# _(ii) Measuring depletion and saving based on proven reserves plus expected probable resources_

In our empirical discussion so far, we have looked at inferred discoveries only. We now turn to the total expected resource approach to wealth measurement as given by expression (24), and then derive measures of depletion and net saving based upon this revised wealth estimate. Critical to this is sufficient geological information not only on _S_ but also _X_ .<sup>19</sup> However, it is important to note that there is no definitive typology or even a uniform interpretation of each recognized classification of ‘undiscovered’ resources (for a discussion, see Rogner, 1997). The key point is that there is some probability that a given amount of resource could be added to proven reserves at some point in the future. What will determine these additions to reserves is the probability of technical and economic conditions shifting favorably over the passage of time or through learning or geological predictions being confirmed (or some combination of these developments).

The United States Geological Survey (USGS 2000, 2012) provides periodic assessments of undiscovered resources in the case of oil (see Rogner, 1997 and Mitchell, 2004).<sup>20</sup> What these USGS data describe is the extent of undiscovered resources along with given probabilities of those stocks being recoverable.<sup>21</sup> In Table 2 we use these data to show how the estimates in USGS (2012) on expected discoveries in regions of the world affect our accounting for the depletion of oil resources. The table values oil assets and depletion on the basis of proven resources ( _S_ ) only and total resources ( _S_ + _X_ ).

Expression (24) indicates that in order to value to the _total_ resource stock value ( _S_ + _X_ ), we require an estimate of discovery costs. In Table 2 we use an estimate of 5.0% of resource rent based on data on exploration and discovery costs for Norway’s oil resources as reported in Annex Table A2. Since (in contrast to our theoretical model) resource discoveries are only loosely connected to discovery expenditures in any given year, our estimate of this value is based on the average cost per tonne of discovered oil from 1985 to 2010 (calculated as the mean value 19 Rogner (1997) provides a good discussion of nuances in established definitions of what constitutes proven reserves for energy resources. These different definitions may result in distinct estimates of reserve extent with this difference largely explained by the specificity of readiness for economic exploitation in a definition. Moreover, Rogner along with a number of authors including Owen _et al_ . (2010) and Mitchell (2004) all urge caution generally in the interpretation of available data on the extent of resources and reserves. This is not only because of the scientific and economic uncertainties but also the incentives that relevant agents have to report accurately these data. 20 USGS (2000, 2012) indicates that this assessment is based primarily on geological assurance although some consideration is also given to technical and economic factors in determining extent. In using these probabilities, in this paper, we are in effect assuming that to evaluate these expected discoveries will be recoverable (i.e. added to proven reserves) with that likelihood. In practice, previously undiscovered resources might be added to proven resources or contingent resources (i.e. possible or probable reserves) with the latter being associated with some probability of ultimately being transferred to the former.

21 Specifically, these probabilities are 95%, 50% and 5%. While not the complete probability distribution for (expected) undiscovered reserves, these data give some indication of the possible extent of resources at three points of the (truncated) lognormal distributions estimated in USGS (2000, 2012). While incomplete this provides at least some approximate basis with which to illustrate our approach to accounting for the case of expected probable reserves.

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