Valuation and Treatment of Depletable Resources in the National Accounts
  • 1 0000000404811396 Monetary Fund

To assess the feasibility of the national accounts treating as assets depletable resources extracted for sale, the paper examines three issues: 1. whether treating natural resources as assets when they are used requires symmetrical accounting when they enter economic reserves; 2. at what stage between existence in nature and extraction entry to reserves could be counted; and 3. how the value of the in-ground natural resource component could be determined. It suggests treating natural resources entering reserves as “imports” from the environmental account added to the capital account, registering additions to reserves at a stage involved in economic activities, and valuing reserves by procedures related to market price.


To assess the feasibility of the national accounts treating as assets depletable resources extracted for sale, the paper examines three issues: 1. whether treating natural resources as assets when they are used requires symmetrical accounting when they enter economic reserves; 2. at what stage between existence in nature and extraction entry to reserves could be counted; and 3. how the value of the in-ground natural resource component could be determined. It suggests treating natural resources entering reserves as “imports” from the environmental account added to the capital account, registering additions to reserves at a stage involved in economic activities, and valuing reserves by procedures related to market price.

I. Introduction

From the earliest times, as the bronze and iron ages testify, the extraction of natural resources for human use has been an important part of man’s relation to nature. At the very beginnings of American history, English explorers searched the New England coast for what Richard Haklyut, in his classic Discourse Concerning Western Planting of 1584, had called “merchantable commodities,” goods that were scarce in Europe and would pay the cost of transporting them across the ocean. 2/ In our own day, as a growing awareness of the human interaction with nature draws greater attention to its economic measurement, appropriate characterization of this relationship poses a significant challenge. As Carl Sauer wrote of soil and species destruction in 1938, “We have not yet learned the difference between yield and loot. We do not like to be economic realists.”3/

This issue has come more clearly into focus as part of the current effort to adjust the national accounts’ measurement of overall economic activities so as to better reflect interaction with the environment. Attention has focused on national accounts treatment of three issues: depletion of natural resources extracted for sale, “defensive” expenditures to prevent or correct environmental damage, and degradation of the quality of the environment as a result of economic activity. On the first issue, it is argued that the extraction of depletable natural resources should be viewed as the use of an existing asset rather than as an addition to income, constituting instead either the use of an inventory carried over from previous periods, which should not be counted as a part of production—Gross Domestic Product—in the current period, or the depreciation of a capital asset which, though contributing to production, should not be counted in Net Domestic Product or income. 4/ To help assess the feasibility of such a change, and the alternative means by which it might be implemented, this paper deals with specific aspects of this issue, that is, the valuation and treatment of nonrenewable natural resources extracted for sale.

Whether or not the nonrenewable resources extracted from nature should be counted as part of economic production and income can have wide implications for the evaluation and conduct of development in many countries, and particularly those countries which are dependent upon the extraction and sale of such products. In considering solutions to the conceptual problems involved, one important question is how such economic interactions could be measured, what values can be put on the flows between nature and economic activity, and how they may be entered in the accounts.

This issue presents difficulties because, while the eventual sale of the extracted product provides a market price, this may not be true of its natural resource component, as distinct from the value added by its subsequent costs. Having crossed the line between geological accretion and economic exploitation without the benefit of market price, the natural resource component poses a number of questions which are examined here in turn: 1) what is to be valued, only withdrawals or also additions to economic reserves? 2) at what stage in the nature-to-market process could valuation of such additions to reserves take place? and 3) how could valuation be carried out?

This paper examines varying perspectives on these three issues, drawing upon earlier works concerned with measuring the value of natural resources, and advancing its own suggestion as to how this value may be entered in the national accounts. It does not deal with possible future costs, such as those for mine land restoration, which, like imputed employer contributions to unfunded pension schemes, could conceivably be counted as current period costs.5/ Nor does it deal with the externalities of social costs or the contingent costs of possible future occurrences, such as oil spill damage, for example.6/

II. Treatment of Additions to Reserves

The impetus for revised national accounts treatment of depletable resources extracted for sale comes from a belief that, since their existence precedes the accounting period in which their extraction takes place, their depletion constitutes a reduction in wealth rather than an addition to income. It is argued that extraction should therefore be reflected in either a subtraction from income to show depreciation, like that of a fixed capital asset, or a subtraction also from production to show use of preexisting inventories, since the natural resource component was not produced in the current period.7/ Either view requires valuation and subtraction of the natural resource component of the product extracted for sale.

