# r= δ+ η∙g

for pure rate of time preference δ, elasticity of the marginal utility of consumption η, and consumption growth rate g.

Strictly speaking, the discount rate used in the World Bank’s work (i.e. the social rate of return to investment) differs from that in the OECD project. The former is a kind of social discount rate from a social planner’s point of view, while the latter is a long-term private return from an individual perspective (Fraumeni, 2011). The difference can be illustrated by the following example.

Consider an individual deciding to undertake formal education. Since the risk that he or she faces cannot be easily diversified, a relatively high rate of return may be needed to induce this person to remain in school. On the other hand, from the perspective of the society as a whole, investment in formal education is diversified across individuals and thus considerably less risky, meaning that future returns to this investment should be discounted at a lower rate (Abraham, 2010). The question of whether there are positive externalities from human capital accumulation (so that social returns exceed private returns) is contested in the recent literature<sup>10</sup> and is not further considered in what follows.

More discussion on the choice of real rates in general, and the income growth rates and the discount rate in particular, are beyond the scope of this paper. For our purpose, we take the total wealth estimates from the World Bank wealth accounts as given, and run a sensitivity analysis with respect to the discount rates applied for calculating both human and natural capital. Our central discount rate is 4.58%, while variants of 4% and 5% are reported in Annex III (note that discount rates of 4.58% and 5% result in slightly different values of natural capital compared with the figures published in World Bank (2011)).

# **_4.3. The choice of time horizon_**

The third issue involved in aligning the OECD and World Bank capital estimates concerns the choice of time horizon over which future consumption, resource rents and labor income are discounted. The World Bank accounting sets the time horizon to 25 years, roughly corresponding to a generation, for the calculation of both total wealth and natural resource wealth (World Bank, 2011).

In the OECD project, the lifetime for working is truncated at age 15 as lower bound and age 64 as upper bound beyond which the labor income is assumed to be zero. Thus, the remaining working years for an individual at age x ≥ 15 is just (64-x), and the remaining working years for the whole population is calculated as the weighted average of the remaining working years of each individual, with the weight being the number of people in the corresponding (5-year) age groups.

As shown in Table 2, the weighted average remaining working time for all countries selected is slightly above 25 years, roughly in line with the assumptions made by the World Bank wealth accounting. Note that for simplicity, the calculation of remaining working years as shown in Table 2 does not take into account the labor force participation, employment and mortality rates. If these adjustments were made, the results would be slightly smaller.

10 . See Lange and Topel (2006).

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