Even More Speculation

Paul Krugman with even more on speculation:

Speculation and Signatures, by Paul Krugman: I’m trying to get my own thoughts on the oil stuff clear; so for the econowonks, a tiny theoretical paper for your enjoyment and/or detestation.

After reading the paper, which explains when you would and would not expect to see inventories, what contango and backwardization mean, and importantly the signatures of speculation, some of you may wonder how monetary policy fits into the model. Here's a quick first pass at showing how this works (the two graphs in the top row mimic the graphs in Krugman's model in the paper, I'm adding the money-demand money supply diagram much as Krugman and Obstfeld do in their analysis of exchange rates in their book on international economics):

In this graph, starting in the upper left-hand diagram. E is the expected appreciation in oil prices, i.e. E=E(p, pf)=(pf-p)/p, where p is the spot price and pf is the future price. E is decreasing in p and increasing in pf. The line s+i represents the sum of interest foregone on stored inventory, i, and the actual storage cost, s. The storage cost is exogenous to the model, and the interest rate is assumed to be set by monetary policy. (Think of E as the expected benefit and s+i as the cost, the equilibrium (pf-p)/p = s+i sets the marginal cost of holding one more unit in inventory equal to the marginal benefit).

The diagram on the upper right is the flow supply and demand diagram for oil. The distance ab, the excess of flow supply over flow demand at the initial spot price of p₁, is the initial level of inventories. [The supply and demand curves are drawn relatively flat for ease of illustration.]

The diagram in the bottom row is the supply and demand diagram for money. Real money demand is L(y,i), nominal money demand in PL(y,i), and as usual L is increasing in y and decreasing in i. The money supply is M, and it is controlled by the monetary authority. It is assumed the i is the policy variable, so that M takes whatever value is needed to hit the target value of i for a given level of money demand.

The initial target for the interest rate is i₁. At i₁, the spot price of oil is p₁ and inventories are ab. Now let the monetary authority ease up and lower the interest rate to i₂. This will cause the i+s line to shift to the left, and this in turn will increase the spot price of oil to p₂. At the higher price of p₂ inventories increase from ab to cd, so the net result of easing is to increase the price of oil in spot markets, and to increase inventories. Thus, an increase in liquidity from an easing of monetary policy would have an increase in the spot price and increases inventories as a signature.

Intuitively, the model starts in equilibrium with (pf-p)/p=s+i. Then, i falls due to the increase in liquidity causing (pf-p)/p>s+i. Since the benefits of speculation now exceed the cost at the margin, there is more demand for oil to be put into inventory, and this drives up the spot price until (pf-p)/p=s+i once again.

[I should add that if the market is in backwardization, which Krugman argues has been the case recently  - see figure 3 in Krugman's paper and the associated discussion - then variations in the i+s line will not change the equilibrium. Thus, in this case changes in the target interest rate will not change the spot price or change inventories (which are zero, again, see figure 3 and picture the i+s line shifting left or right).]

There are lots of thought experiments one can conduct with this model, e.g. ask what might happen if pf goes up, y goes down, etc., and I should stress that this is partial or short-run equilibrium, for example there are no feedback effects through the aggregate price level P or output y, both of which are held constant in the analysis, and if p is permanently higher, pf might increase as well (and these sorts of "chase your tail" mechanisms can lead to bubbles, e.g. pf goes up for some mysterious reason shifting E to the right, this causes an increase in p, which could increase pf if it's thought to be permanent, which increases p, then pf again, etc., until it eventually peaks and then comes crashing back to fundamentals), but this should give some idea of how it all fits together.