The need for this subtraction follows from application of the Hicksian concept of income, that is “maximum potential consumption while maintaining capital intact.” This is contrasted by Michael McElroy with the Irving Fisher (1930) definition of income as the sum of pure consumption expenditures and the implicit rental value of consumer durables, counting only the economic “ends” rather than “changing prospects for future consumption resulting from current expenditures on economic means,” that is, capital. The difference between Fisher and Hicksian definitions, McElroy explains, lies only in periodization, that is, the allocation of these events in specific intervals of time. The Fisher definition counts neither capital formation nor its subsequent depreciation. The Hicksian definition, on the other hand, counts both current consumption and the present value of expected net increments in future production (or consumption) possibilities, but avoids double counting by subtracting depreciation allowances as the value of the capital stock “embodied” in current production.8/

Implied in strict adherence to the Hicksian definition of income as potential consumption plus changes in net worth is symmetry between additions to wealth and their subsequent subtractions from wealth, or, more to the point, between subtractions from wealth, as in depletion or depreciation, and their previous addition to wealth. Besides valuation of the natural resource component extracted for sale, therefore, valuation of the natural resource as it becomes a part of wealth would also be necessary.

Questions arise, however, as to whether such symmetry in the registration of natural resources as they enter the national wealth is possible, necessary, and advisable. Unlike private mineral holdings, which can be entered as increases in wealth at the time of acquisition, a nation’s subsoil mineral wealth predates existence of the nation. One could conceivably view such mineral wealth as having entered the balance sheet in a previous period, or at the opening of accounts, with no addition to the production or income accounts symmetrical to subsequent subtractions.9/ Alternatively, to maintain symmetry, one could take the occasion of their discrete entry into economic affairs to mark the addition of such natural resources to the nation’s wealth. As noted in the next section, this could come at discovery, at the establishment of proved reserves, or even at recognition of the economic worth of a natural resource as a result of technological developments.10/ The addition of such economic reserves would distinguish a country which possesses them from a country in which the prospect of their impending extraction and sale does not exist.

In the past, the uncertain value of mineral resources at the time of their addition to national wealth, the uneven impact of such additions upon production and income, and perhaps hesitation over attributing to production and income resources emerging from nature, have prompted the exclusion from the national accounts’ production and income accounts of both the addition of natural resources to national wealth and their subsequent depletion.

Given the increased importance now attached to reflecting the interaction between the economy and the environment in the national accounts, however, a solution to this dilemma may now be possible. This would lie in the growing recognition of the environment or nature as constituting a separate sector or account, similar to the rest-of-the-world account. In this context, the national economy may be viewed as “importing” natural resources from the environment, through discovery or development, for example. These “imports” would enter the capital account as an addition to inventories, or fixed capital, paid for by a corresponding capital transfer from the environment.11/ The import of the natural resource would not enter the production account, thus avoiding distortionary effects upon GDP. However, the value added to reserves by expenditures for the discovery or development of the natural resource would enter the production account, with its product added to the value of the reserves in the capital account as a form of saving.

Upon extraction and sale, the value of the reserves utilized would be netted from GDP as intermediate consumption if treated as use of inventories, or from Net Domestic Product alone if treated as consumption of fixed capital, since use of inventories is excluded from GDP, NDP, and income, while consumption of fixed capital is excluded only from NDP and income. The value of the utilized reserves would not result in an increase in the operating surplus in the production account but in a decrease in inventories, or fixed capital assets, in the capital account, giving rise to a corresponding increase in the financing account. Any use of the proceeds from sale of the reserves for current, rather than capital, expenditures, therefore, would be reflected in dissaving.

The requirements of symmetry would be satisfied by this treatment. The symmetry would come in the addition and subtraction of inventory in the capital account, however, and not in the production account. This would be appropriate, since it is not the production and subsequent use of natural resources that is to be measured but their addition to available supplies and subsequent use. The parallel with imports added to inventories is thus instructive.

