Accounting for Subsoil Mineral Resources · eVorts to incorporate subsoil mineral assets into the...

February

Accounting for Subsoil Mineral Resources

, A blue-ribbon panel of the National Academyof Sciences’ National Research Council completed a congres-sionally mandated review of the work that the Bureau ofEconomic Analysis () had published on integrated eco-nomic and environmental accounts. The panel’s final reportcommended for its initial work in producing a set of soundand objective prototype accounts. The November issueof the S C B contained an article byWilliam D. Nordhaus, the Chair of the Panel, that presentedan overview of the major issues and findings and a reprintof chapter , “Overall Appraisal of Environmental Accountingin the United States,” from the final report. As part of itspromise to inform users of the results of this evaluation, isreprinting additional chapters from the panel’s report; belowis a reprint of chapter , which reviews ’s development ofa set of subsoil mineral accounts.

This article is reprinted with permission from Nature’sNumbers: Expanding the National Economic Accounts toInclude the Environment. Copyright of the National AcademyPress, Washington, . This is a report of the NationalResearch Council, prepared by the Panel on Integrated Envi-ronmental and Economic Accounting and edited by WilliamD. Nordhaus and Edward C. Kokkenlenberg.

INTRODUCTION

S minerals—particularly petroleum,natural gas, and coal—have played a key role

in the American economy over the last century.They are important industries in themselves, butthey also are crucial inputs into every sector ofthe economy, from the family automobile to mil-itary jets. In recent years, the energy sector hasbeen an important contributor to many environ-mental problems, and the use of fossil fuels ishigh on the list of concerns about greenhousewarming.

The National Income and Product Accounts() currently contain estimates of the produc-tion of mineral products and their flows throughthe economy. But the values of and changes inthe stocks of subsoil assets are currently omit-ted from the . The current treatment ofthese resources leads to major anomalies and in-accuracies in the accounts. For example, bothexploration and research and development gener-ate new subsoil mineral assets just as investmentcreates new produced capital assets. Similarly,the extraction of mineral deposits results in thedepletion of subsoil assets just as use and time

cause produced capital assets to depreciate. The include the accumulation and depreciationof capital assets, but they do not consider thegeneration and depletion of subsoil assets.

The omission is troubling. Mineral resources,like labor, capital, and intermediate goods, arebasic inputs in the production of many goods andservices. The production of mineral resources isno different from the production of consumergoods and capital goods. Therefore, economicaccounts that fail to include mineral assets mayseriously misrepresent trends in national incomeand wealth over time.

Omission of minerals is just one of the issuesaddressed in the construction of environmentalaccounts. Still, extending the to includeminerals is a natural starting point for the projectof environmental accounting. These assets—which include notably petroleum, natural gas,coal, and nonfuel minerals—are already part ofthe market economy and have important links toenvironmental policy. Indeed, production fromthese assets is already included in the nation’sgross domestic product (). Mining is a signifi-cant segment of the nation’s output; gross outputoriginating in mining totaled billion, or .percent of , in . This figure masks theimportance of production of subsoil minerals incertain respects, however, for they are intimatelylinked to many serious environmental problems.Much air pollution and the preponderance ofemissions of greenhouse gases are derived di-rectly or indirectly from the combustion of fossilfuels—a linkage that is explored further in thenext chapter. Moreover, while the value of min-eral assets may be a small fraction of the nation’stotal assets, subsoil assets account for a large pro-portion of the assets of certain regions of thecountry.

Current treatment of subsoil assets in the U.S.national economic accounts has three major lim-itations. First, there is no entry for additions tothe stock of subsoil assets in the production orasset accounts. This omission is anomalous be-cause businesses expend significant amounts ofresources on discovering or proving reserves forfuture use. Second, there is no entry for the usingup of the stock of subsoil assets in the production

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. Two additional categories of mineral endowment are worth notingsince they are commonly encountered. The reserve base encompasses thecategories of reserves and marginal reserves, as well as part of the categoryof demonstrated subeconomic resources shown in Figure –. While reservesand the reserve base are typically a small subset of resources, resources inturn are a small subset of the resource base. The resource base, not illustratedin Figure –, encompasses all of a mineral commodity found in the earth’scrust.

or asset accounts. When the stock of a valu-able resource declines over time through intensiveexploitation, this trend should be recognized inthe economic accounts: if it is becoming increas-ingly expensive to extract the subsoil mineralsnecessary for economic production, the nation’ssustainable production will be lowered. Third,there is no entry for the contribution of subsoilassets to current production in the productionaccounts. The contribution of subsoil assets iscurrently recorded as a return to other assets,primarily as a return to capital.

