TheDude wrote:The ELM is an interesting notion but there are a flock of parameters that could affect how things turn out for a producer on the downslope
There are two ways to work with models like this - the logistic equation of King Hubbert or more elaborate versions like the ones I am playing with. This paper:
http://www.ifi.uib.no/sd/workingpapers/ ... oversy.pdf
helped me see these two approaches more clearly. One can use the model to get a feel for the basic shape of the likely trajectories a system is liable to traverse. Or, one can be looking for specific predictions. Probably this just comes down to long term versus short term, since long term predictions are impossible anyway.
Perhaps it's like climate modeling versus weather prediction. Climate modeling is useful for trying to get a handle on large scale phenomena like el nino etc. Weather prediction is more about whether it will rain on my picnic tomorrow.
Here are a couple aspects of my model that I don't like.
1) I treat money just as a way to facilitate trading, to find the market balance so that the total amount consumed is the total amount produced. Somebody on TheOilDrum commented that I don't take profits into account. Another way to look at that is that I don't take borrowing and lending into account. Someday the Saudis will stop buying T-bills and start selling them instead. What is that going to look like?
2) I am not so happy about treating each producer as its own little pseudo-logistic. What a logistic does is plot a transition between an exponentially increasing production rate at the beginning of history, to an exponentially decreasing rate at the end. It seems clear enough why the production rate decreases as the resource becomes depleted.
But why does the production rate increase gradually at the beginning? If we start with scads of petroleum in the ground, why doesn't the production rate just start at its maximum? Somehow this has to do with our extraction technology. There are two aspects to extraction technology: quantitative and qualitative. We use energy to make drilling rigs, and we use drilling rigs to produce energy. That's the quantitative aspect. But we also learn how to make better drilling rigs - that's the qualitative aspect. Or we learn what sorts of seismic signatures indicate likely pools of crude underground.
What bugs me is that a lot of the technological growth should not be producer-specific. The energy, materials, and skills that one producer uses to build drilling rigs - those rigs can be used by a different producer. Perhaps a different producer will have to borrow some money to buy those rigs, though.... which begs the question: what is a producer, anyway? Is Exxon a producer, or is Texas a producer, or what?
Oftentimes it turns out that adding lots of model details like these won't really change the structure of the equations - the details all just get combined into the various constants. But sometimes an extra term can become crucial. The interesting thing is to look at such models in terms of regimes, the way the nonlinear systems or chaos theory folks do. A system will often stay in one pattern for a while, then flip into a different pattern. Each single pattern can be modeled simply, with something like maybe a logistic. But more terms can be needed to see how the system can shift from one mode to another.