III. Stages of Valuation

While depletion of the natural resource is necessarily valued when extraction and sale occurs, valuation of its addition to national wealth may come at various points between its prediscovery existence in nature and eventual extraction. A number of stages have been delineated and at times used for measurement purposes in the past.

Valuation of all existing supplies of a mineral in the earth is discouraged by M. A. Adelman, who finds the total mineral in the earth to be “an irrelevant, non-binding constraint. If expected finding-development costs exceed the expected net revenues, investment dries up, and the industry disappears. Whatever is left in the ground is unknown, probably unknowable, but surely unimportant; a geological fact of no economic interest.”12/

A somewhat less inclusive measure is referred to by J. Steven Landefeld and James Hines as the “resource base” and includes reserves capable of being extracted under both current and future economic conditions and technology. They view such estimates as being very uncertain, relying on forecasts of prices, demand, and technology 50 to 75 years into the future and including undiscovered reserves inferred from geological information.13/

A more limited variation of total existing minerals is utilized by Michael Boskin and associates, who are concerned with measuring government wealth (and debt) as it affects taxpayer behavior in anticipation of future revenue requirements. They base their valuation of U.S. government wealth from future mineral lease and royalty payments on U.S. Department of Interior estimates of “economically recoverable undiscovered reserves .… estimated to be recoverable and profitable to extract at current prices and technology.”14/ They point out that ignoring undiscovered reserves can cause the government’s sale of mineral rights leases, which precede exploration, to be treated in the income and wealth accounts as an increase in government receipts and wealth rather than as an assets sale.15/

To provide a comprehensive classification of mineral deposits, a diagram developed by V. E. McKelvey arrays gradations in their economic feasibility along one side and degrees of geologic assurance along another. Economic feasibility is indicated as either economic, paramarginal, or submarginal while geologic assurance is divided between identified and undiscovered. Identified is subdivided between demonstrated—either measured or only indicated—and inferred, and undiscovered subdivided between hypothetical (in known districts) and speculative (in undiscovered districts). Resources may be characterized as moving from speculative resources, to possible resources, to probable reserves, to proved reserves.16/

Proved reserves, sometimes referred to as developed reserves, of oil and gas are defined as those which “geological and engineering data demonstrate with reasonable certainty to be recoverable in future years from known reservoirs under existing economic and operating conditions,” that is, under current prices and costs. Probable reserves cover what may be produced from the undrilled portions of known reservoirs, from the new horizons in those reservoirs, and from adjacent pools. In the U.S., probable reserves were reported to be two to three times the total of proved reserves. Probable reserves are defined by the Canadian Petroleum Association as “a realistic assessment of the reserves that will be recovered from known oil or gas fields based on the estimated ultimate size and reservoir characteristics of such fields.”17/

An additional concept referred to as “oil in place” in particular oil fields, meaning the total amount of oil remaining in a field regardless of the cost of extracting it, is discussed by Hendrik Houthakker.18/

Physical parameters of deposits are used to identify the reserves of some resources. For coal, the U.S. Bureau of Mines has defined a “demonstrated reserve base” consisting of measured and indicated reserves in bituminous seams greater than 28 inches and subbituminous and lignite seams greater than 5 feet, which are up to 1,000 feet below the surface and can be economically mined at the time of determination.19/

For uranium, unlike other minerals, reserves and resources are presented by a particular measure of cost, “forward cost,” denoting all expected future costs associated with production from the time of analysis. Reserves comprise known deposits, whose grade and physical shape are usually delineated by developmental drilling, that can be recovered at costs equal to or less than the selected forward cost category. A resource, inferred by some process that gives an expectation of ore occurrences, is converted into reserves by the exploration and development phase.20/

Particularly in the oil and gas mining industries, only a small part of proved reserves is established at discovery, roughly one-seventh during the 1946-1974 period in the U.S., for example.21/ Most additions to reserves come through extensions of existing reservoirs through the drilling of additional development wells after the year of initial discovery, or through revisions arising from additional information concerning the performance of a reservoir, from new processes that increase recovery, or from other cost or price changes that affect feasibility of recovery.22/ John Soladay refers to the resulting proved reserve figures as “a working inventory” of oil that can eventually be produced under current operating conditions.23/ M. A. Adelman refers to proved reserves as a measure of “shelf inventory.”24/ To delay costly exploration and development expenditures, firms “prove” only enough of an inventory to meet short- and intermediate-run demand.25/ Bain notes that for technical and financial reasons, it is sometimes inadvisable to develop ore reserves too far in advance. Under conditions in the great Mother Lode gold mine in California, for example, it was frequently “difficult and expensive to hold a drift for more than two years without retimbering,” so that ore reserves in sight would seldom show more than a two years’ supply.26/