There is a well-developed literature ineconomics and accounting with regard to the ap-propriate treatment of mineral resources. Themajor difficulty for the national accounts hasbeen the lack of adequate data on the quanti-ties and transaction prices of mineral resources.Unlike new capital goods such as houses or com-puters, additions to mineral reserves are notgenerally reflected in market transactions, but aredetermined from internal and often proprietarydata on mineral resources. Moreover, there areinsufficient data on the transactions of mineralresources, and because these resources are quiteheterogenous, extrapolating from existing trans-actions to the universe of reserves or resources isquestionable.

Notwithstanding the difficulties that arise inconstructing mineral accounts, the Bureau ofEconomic Analysis () decided this was thebest place to begin development of its IntegratedEnvironmental and Economic Satellite Accounts(). in the United States and compa-rable agencies in other countries have in recentyears developed satellite accounts that explicitlyidentify mineral assets, along with the changes inthese assets over assets, along with the changes inthese assets over time. This chapter analyzes gen-eral issues involved in minerals accounting andassesses the approach taken by (as describedin Bureau of Economic Analysis [b]). Thefirst section provides an overview of the nature ofsubsoil mineral resources and describes the basictechniques for valuing subsoil assets. The secondsection describes ’s approach to valuation, in-cluding the five different methods it uses to valuesubsoil mineral assets. The third section high-lights the specific strengths and weaknesses of’s approach, while the fourth considers otherpossible approaches. The chapter ends with con-clusions and recommendations regarding futureefforts to incorporate subsoil mineral assets intothe national economic accounts.

GENERAL ISSUES IN ACCOUNTING FORMINERAL RESOURCES

Basics of Minerals Economics

A mineral resource is “a concentration ofnaturally occurring solid, liquid, or gaseous ma-terial, in or on the earth’s crust, in such formand amount that economic extraction of a com-modity from the concentration is currently orpotentially feasible” (Craig et al., :). Thesize and nature of many mineral resources arewell known, whereas others are undiscovered andtotally unknown. Figure – shows a spectrum ofresources that differ in their degree of certainty,commonly described as measured, indicated, in-ferred, hypothetical, and speculative. Anotherimportant dimension is the economic feasibil-ity or cost of extracting and using the resources.Some resources are currently profitable to exploit;others may be economical in the future, but cur-rently are not. Along this dimension, mineralresources are conventionally described as eco-nomic (profitable today), marginally economic,subeconomic, and other.

Resources that are both currently profitable toexploit (economic) and known with considerablecertainty (measured or indicated) are called re-serves (or ores when referring to metal deposits).This means reserves are always resources, thoughnot all resources are reserves.

Over time, reserves may increase. Explorationmay result in the discovery of previously un-known deposits or demonstrate that a known de-posit is larger than formerly indicated. Researchand development may produce new techniquesthat allow previously known but uneconomicresources to be profitably extracted. A risein a mineral commodity’s price may also in-crease reserves by making previously unprofitableresources economic.

The exploration required to convert resourcesinto reserves entails a cost. As a result, compa-nies have an incentive to invest in the generationof new reserves only up to the point at which re-serves are adequate for current production plans.For many mineral commodities, therefore, re-serves as a multiple of current extraction tend toremain fairly stable over time.

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. Where the relevant market for a mineral commodity is global andtransportation costs are negligible, Figure – reflects cost classes for reserves

While by definition all reserves can be exploitedprofitably, the costs of extraction, processing, andmarketing, even for reserves of the same min-eral commodity, may vary greatly as a result ofthe reserves’ heterogenous nature. Deposit depth,presence of valuable byproducts or costly impu-rities, mineralogical characteristics, and access tomarkets and infrastructure (such as deepwaterports) are some of the more important factorsthat give rise to cost differences among reserves.

Figure – reflects the heterogenous nature ofmineral resources by separating the reserves andother known resources for a particular mineralcommodity according to their exploitation costs.

