Global savings glut & the time-to-exhaustion of world oil supplies

An interesting paper at the recent PhD conference I attended (due to the ANU’s Vipin Arora) drew attention to the fact that the recent global savings glut would influence oil extraction rates via something akin to the well-known Hotelling rule provided that oil and bonds were substitute assets.  I prefer to think of this issue in terms of an unadorned Hotelling model where, in equilibrium, and assuming perfect substitutability of the oil and bond assets, the proportionate change in oil prices dln(p(t))/dt  must equal the rate of interest r.  This says something that is simultaneously trite and deep. It is trite in the sense that it states that the prices of two perfect substitute assets must grow at the same rate – oil stocks in the ground must increase in value at the rate of interest for them to be willingly held there, otherwise they would be sold off and the proceeds used to purchase bonds.  The deep insight was the recognition by Harold Hotelling that oil and other exhaustible resources could be treated as capital assets.

The attractive feature of the original Hotelling model is that the comparative dynamics of something like an interest rate fall are simple to trace out.  A fall in the interest rate due, for example, to a world savings glut will leave oil prices instantaneously appreciating faster than interest rates creating incentives to withhold oil from the market thereby leading to a pulse increase in oil prices.   Once this pulse has occurred oil prices will grow proportionately at the new lower interest rate.  

How large must the initial pulse be?  Suppose that at some future oil price p_b the price of oil hits the price of some inexhaustible backstop resource – say solar energy – which can be used as an inexhaustible alternative to oil.  Then the pulse must be large enough so that, when oil prices grow at the new interest rate, that no unused oil reserves are left unused when, growing at the new interest rate, p(t) eventually hits p_b.

It is easy to see that the new Hotelling price path must hit the old Hotelling price path at some unique time in the future say T. Up to this the new price path lies uniformly above the old oil price path so that cumulative oil extraction up to T will be less with the new price path than the old.  Thus oil reserve use is stretched out by the lower interest rate – world oil reserves last longer with a savings glut.

It is just not possible for the new oil price path to hit the backstop price at a time equal to or less than T since this would involve higher (or perhaps, at the endpoint, the same) oil prices than arose with the original Hotelling time path so that reserves would be left over when a switch to the backstop occurs – a proposition that is inconsistent with optimal oil extraction.

In short, the savings glut alone could rationalize sharply increased oil prices followed by slower subsequent growth in oil prices. The glut also means that oil reserves will last longer than they otherwise would have.  Oh yes, I know I have not considered extraction costs and endogenous links between oil revenues and the advent of the glut.