In mining industries other than oil and gas, Landefeld and Hines state that additions are generally equal to new discoveries.27/ Adelman states, however, that not only in oil, but also in uranium, copper and iron ore, a discovery initiates a long sequence of reserve additions.28/

One significant aspect of the various possible stages at which natural resources may be recognized as additions to national wealth is the information available on each. Estimates of the resource base, as noted above, are very uncertain. As regards U.S. data for proved reserves, Landefeld and Hines concluded that while company-to-company reserve estimates are subject to random variation, it appears that aggregate oil and gas reserve statistics are more reliable. They found that proved hard-mineral reserves, though also subject to uncertainties, are known with more certainty than proved oil and gas reserves.29/ A summary of the estimating procedures for proved reserves in the U.S. and Canada in earlier years is provided by Adelman and associates.30/

The United Nations’ Guidelines on Statistics of Tangible Assets recommends including in the stock of tangible assets only those subsoil resources which are economically exploitable at the current level of technology, as they are more closely linked to current production than the total discovered resources.31/

IV. Valuation Methods

The first question in the valuation of natural resources in the national accounts is whether they are to be assigned any value at all, it being understood that it is their role in economic activity, rather than any inherent physical quality, that would be valued. To simplify, one may ask whether a natural resource discovered, extracted, and sold within a single accounting period is to be assigned any part of the value at which it is sold. With the present national accounts production boundary, which counts only produced goods in production, no value is assigned to the natural resource; all of its value is assigned to the operating surplus, or profits. As George Jaszi wrote in 1958, positing, for the sake of simplicity, the sale of coal which requires neither labor nor capital for its extraction, this gives rise to the anomaly of “the inclusion in consumption of the value of natural resources that have not been counted as production.”32/

This difficulty can be overcome by the treatment of natural resources as imports from the environmental account added to the capital account as inventories, or fixed capital, and subsequently utilized in the production process as intermediate consumption, or depreciation, as outlined above.

The fact that discovery, development, and extraction generally take place over more than one accounting period complicates the valuation of natural resources, which by providing returns in future periods take on the character of capital assets. Like other capital assets, natural resources may be valued as additions to capital at the time they enter the economic system and as subtractions from capital in the later periods when they are used. Consistent accounting requires symmetry between the addition and subtraction, so that the full value of a building, for example, is written off over its useful lifetime.

For purposes of the national accounts, to measure the values of production, income, and capital, both the addition and subtraction of the capital asset are registered at current value, whether it is a fixed capital asset or inventories acquired at one price and disposed of at another.33/ Holding gains or losses accumulated between acquisition and disposal are not counted as production or income and enter the balance sheet valuation of assets only through the reconciliation (or revaluation) account. This procedure would apply also to the valuation of additions and subtractions of natural resources to economic reserves, requiring the use of the current value at whatever stage addition or subtraction is registered. In physical terms, and at base year prices but not current prices, the amount of a given addition to reserves would be equal to the total amount of extractions subtracted as it is used over the life of the reserves. To be consistent with the measurement of production, income, and capital in each period, measurement of depletion would have to be in current value even if additions to reserves were not to be registered.

Ideally, the current value of natural resources would be identified from the price they fetch, or would fetch, in a market sale. Though eventually sold in their extracted state, however, many natural resources may not be bought and sold at earlier stages, while they remain in the ground. Instead, to estimate their current value when no market price exists, the natural resources’ share of the extracted sales price has been calculated as either 1) the residual after the subtraction of other costs, 2) the equivalent of a particular element of the price, such as royalties, 3) some fraction of the final sales price based on an industry rule-of-thumb, or 4) a value representing expert opinion or market consensus. Because both additions and subtractions impact fungible reserves whose extraction extends over a period of years, their in-ground market price reflects a discounting of prospective earnings over the useful life of the reserves, as well as expectations of future prices, costs, and the time path of production. In the absence of a market price, estimates of current value would reflect similar considerations.