The lowest-cost reserves are in class A ; theirquantity is indicated in the figure as 0A and theirexploitation costs as 0C1. The next least costlyreserves are found in class B, with a quantity ofAB and a cost of 0C2. The most expensive re-serves are found in class M . These reserves are

. Similar comparative cost curves are used to illustrate the relative costsof mineral production for major producing countries or companies. See, forexample, Bureau of Mines () and Torries (, ).

marginally profitable. The market price 0P justcovers the extraction cost of class M (0Cm ) plusthe opportunity cost (Cm P) of using these re-serves now rather than saving them for futureuse. This opportunity cost, which economists re-fer to as Hotelling rent (or sometimes scarcity rentor user cost) is the present value of the additionalprofit that would be earned by exploiting thesereserves at the most profitable time in the futurerather than now.

Known resources in Figure – with costs abovethose of class M , such as those in classes N , O ,and P, are by convention not reserves. In thiscase, mineral producers, like other competitivefirms, will have an incentive to produce up to thepoint where the current production costs of thenext unit of output, inclusive of rents, just equalsthe market price. When Hotelling rents exist,

and other known resources throughout the world. Where a mineral com-modity is sold in regional markets, a separate figure would be required foreach regional market, and the cost classes shown in any particular figureare only for the reserves and other known resources in the regional marketportrayed.

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. The total value of reserves is V =∑i v i Ri , where v i is the unit

value of reserves in class i (i = A ,B,. ..,M ), and Ri is the quantity ofreserves of class i .

they are the same for all classes of reserves for aparticular mineral commodity market. Thus, thetotal Hotelling rent shown in Figure – is simplythe Hotelling rent earned on marginal reserves(Cm P) times total reserves (0M ).

Those reserves whose marginal extraction costsare below those of the marginal reserves in classM are called inframarginal reserves. As a resultof their relatively low costs, they yield addi-tional profits when they are exploited. Mineraleconomists refer to these additional profits as Ri-cardian rents. In Figure –, the Ricardian rentsper unit of output equal C1Cm for reserves inclass A , C2Cm for reserves in class B, and so on.

Unless technical or other considerations in-tervene, mineral producers will generally exploitfirst those reserves that have relatively low pro-duction costs and thus high Ricardian rents (likeclasses A and B). This implies that the reservescurrently being extracted have lower costs thanthe average of all reserves and that their Ricardianrents are likely to be above average.

Since reserves by definition are known andprofitable to exploit, they are assets in thesense that they have value in the marketplace.Although mineral resources other than thoseclassified as reserves might have in-completely

defined characteristics (in terms of costs andquantities) or be currently unprofitable to exploit,they still may command a positive price in themarketplace. Petroleum companies, for exam-ple, pay millions of dollars for offshore leases toexplore for oil deposits that are not yet provedreserves. Mining companies pay for and retainsubeconomic deposits. The option of develop-ing such deposits in the future has a positivevalue because the price may rise, or some otherdevelopments may make the deposits economic.

Thus, a full accounting of subsoil assets shouldconsider not only reserves, but also other mineralresources with positive market value. In the caseof reserves, market value may reflect Hotellingrent, Ricardian rent, and option value. In thecase of mineral resources other than reserves, apositive market value is due solely to their optionvalue.

Key Definitions in Mineral Accounting

Changes in the value of the mineral stockcome about through additions, depletions, andrevaluations of reserves.

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• Additions are the increases in the value ofreserves over time due to reserve augmenta-tions. They are calculated as the sum of theprice of new reserves times the quantity ofnew reserves for each reserve class.

• Depletions are the decreases in the valueof reserves over time due to extraction.They are similar to capital consumption(depreciation) and parallel the concept ofadditions.

• Revaluations are changes in the value ofreserves due to price changes. They measurethe residual change in the value of reservesafter correcting for additions and depletions.

Techniques for Valuing Mineral Assets

As noted in the last section, the major challengein extending the national accounts to includesubsoil minerals is to broaden the treatment ofmineral assets to include additions and depletionsand to incorporate depletion in the productionaccounts. This task involves estimating the valueof the subsoil assets. A specific subsoil asset con-sists of a quantity of a mineral resource and theinvested capital associated with finding and de-veloping that resource. Invested capital includesphysical structures such as roads and shafts, aswell as capitalized exploration and drilling ex-penses. The total value of the subsoil assetsequals the sum of the value of the mineral andthe value of the associated capital (see Figure –). Currently, U.S. national economic accountsinclude the value of the associated capital, butexclude the value of the mineral resource. Oneof the goals of natural-resource accounting is toestimate the total value of subsoil assets and to

separate this estimate into the value of the min-eral and the value of the associated capital. Anadditional goal is to track over time changes inthe value of the stock that result from additions,depletions, and revaluations.

