What models exists for explaining the price of nonrenewable resources? It seems to me that the seminal model for the price of nonrenewable resources is Hotelling's rule. However, as the Wikipedia article describes, Hotelling's rule has empirically performed poorly. I know there are some variations that seek to improve on the original model, such as by accounting for changes in extraction cost or other factors. However, I am unfamiliar with this literature. Can anybody provide some more detail about variations on Hotelling's rule? Also, what, if any, alternative hypotheses exist to explain the prices of nonrenewables?

Notes:

This questions is related to a previous question about the impact of fracking on oil prices.
Based on my understanding, Hotelling's Rule is a pretty good first step. Like many first steps, it doesn't perform particularly well empirically. I would expect that when technological change is considered, in the very long run, it isn't too bad.

There are a few extensions of this model which are popular.
-Exogenise extraction costs
    The standard idea is that extraction costs increase as the resource moves towards depletion. Something which isn't included in the standard model is that technology is changing, making some previously unprofitable reserves cost effective. At the same time, exploration can uncover more reserves. Whilst the total amount of non-renewable resource doesn't change, the amount available for extraction isn't static.
- Account for substitutes
    The demand for oil for example is constantly growing, but it must remain competitive with substitutes. A rise in prices make substitutes more attractive. This is a phenomenon we have seen with ethanol and into our petrol.

This pdf provides a broad overview of such extensions. It also provides references for further reading. I borrowed heavily from it above. I'll list a few


Chapman, D. (1983). World Oil: Hotelling Depletion or Accelerating Use?Nonrenewable Resources.2(4): 331-339
Extends the Hotelling model to so that the marginal extraction cost is independent of quantity demanded.
Stiglitz, J.E. (1976). Monopoly and the Rate of Extraction of Exhaustible Resources. American Economic Review,66(4): 655-661
Straightforward paper showing that extraction rate under monopoly is lower than under perfect competition.