These alternative approaches are evident in a number of studies estimating the value of reserves, particularly in the United States, in recent years. One approach has been based on the market price for a natural resource before the addition of other costs. Attempts have been made to identify such a value in the payments made to landholders for their lands or for the mineral rights to their lands, on the theory that “under conditions of long-run equilibrium in perfect competition the purchase price for a piece of physical capital or land should be equal to the present value of that asset.”34/ Extending this method to payments for lands leased, rather than purchased, for oil and gas exploration and extraction in the U.S., Landefeld and Hines emerge with estimates of the economic value of oil and gas reserves only 15 to 50 percent of the values they arrive at by alternate methods. They attribute these low estimates, however, to several factors: 1) incomplete coverage, since some firms owned lands and most production on federal onshore lands came from noncompetitively leased lands for which firms paid no bonuses; and 2) the competitive advantage of large integrated oil and gas companies dealing with individual landowners and even in bidding for federal mineral rights.35/ Boskin and associates attribute the low estimates also to Landefeld and Hines’ use of royalties, in their valuation equation, as a percentage of net rather than gross revenue.36/

Most market sales of natural resources entering the economic sphere come after their mixture with other costs and in later time periods. This poses two problems: identifying the natural resource component of the market sales price, and determining the present value of its receipt over a string of future years.

As natural resources advance from an undiscovered state, through discovery, development, extraction, and sale, other expenditures are added to the natural resources’ original value.37/ While extraction costs may come in the same period as sale, earlier costs, for development for example, are generally attributable to sales in later periods, implying the need to treat them as capital. Some development expenditures may be capitalized separately, and depreciated as structures forming a part of fixed capital assets, for example. Others may be assimilated to the natural resource and reflected in a higher valuation of reserves to be treated as capital assets.38/ This could be as the costs of inventories carried over to future periods, or as the components of capital assets which will produce in future periods, depending upon whether use of the natural resource at sale is to be treated as a reduction in stocks39/ or as depreciation, similar to that of fixed capital.40/

Estimates of oil development and operating costs for 41 oil-producing nations from 1955 to 1985 have been prepared by M. A. Adelman and Manoj Shahi, using U.S. drilling costs and publicly available data on drilling.41/ Several works noted below have utilized subtraction 1) of dollar per barrel extraction costs to obtain net prices, 2) of discounts to obtain the in-ground value of developed reserves, and 3) of development costs to estimate the value of undeveloped reserves.

Data on worldwide exploration expenditures are presented in a recent study by Phillip Crowson.42/ Identification of dollar per unit finding or exploration costs, however, is more difficult, since the extent of discoveries is not fully identified until subsequent development.43/ Unsuccessful exploration expenditures, that is, those which do not lead to discovery, may be treated as losses expensed in the period in which they are made, or aggregated with successful exploration expenditures, in which case they could lead to possible negative operating surpluses at sale. H. Foster Bain has stated, for example, that while U.S. gold mining brought profits to particular companies or individuals, it was not enough to return the invested capital plus a profit to the industry as a whole.44/

The market price—and current value—of in-ground natural resources is likely to reflect a somewhat different valuation of future income streams than valuation of other capital assets. A potential purchaser of natural resource reserves, comparing their rate of return with that on other investments of comparable risk, would note that the return on other investments, such as manufacturing or real estate, would be calculated after provision for the maintenance of the capital itself, through the use of funds made available by regular depreciation allowances. The capital value of other investments, therefore, would be maintained and available in the future, should their sale become necessary. Comparable returns on the mining investment—where exhaustion of the mined resources makes maintenance of the capital impossible—would have to provide for the replacement of capital instead through regular contributions to a sinking fund whose investment, at a more moderate, lower-risk, rate, would replace the initial value of the investment when the resource is exhausted.45/ Valuation of mining properties on this basis, referred to as the Hoskold formula, is similar to capitalization of the annual net income of an ordinary enterprise, with an annual allowance for depreciation computed on a sinking-fund basis.46/ To facilitate such calculation, for example, Herbert Hoover included in his 1909 book, Principles of Mining, a table showing the “Present Value of an Annual Dividend over 1 to 40 Years at 5 to 10 Percent and Replacing Capital by Reinvestment of an Annual Sum at 4 Percent.”47/

Some more recent works estimating the value of total national reserves of particular natural resources, rather than of individual mining properties, have provided for an annuity-like sinking fund48/ while others have not.49/

Besides such differences in the setting of appropriate interest rates, various approaches have been taken also toward the projection of future prices and costs and of the production time path along which this net revenue will be realized.