Three alternative methodologies are used invaluing mineral resources: () transaction prices,() replacement value, and () net present value.In developing its mineral accounts, used oneversion of the first method and four versions ofthe third. This section explains the basic elementsof each approach.

Transaction Prices

The most straightforward approach to valuingmineral resources relies on market transactionprices. This is the standard approach used acrossthe national economic accounts for capital assets.When resources of petroleum, copper, gold, andother minerals are sold, the value of the transac-tion provides a basis for calculating the marketvalue of the mineral component of the asset.

A close look at the transaction-prices approachreveals, however, a number of difficulties thatneed to be resolved. The major difficulty is that amarket transaction usually encompasses a num-ber of assets and liabilities, such as the associatedcapital (e.g., surface roads, shafts, and refiningoperations), taxes, royalty obligations, and en-vironmental liabilities. Because the transactionusually includes not only the mineral resources,but also associated capital, the value of the capitalmust be subtracted to obtain the mineral value.In addition, the property is usually encumberedwith royalty obligations to prior owners or toowners of the land. Many mineral properties alsohave associated environmental problems, such ascontaminated soils and water, and they may evenbe involved in complicated legal disputes, suchas connection to a Superfund site with joint andseveral liability. Some of these associated assetsand liabilities (such as mining structures) are truesocial costs or assets, while others (such as royaltyobligations) are factor payments.

Another difficulty with using transaction pricesis the sporadic nature of the transactions. Theinfrequency of the transactions, coupled with theheterogeneity of the grade of the resource, makesit difficult to apply the transaction price for onegrade or location of the resource to other gradesin other locations.

Because of the complex assortment of assetsand liabilities associated with transactions ofmineral resources, the price must be adjustedto obtain the value of a resource. As noted

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above, the working capital and the associatedcapital must be subtracted from the transactionprice, while any extrinsic environmental liabilitiesshould be added, as should any factor payments,such as royalties or taxes, to obtain the value ofthe underlying resource.

Box – provides an example of how to ad-just the transaction price to obtain the marketvalue of a mineral resource for a hypotheticalsale involving the purchase of , barrels ofoil. In this example, the buyer pays millionfor a property containing , barrels of oil,and this is recorded as the transaction value. At-tached to those reserves is a long-term debt of. million; this liability must be added to thepurchase price. If the acquired reserves also in-clude associated working capital of . million,this amount must be deducted from the purchaseprice. Correcting for these two items creates aneffective purchase price or market value of theasset of . million.

An additional issue arises because of paymentssuch as future taxes and royalties. In acquiringthe above property, the new owner must, for ex-ample, pay a percent overriding royalty to thelandowner. Such payments should be includedin the value of the resource even though they donot accrue to the seller of the property. In theexample shown in Box –, future royalties andtaxes are assumed to have a present value of .million. These payments introduce a major newcomplication because taxes and royalties dependon future production. Not only are they un-certain, but they also cannot be easily estimatedfrom market or transaction data. One approachis to adjust the transaction price by marking upthe value of the transaction by a certain amount.Adelman and Watkins (:), for example, sug-gest that percent be added to the “effectivepurchase price” to account for transfers. Afteradjusting for royalties, this yields a social assetvalue for the above property of . million. Thefinal adjustment is for associated capital, which isassumed to have a value of . million. After thisamount is subtracted, the estimated social valueof the underlying petroleum reserve is calculatedto be . million.

Replacement Value

A second approach uses the costs of replacingmineral assets to determine their value. Underthis approach, it is assumed that firms have anincentive to undertake investments to find newresources up to the point where the additionalcost of finding one more unit just equals the price

Box –: Transaction Price Methoda

Recorded Dollar Transaction (,barrels) ............................................... . millionAdjustments

Add: assumed liabilities .............. . millionSubtract: working capital ............. . million

Effective Purchase Price of Asset ....................... . millionAdd: present value of taxes, royalty

transfers ............................ . million

Value of Assets ......................................... . millionSubtract: value of associated capital ..... . million

Value of Petroleum Reserve ............... ............ . million

aThis methodology is not followed in the conventional accounts. Forinstance, in valuing the stock of cars, we do not subtract tax credits, nordo we add in future liabilities such as property taxes. Similarly, to theextent that royalties are regarded as a sharing of profits (like dividends),they should not affect the value of an asset; to the extent that royaltiesare actually a deferred part of the purchase price, they can be capitalizedto increase the value of an asset.

