The problem with assuming depletable natural resources are... er... depleting

My thesis research this year, on modelling the effects of natural resources on economies, has led me to ask a particular problem: is it reasonable to model depleting natural resources as actually depleting?

At first glance, it seems as though depletable natural resources should of course be modelled as depleting. How dare I suggest not! That is the approach taken by some really big names: Dasgupta & Heal (1974), Stiglitz (1974), Romer (in his textbook), Jones (in his textbook), Vernon Smith (in a bunch of papers in 69 and 69), etc.

The problem with this approach---despite it being correct physically---is that the amount of natural resources we know about has not actually been depleting.

Below is a little graph I did using data from the BP Statistical Survey 2009, graphing the aggregate stocks of "proven" reserves. These reserves may come on and off-line as prices fluctuate. A good example is Canada's Athabasca oil sands, which were included in Canada's proven reserves in the early 80s, only to be partially removed during the late 90s when oil prices were too low to make them viably extracted.



The surprising trend is that known oil reserves, despite rising extraction, have increased continually.

Given this, and given the fact we know one day proven oil reserves must fall, should depletable natural resources be modelled as depleting?