The difficulties of projecting future prices, costs, and production time paths are avoided in studies of past periods, an outstanding example being John Soladay’s measurements for the U.S. oil and gas mining industries for the 1948-1974 period. Soladay derived the average production time paths for oil and gas from data for reserves, new additions to reserves, and production for each of 18 oil producing states representing 98 percent of U.S. production and reserves. Applying these time paths to national data for total reserves, new additions to reserves, mining companies’ acquisition costs (including both expensed and depreciated capital outlays), and subsequent net revenues, he was able to attribute to each year a string of subsequent net earning, valued at alternative rates of discount. This yielded values, that is, the present value of discounted future net revenues, for total reserves and for new additions to reserves each year.

By subtracting acquisition costs from the value of new additions to reserves, Soladay derived the value of the underlying natural resource, which he referred to as capital gains on acquisition. At a 5 percent real rate of discount, acquisition capital gains averaged 61 percent of the value of new oil acquired each year. Depreciation, estimated as the change in the value of the existing stock of developed oil reserves (net of new additions), averaged 13 percent of the mean value of oil stocks.50/

Another approach, based on a presumed resource share of sales price rather than the subtraction of acquisition costs, was followed by H. Foster Bain. To estimate the value of proved U.S. oil and gas reserves in the ground in 1929, 1939, and 1946, exclusive of values added by drilling and equipping wells, he used the average royalty rates paid to landowners—12.5 percent for oil and 10 percent for natural gas—as an approximation of the natural resource share. Applying these rates to the dollar value of production in 1929, 1939, and 1946, he obtained an annual amount assignable (on the assumption of constant prices and a straight-line time path of production) to each subsequent year in which production from existing reserves at the current year’s rate could continue—13, 19, and 14 years, respectively. The present value of the reserves in the three base years, was then calculated assuming an 8 percent return on invested capital with sinking fund rates at 4 percent in 1929, 3.5 percent in 1939, and 3 percent in 1946.51/

For the valuation of iron ore, Bain applied to 1945 reserve tonnage the value fixed by another source, the 12.5 cents per ton assessed by the Minnesota Tax Commission in its taxation of reserves in the ground between discovery and production. 52/

An approach using a rule-of-thumb ratio to move from sales price to the in-ground value of developed reserves, which reflects the discount element, was used by Adelman. He prepared “very rough” estimates of reserve values in the United States using for the years 1970-73 an industry rule-of-thumb that developed oil reserves in the ground were sold for about one-third of the market price, a ratio regained, after some interruption, by the mid-1980s.

In an additional set of estimates, Adelman also subtracted identified costs from sales price to arrive at resource value. By subtracting from the market price the sum of operating plus development costs, he calculated for the 1970-1986 period the resource value of an undeveloped unit in the ground. This he utilized as an explanatory and predictive indicator, which, when it is above finding costs, serves to stimulate exploration efforts.53/

A comparison of several approaches was undertaken by Landefeld and Hines. They subtracted extraction costs, but not the discount element, to move from sales price to the net price, but employed various projections of future net price and a standard discount rate to estimate the in-ground value of developed reserves. They presented several sets of estimates for the value of U.S. oil and gas reserves during the 1948-79 period, in addition to the estimates based on mineral rights payments discussed above. They calculated the net price per unit of oil and gas, after removal of both variable costs and the current replacement value of producers’ net stock of physical capital, and applied it with specified adjustments to the physical quantity of proved reserves and to changes in proved reserves.