Box –: Definitions of Symbols and Basic Concepts in MineralsAccounting

For this discussion, assume that there is only one class of a mineral reserve,that extraction costs are constant, and that the unit value of the reserve risesat the social rate of discount. Variables are:

Rt = total quantity of reserves of the mineral commodity at year endHt = unit value of the reserves (say, petroleum reserves), which equals

Hotelling rent under the above assumptionsAt = quantity of new reserves discovered during the yearqt = quantity of extraction or production during the yearVt = total value of the reserves at year end

In a given year, petroleum firms might discover new reserves totaling At .Then the additions are given by:

additionst = Ht At (.)During that year, petroleum production, and therefore depletion of existing

reserves, is measured by qt . Depletion is, under the special assumptions listedabove, quantity times the value of reserves:

depletionst = Ht qt (.)

The total value of reserves at year end is:

value of reserves = Vt = Ht Rt (.)The change in the value from the end of year t − 1 to the end of year t isgiven by:

change in value of reserves = Vt − Vt−1 = Ht Rt −Ht−1Rt−1 (.)

Revaluations are the change in the value corrected for the value of additionsand depletions:

revaluation = Ht Rt − Ht−1Rt−1 −Ht At + Ht qt (.)

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at which firms can buy that unit—that is, upto the market value. Therefore, the additionalor marginal cost of finding a mineral resourceshould be close to its market price. Associatedwith this approach, however, are many of thesame issues discussed above under transactionprices. For example, a particular replacementcost is relevant only for valuing deposits of com-parable quality and cannot be used to valueresources of another grade. This point can beillustrated using Figure –. Assume that explo-ration is resulting in the discovery of resourcesof class M . The market value of this class wouldbe a function of the difference between 0P andproduction cost 0CM . It would be profitablefor firms to continue exploring for such depositsuntil the finding costs (that is, the replacementcosts) just reached the value of this class of re-source. However, the replacement cost of classM cannot be used to value other classes, such asclass A , which have a lower extraction cost andtherefore a higher value. Because of cost differ-ences, using class M to value classes A throughL would yield an underestimate of the value ofthese reserves.

Net Present Value

A third valuation technique, the net presentvalue or method, entails forecasting thestream of future net revenues a mineral re-source would generate if exploited optimally,and then discounting this revenue stream usingan appropriate cost of capital. Under certainconditions—such as no taxes—the sum of thediscounted revenue values from each time pe-riod will equal the market value of the resource.For example, assume that a million-ouncegold asset generates a stream of net revenues (af-ter accounting for all extraction and processingcosts) that, when discounted at a rate of per-cent per year, has a present value of . billion.According to this approach, the value of the as-set is taken to be . billion. If the value of theplant, equipment, and other invested capital ul-timately associated with the asset is estimated tobe million, the current value of the gold re-serves is billion, and their unit value is perounce. Again, as with the previous two methods,each class of resource should be separately val-ued, since the stream of revenues from a higherclass of resource will be greater than that from alower class.

. The appropriate discount rate for energy and environmental resourcesis debatable. See Lind (, ) , Schelling () , and Portney andWeyant ().

A special case of the approach, known asthe Hotelling valuation principle (see Miller andUpton, ), avoids the difficulties of forecastingfuture net revenues and then discounting themback to the present. This approach makes thestrong and generally unrealistic assumption thatthe unit value of a resource grows at exactly thesame rate as the appropriate discount rate. In theabove example, this would imply that the unitvalue of the gold resource would grow at the dis-count rate of percent per year; that is, theunit value would be in the first year, inthe next year, . in the following year, and soforth. Under this assumption, the present valueof the resource would easily be calculated as thecurrent period’s resource price multiplied by thecurrent physical stock of the resource. Under afurther set of assumptions, such as homogeneousresources and constant extraction costs, the cur-rent period resource price is simply the currentnet revenue (unit price less unit extraction cost).

For example, assume that in a given year theUnited States has million ounces of homo-geneous gold reserves, that the price of gold inthat year is per ounce, and that the av-erage extraction cost is per ounce. Underthe Hotelling valuation principle, the price of thegold reserves would be per ounce, and thetotal value of the gold assets would be calculatedas . billion. Note that it would still be neces-sary to deduct the value of capital from the .billion to obtain the value of the mineral reserve.Again, for this approach to be valid, the per unitprice of gold reserves ( in this example) wouldneed to grow at the discount rate appropriate forthese assets.

