Here is Paul Krugman’s model, Mark Thoma covers related ground. I view this as an intertemporal Hotelling model and not as analogous to a currency model as Krugman suggests. In the bottom right hand graph of the four graphs in Krugman’s post, I don’t understand what institutional force hinders a market-clearing price. More concretely, if expected future price goes up (or interest rates fall), the supply curve in that graph should shift back to the left (wait and pump more later for the higher price) and/or the demand curve in that graph should shift out to the right (buy now rather than later at the higher price). Measured inventories will rise to the extent the demand curve does the shifting; if the supply curve does the shifting the "excess inventories" stay in the ground.
It is possible to derive Krugman’s desired result through another and indeed simpler channel. Define speculation as the desire to hold more oil because of the perception that oil now has a greater convenience yield. As Jeffrey Williams points out, a big part of convenience yield is the option value of selling the oil on favorable terms. If you’re guessing that option value will pay off, it’s not unreasonable to call that speculation. We now have a one-line proof: because of "speculation" the demand to hold oil goes up, and so the stocks of oil held will rise.
This again illustrates the value of starting with Holbrook Working when analyzing futures markets.
And it’s fair to say, as Krugman still does, there is no evidence that this mechanism is what is driving the higher oil prices. Of course the people who are blaming "speculation" don’t seem to have any coherent definition of the concept in mind; that’s another problem with their argument.