One set of estimates employed no real increase in net prices and a constant real 10 percent rate of discount, the assumptions required of companies’ supplementary disclosure forms by the U.S. Securities and Exchange Commission. Another assumed that future net prices would increase or decrease at a rate equal to the average change over the previous five years, and applied a constant real 10 percent rate of discount. A third set of estimates, which they referred to as the net price method and which was based on the Hotelling Theory, assumed increases in net prices equal to the rate of discount, so that valuation of total reserves, additions to reserves, and depletion, could be calculated by multiplying their physical quantities by the current net price.54/

Considerable simplification is brought to valuation by the assumptions of the Hotelling Theory, which was formulated in 1931 by Harold Hotelling and forms the basis for most subsequent theoretical work. This holds that “the unit price of an exhaustible natural resource, less the marginal cost of extracting it, will tend to rise over time at a rate equal to the return on comparable capital assets,” the upward trend serving to guide resource owners in their choice between current and future extraction.55/ Application of the Hotelling Theory obviates the need for discounting or forecasting prices, makes the production time path irrelevant, since the net return rises with the interest rate, and permits valuation of reserves at the net return in the current period.

These assumptions have been challenged on several grounds, however. Houthakker has noted that “empirical studies of mineral prices have found little or no support for Hotelling’s proposition,” suggesting rather that “for a wide range of minerals net prices have remained constant in real terms when averaged over long periods of time.”56/ Other objections, by Adelman, center on the model’s “major implicit premise [of] … zero investment,” that is, neglect of the development phase, which can involve considerable investment, between discovery and extraction.57/ While higher interest rates lower the discounted value of future alternative use and hence the opportunity cost of earlier extraction, they also increase the opportunity cost of investment in the development of discovered reserves, thus discouraging earlier extraction. On balance, Adelman concludes, interest rates have a minor and indeterminate effect on resource owners’ choice between present and future extraction. It is increasing marginal costs that limit the expansion of extraction in the current period to avoid the interest cost of waiting.

Rather than the Hotelling problem of a fixed stock of available reserves to be divided between periods on the basis of net returns and interest rates, Adelman sees flows from unknown resources into a reserve inventory, influenced by rising marginal costs offset by increasing knowledge of new fields, geological conditions, and improved technology, with the result that in the long run practically all mineral prices have declined.

To illustrate the discounting of future returns influenced by the interplay of increasing costs, the depletion rate of reserves, and the discount rate, Adelman cites the case of U.S. oil in the post-World War II period, during which the depletion rate—extraction divided by reserves—was approximately equal to the discount rate. Reflecting a relationship between in-ground value and net price roughly equal to the depletion rate divided by the sum of the depletion rate and the discount rate, he writes, “the in-ground value per barrel [of proved reserves] has long fluctuated around a mean near one-half of the net price (one-third of gross wellhead price), in conformity with an industry rule of thumb.”58/

One possible illustration of a relationship between resource values at various stages may be constructed—without any claim as to its validity—by combining these proportions with Soladay’s findings, discussed above, of acquisition costs averaging 39 percent and acquisition capital gains 61 percent of the value of new additions to proved oil reserves in the U.S. in the 1948-74 period. This yields the following proportions:

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The value of the resource, before the addition of other costs, in this case equals 20 percent of the gross wellhead price, 30 percent of the net price, and 61 percent of the in-ground value of proved reserves.

While these relationship vary between wells, mines, minerals, countries, and periods, the calculation of similar relationships for other minerals, countries and periods may suggest one approach to valuation in the absence of continuing availabilities of complete data on market prices and costs.

In the valuation of depletion, that is the withdrawal of natural resources from reserves, it is important that the same principles be used as in arriving at the current value of additions to reserves. The acquisition costs incurred in previous periods for resources sold in the current period would be reflected in either the separate depreciation of fixed capital assets or in the value of reserves to be treated as depletion. The current value of the withdrawn reserves would be determined by either market price or its various approximations—subtraction of costs59/, use of rule-of-thumb ratios or expert opinions, identification with particular elements such as royalties, or the discounting of net price with assumptions on its future movement. Whether withdrawn reserves fully offset the physical amount or base year value of previous additions would depend on how closely the estimates of the volume of added reserves turn out to match the volume of eventual extractions. In any case, and even without the registration of additions to reserves, valuation of withdrawals by market price, or by the other approximations of current value, is necessary for consistent measurement of production and income.