BEA’S VALUATION OF SUBSOILMINERALS

This section presents a more detailed descriptionof ’s valuation methods (as set forth in Bureauof Economic Analysis, b). In the absence ofobservable market prices for reserves, esti-mates mineral reserve and flow values using fivevaluation methods. These calculations are per-formed for reserves of fuel minerals (petroleum,natural gas, and coal) and other minerals (ura-nium, iron ore, copper, lead, zinc, gold, silver,molybdenum, phosphate rock, sulfur, boron, di-atomite, gypsum, and potash) for each year from through (oil and gas figures are calcu-lated from to ). In addition, aggregatestock and flow values for five mineral categories(oil, gas, coal, metals, and other minerals) are en-

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tered in the appropriate rows and columns of the Asset Account for . This section firstexamines the five methods used by in esti-mating mineral values, along with the data theyrequire, and then describes ’s findings. Box– provides definitions of the symbols used inminerals accounting.

BEA’s Five Basic Valuation Methods

Current Rent Method I

Current rent methods I and II are methodsbased on the Hotelling valuation principle. Theattraction of the Hotelling valuation principleis the ease with which the calculation can beperformed, avoiding the need to forecast min-eral prices and to assume an explicit discountfactor. In both methods, the value of the ag-gregate stock is calculated as the net price timesthe quantity of reserves, where the net price isas described below. Additions or depletions aresimilarly calculated as net price times the quantityof additions or depletions. One of the difficultieswith this approach is that the Hotelling valuationprinciple tends to provide a systematic overvalua-tion of reserves, the reason for which is discussedin a later section.

Current rent methods I and II are quite simi-lar in construction. They differ primarily in themethod of adjusting for the value of associatedcapital. (The algebra of the different formulas isshown in the boxes in this section.) Current rentmethod I (see Box – ) uses the normal rate ofreturn on capital to determine the return on asso-ciated capital in the mining industry that shouldbe subtracted from revenues. It then calculatesthe “resource rent per unit of reserve” by takingthe net profits from mining, subtracting the re-turn and depreciation on the associated capital,and dividing that sum (called “resource rent” by) by the quantity of resource extracted duringthe year. The method thus yields an estimate ofthe unit value of the reserves currently extracted.

To calculate the total value of the mineralreserve, the current resource rent per unit is mul-tiplied by the total reserves, in the spirit of theHotelling valuation principle. Additions and de-pletions are calculated as those quantities timesthe resource rent per unit. Revaluations are sim-ply the residual of the change in the value of thestocks plus depletions minus additions. It hasbeen observed that the value of the stock can behighly volatile; this volatility is due primarily tothe revaluation effect.

Box –: Formulas for Current Rent Method I

total mineral reserve valuet = Vt =

[p t − a t ]R t − rR t Kt /q t − Rt Dt /q t =

[p t − a t − rK t /q t −Dt /q t ]×Rtadditionst = [p t − a t − rK t /q t − Dt /q t ]×Atdepletionst = [p t − a t − rK t /q t − Dt /q t ]×qt

revaluationst = Vt − Vt−1 + depletionst − additionst

where

Vt = value of mineral reservesp t = price of commoditya t = average cost of current productionRt = total quantity of reservesr = average rate of return on capitalKt = value of associated capital, valued at current replacement costqt = total quantity extractedDt = depreciation of associated capitalAt = quantity of discoveries of new reservesadditionst = value of discoveries of new reservesdepletionst = value of depletionsrevaluationst = change in value of reserves corrected for depletions and

additions

The revaluation term is not directly calculated; it will include any errors incalculating additions, depletions, and opening and closing stock values.

Current Rent Method II

Current rent method II is virtually identical tocurrent rent method I. The only difference is inthe method of adjusting for associated capital.The value of the associated capital is subtractedfrom the total value of the mineral asset to obtainmineral-reserve values in current rent methodII. Again employing the Hotelling valuation ap-proach, the total value of the mineral asset(including the value of the associated capital) iscalculated as the per unit net revenue times thetotal quantity of reserves. The total value ofthe mineral reserve is then calculated as the to-tal value of the asset value minus the value ofthe associated capital. The unit resource value,which is used to price additions and depletions,is just this total reserve value divided by the to-tal quantity of reserves. This approach is definedalgebraically in Box – .

