramatically.  Much of it was stored on ships.  That inventory has been tapped into as demand has risen.  Similarly, the recent oil supply shocks in the Middle East have led commercial inventory holders to draw on those supplies.

There are price implications of these competing stories.  In a Hotelling world, oil futures prices (and the prices of other commodities) are always in full carry, i.e., forward prices exceed spot prices by the rate of interest.  In contrast, the alternative model that I sketch exhibits “backwardations”–situations where forward prices are below spot prices, let alone below spot prices plus interest.

We observe backwardations in the real world.  We observe above ground inventories.  Thus, the Hotelling world is not a precise description of the way the oil market works.

Roughly speaking, Hotelling presents a model of the long run which abstracts from short run rigidities.  The alternative model I discuss focuses on the short run and pays close attention to the implications of these rigidities and the stochastic nature of demand and supply.

It would be nice to have a model that integrates both of these features.  That is very challenging, as it is a high dimensional stochastic dynamic programming problem, with indivisibilities (e.g., fixed costs of exploration, capping and uncapping) and irreversability (there are multiple decision options in oil exploration and production, but investments made when these options are exercised are typically sunk).  Existing models focus on a subset of the relevant features (e.g., including irreversibility while abstracting from above ground storage, including storage but abstracting from adjustments in capacity).

When it comes to SPR, Steve is right to point out the potential interaction between the operation of the SPR and the operations of private storers.  My early posts on this focused on that, focusing on the issue of how commercial storers were affected by the inherently political, and thus difficult to predict, nature of the operation of the SPR.

There is a broader question: Why do we need an SPR in the first place?  Why must the government store?  Why is private storage insufficient?  To determine whether it is optimal to tap SPR today, you need to know why SPR exists in the first place.

One answer is along the lines suggested by the late Earl Thompson (an Alchian student, back in the day) in his analysis of the national defense argument for protectionism.  Thompson argued that one could justify protectionism as a second best response to another market failure.  In particular, government wartime price controls reduce the returns to investing in the production of strategically important materials.  In order to offset the resulting underinvestment, a second best strategy can be to use tariffs and quotas to protect strategic industries.  Protection raises the private rate  of return that is depressed by the possibility of wartime price controls.  This leads to higher investment that offsets the underinvestment resulting from price controls.  Thus, some sort of policy that would otherwise be inefficient (such as protectionism) can be justified on second best grounds for strategic materials that are likely to be subject to wartime price controls or other policies (e.g., taxes) that essentially expropriate from those who have invested in the capacity to produce such materials.

I think you have to make a similar argument for SPR.  It is plausible that in the event of a war the US government would impose price controls on oil.  The anticipation of this would reduce the private returns to investing in oil production capacity.  Filling SPR increases the demand for oil, thereby lifting prices.  This tends to offset the effects of price controls anticipated during wartime.

Moreover, SPR provides a stock of oil that can be utilized for military purposes in the event of a war.  For instance, private storers may hold too little oil in inventory if they anticipate that during a war the government will require them to sell it at below market prices.  SPR can be a second best response to this problem.

Maybe this isn’t exactly the right story, but to justify government provision of storage you need to identify a market failure–or, as in the case of the Thompsonesque story, a government failure–that leads to underprovision of storage and/or investment by private actors.   Once you have this story, you can identify what the appropriate strategy for SPR should be, and can then evaluate whether it is optimal to draw down on this inventory under current conditions.

If it were operated on commercial principles, it would make sense to draw down on SPR inventories: the lack of full carry in the oil market is signaling that there is a short term shortage that can be mitigated by drawing down on inventories, and that’s what commercial storers are doing.  If operated on commercial lines, SPR could generate profits under current conditions by following a similar policy.  But if SPR is instead intended to address a government failure (or a market failure) in which there is a divergence between private incentives and the social optimum, it should not be operated according to the same principles as commercial storage (which only takes into account private benefits and costs).

That’s the direction you need to take to evaluate the prudence of drawing down on SPR.  Hotelling’s Rule doesn’t really help you because it abstracts from crucial aspects of the economics of above ground inventories.  Moreover, even the storage models abstract from the potential for market and government failure.

* This terminology is confusing because some “above ground” inventories are held below ground.  SPR, for instance, is held in subterranean salt caverns.  The relevant distinction is that “above ground” oil has been extracted from its original formation, and moved to some other storage location.

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  1. Hotelling’s rule has no application for entities that can arbitrarily determine their own interest or discount rate. I’m not suggesting Govts. do this all the time- but, when faced with an existential threat, they are bound to. This begs a further question- can we conceive of an entity, or can an entity self-consciously function, without an existential threat? Do the things we think of as having a life of their own need a ‘life-cycle’ punctuated by existential threats such that time preference does not flow uniformly but abruptly deforms? If so, some more observational approach might illuminate Strategic Reserve policy.

    Comment by vivek — March 22, 2011 @ 1:48 am

  2. […] this year, I blogged about potential economic justifications for a strategic petroleum reserve, and how the reserve should be used based on such justifications. In brief, something like the SPR […]

    Pingback by Streetwise Professor » Will the CFTC Prosecute Obama and the IEA for Manipulation? — June 25, 2011 @ 10:36 am

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