A number of suggestions have been advanced for the estimation of depletion in the absence of more complete information. Salah El Serafy, to indicate the amount a nation should invest so as to replace the income it received from a nonrenewable asset, proposes a depletion allowance calculated as a proportion of total receipts, net of extraction costs, on the basis of the ratio of total reserves to current period extraction (the life expectancy in years) and a discount rate chosen to approximate a market parameter for prudent behavior.60/

Michael Ward has proposed an annual depletion fund appropriation equal to the present discounted value of total reserves at current prices, or at a base year price, divided by the number of years’ output in reserves at the current annual physical output.61/

Robert MacNamara, former president of the World Bank, is cited by Thomas Stauffer as proposing an arbitrary adjustment to oil exporters’ incomes of 25 percent to reflect the otherwise elusive measure of depletion.62/

V. Conclusion

While persuasive arguments have been advanced for the registration of additions to reserves symmetrically with withdrawals, the appropriate point of addition and subtraction would appear to be the capital account rather than the production account, since the natural resource is not produced by the economy but imported from the environment. Only the value added by expenditures for exploration or development would pass through the production account before registration as an addition to assets in the capital account. There need be no concern, therefore, over a possibly uneven impact of additions to reserves upon production and income totals since both would be unaffected by the addition of natural resources as assets in the capital account. The use of reserves, moreover, would be appropriately reflected as the use of a capital asset, giving rise to dissaving if the proceeds are used for consumption rather than investment.

Additions of reserves may be recognized at various stages in the nature-to-extraction process, but there are advantages in registering entry at a stage representing a close involvement in the economic system. At the stage of proved or developed reserves, for example, the quantity of reserves is delineated by economic activity and their status is viewed by some in the mining industry as a kind of working inventory.

The availability of data may be expected to vary substantially from country to country. The commercialized nature of the extraction and sale of depletable resources, however, should add materially to the possibilities for valuing natural resources added and withdrawn from reserves. The variety of approaches demonstrated in the studies cited above, finally, suggests that the valuation of depletable resources by procedures related to market price should be feasible.


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This paper was presented at the Special Conference on Environmental Accounting of the International Association for Research in Income and Wealth (Baden, Austria, May 27-29,1991) and will be published in the proceedings of the conference. The author thanks Carol Carson, Arnold Katz, and Timothy Muzondo for helpful discussions.


Levin (1990) 161,168-169.


McElroy (1976) 228-229. James Bonbright describes a third concept of income, referred to as the accounting concept, which is a compromise between the other two. It pro-rates receipts and disbursements over the years to which they are deemed applicable, values inventories at the lower of cost or market so that their unrealized losses but not their unrealized gains are registered, carries the book value of fixed assets at original cost minus depreciation, and charges unrealized capital gains and losses not to income but to some special surplus account. Bonbright (1937) Vol. 2, 902-906.


Dan Usher refers to this possibility as follows: “At one extreme, the stock of subsoil assets is looked upon as given at the beginning of time, and all production represents a kind of depreciation.” Usher (1980) 12.


As James Bonbright writes in his classic work on valuation, “Certainly, for the purpose of monetary valuation, property has no value unless there is a prospect that it can be exploited by human beings.” Bonbright (1937) Vol. 1, 21.


Andre Vanoli proposes the concept of capital transfers in kind from nature. Vanoli (1991) 11.


Adelman (1983) 33, 49, 52. A comparison of the characteristics of proved and probable reserves is presented on pages 50-51.


Adelman (1983) 338, 346-347.


Jaszi (1985) 94.


Landefeld (1985) 12. Adelman, however, refers to lease bonuses or lease rentals not as costs but transfer payments, that is shares of past or expected profits paid to the landholders. Adelman (1986) 10.


Usher, for example, identifies one alternative approach to counting natural resources as “recognizing both proved and unproved reserves as part of the capital stock, but unproved reserves would have a lower shadow price, so that discovery increases the quantity of capital.” Usher (1980) 12-13.


Treatment of mineral exploration expenditures is discussed in Carson (1988).


Bain, for example, uses investment and sinking-fund rates of 12 and 4 percent, 10 and 4 per cent, and 8 and 3 percent, respectively in calculating the present value of recoverable U.S. gold reserves in 1929, 1939, and 1947. Bain (1950) 256.


For example, Landefeld (1985) 16.


Stauffer raises the question of full economic costs including a rate of return with some premium for exploration risk. Stauffer (1985) 73.

Valuation and Treatment of Depletable Resources in the National Accounts
Author: Mr. Jonathan Levin