As is discussed below, both current rentmethods have major advantages in that they areeasy to calculate on the basis of data currentlyuses in its accounts (primarily profits and capitalstock and consumption data). They both sufferfrom the serious disadvantage that they rely on

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Box –: Formulas for Current Rent Method II


[p t − a t − Kt /R t ]R t

additionst = [p t − a t − Kt /R t ]×Atdepletionst = [p t − a t − Kt /R t ]×qt


where variables are as defined in Box ..

the Hotelling valuation principle, thereby tendingto overvalue reserves.

Net Present Value Estimates

If the basic assumptions of the Hotellingvaluation principle do not hold—and there isstrong evidence that they do not, as discussedbelow—life becomes much more complicatedfor national accountants. One approach thatis sound from an economic point of view isto value reserves by estimating the present dis-counted value of net revenues. To render thepresent value approach workable, makesthree simplifying assumptions. First, it assumesthat the quantity of extractions from an additionto proved reserves is the same in each year ofa field’s life. The quantity of depletions in anyyear is assumed to result equally from all vin-tages (cohorts) still in the stock, i.e., all vintageswhose current age is less than the assumed life.Second, the life for a new addition is assumedto be years until and years thereafter.Third, assumes that the discount rate appliedto future revenues is constant at a rate of either percent per year or percent per year abovethe rate of growth of the net revenues (where thelatter equals the rate of growth of the price of theresource).

These assumptions lead to a tractable set ofcalculations. The present discounted value ofthe mineral stock as calculated using this presentvalue method is simply the stock and flow valuescalculated with current rent method II, multi-plied by a “discount factor” of between . and. for the percent discount rate and between. and . for the per cent discount rate.

. According to , the rates were chosen to illustrate the effects of abroad range of approaches. The percent per year discount rate has beenused by some researchers to approximate the rate of time preference, whilethe percent rate has been used by some researchers to approximate thelong-term real rate of return to business investment.

. At the percent discount rate, the . discount factor holds for theyears through , with the rate edging upward thereafter as a resultof commingling of reserves that were developed prior to (which assumes are extracted over years) with those developed in or later (for

The calculated values are, then, lower than thevalues derived using current rent method II, withthe difference depending on the discount rateemployed.

Additions and depletions are then calculatedin a manner similar to that used with currentrent method II. The average unit reserve valueis calculated by dividing the total reserve valueby the quantity of reserves, and then using thisunit value to value additions and depletions.Additions would be calculated as percent ofthe value of additions according to current rentmethod II if the discount rate is percent peryear, and percent of the value of additionsaccording to current rent method II if the dis-count rate is percent. The calculated valueof depletions would be percent of the valueof depletions under current rent method II at a percent discount rate, and percent at a percent discount rate.

In summary, the present value method as im-plemented by takes the values of additions,depletions, and stocks calculated according tocurrent rent method II and multiplies them bydiscount factors of between and percent.The reason for the discount is straightforward.Under current rent method II, which relies on theHotelling valuation principle, it is assumed thatnet revenues rise at the discount rate. Under thepresent value approach, net revenues are assumedto rise at rates that are or percent slowerthan the discount rate applicable to mineral as-sets. The higher percentage is the discrepancybetween the rise in net revenues and the discountrate; the lower is the discount factor. The approach is shown in Box – .

Replacement Cost

The fourth method of calculating the value ofthe mineral stock is used only for oil and gas re-serves. Despite its name, this approach is similarto the method, not to the replacement costmethod described earlier. It adopts the approachof Adelman (), who calculates the presentvalue of an oil field using special assumptions. Itis assumed that the production from an oil or gasfield declines exponentially over time. Under theassumption that the decline rate is constant and

which a -year life is assumed). For the percent discount rate, the .factor holds for the years through . In , the year for which calculates a more complete set of satellite accounts, the rate is . for the percent discount rate and . for the percent discount rate.

. As with the calculation of mineral values, the factors shown in Box –vary depending on the year of the analysis. The factors reported are those forthe calculation. The factors differ in the various formulas because of thediffering treatment of the timing of depletions and additions from reserves.

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that the net revenue rises at a fixed constant ratethat is less than the discount rate, a barrel fac-tor is calculated. This barrel factor is multipliedtimes net revenue to obtain the present value ofthe reserves. Adelman estimates that the barrelfactor is usually around .. does not givethe barrel factor used in its calculations, whichshould vary by deposit and depend on the rate atwhich future cash flows are discounted, but weestimate that it averages approximately ..

The value of the asset—calculated with currentrent method II using the Hotelling valuation
principle—is then multiplied by the barrel fac-tor. The justification is that this approach,unlike the Hotelling approach, takes the physicalspecifics of oil and gas extraction into accountand accordingly adjusts the unit value of re-serves downward. As with the approachdiscussed in the last section, this adjustmentaccounts for the overvaluation inherent in theHotelling valuation principle.
Once the value has been adjusted downward, must again subtract the value of capital as-sociated with the asset. With this method, thevalue of capital associated with each unit of ex-isting reserves is assumed to be the current-yearexpenditure on exploration and development foroil and gas, divided by the quantity of oil andgas extracted during the year. This approach isloosely based on Adelman’s suggestion that thevalue of capital associated with a unit of pro-duction can be approximated by measuring thevalue of capital associated with finding new re-serves. The replacement cost method is shownin Box – .

Transaction Price Method

When oil and gas firms desire additional reserves,they can either buy them from other firms or findnew ones through exploration and development.In the absence of risk, taxes, and other com-plications, the transaction price of purchasingnew reserves should represent the market valueof those reserves. For this reason, according to, “if available, transaction prices are ideal forvaluing reserves” (Bureau of Economic Analysis,b:).

In fact, transactions in reserves are few and farbetween outside of oil and gas, and even in oiland gas suffer from problems discussed above.To estimate transaction prices, derived pricesfrom publicly available data on the activities oflarge energy-producing firms for the period to . The gross value of reserves was estimatedby dividing expenditures for the purchase of the

Box –: Formulas for Net Present Value Method

total mineral reserve valuet @ percent discount rate =

0.88 [p t − a t ]R t − 0.88Kt

total mineral reserve valuet @ percent discount rate =

0.69 [p t − a t ]R t − 0.69Kt

additionst @ percent discount rate = 0.84 [p t − a t − Kt /R t ]×Atadditionst @ percent discount rate = 0.59 [p t − a t − Kt /R t ]×At

depletionst @ percent discount rate = 0.83 [p t − a t − Kt /R t ]×qtdepletionst @ percent discount rate = 0.60 [p t − a t − Kt /R t ]×qt


where variables are as defined in Box –.

Note: The numerical values in this box apply to . As explained in thetext, slightly different values will apply for different years.

Box –: Formulas for Replacement Cost Method


{0.375 [p t − a t ]−Zt /q t }Rtadditionst = {0.375 [p t − a t ]−Zt /q t } × Atdepletionst = {0.375 [p t − a t ]−Zt /q t } × qt


where Zt = value of exploration and development ex-penditures in year t , and other variables are as definedin Box –.

Box –: Formulas for Transaction Price Method


(TV t /TQ t − Kt /R t )R t

additionst = (TV t /TQ t − Kt /R t )×Atdepletionst = (TV t /TQ t − Kt /R t )×qt


where TVt = value of reserve transactions, and TQt =total quantity of reserves transacted, and other variablesare as defined in Box –.

rights to the proved reserves by the quantity ofpurchased reserves. The result was then adjustedfor associated capital using the same method as

• February

in current rent method II. The transaction pricemethod is shown in Box – .

Data Requirements

On the whole, the five valuation methods used by are relatively parsimonious, and therefore thedata requirements are not unduly burdensome.For quantity data, only reserves are considered,so the quantities of mineral stocks are easy toobtain. Most of the data required for valua-tion under the five methods either are alreadyused by in their construction of the or are publicly available or available at a mod-est cost from private sources. Constructing theaccounts for subsoil minerals, therefore, requiredno independent data collection or survey by. Nevertheless, there is no single consolidatedsource for the data needed, and considerable ef-fort was expended by staff in collecting thedata.

Preliminary Results

The first set of estimates in the containsmany important and useful conclusions. Wehighlight some of the key findings in this section.

The calculations present a number of interest-ing findings for the overall economy. All fiveevaluation methods indicate that the value of thestock of oil and gas reserves in the United Statesexceeds the value for all other minerals combined.For all subsoil minerals, the calculated value ofreserve additions has approximately equaled thevalue of depletions over the – period.Consequently, the value of reserves (in constantprices) has changed little during the reportingperiod. finds that the value of the mineralcomponent of a mineral asset is about to times the value of the associated capital, so thevalue of the mineral makes up to percentof the total value of any mineral asset.

The results are also helpful in understandingreturns to capital of U.S. companies. Standardrate-of-return measures include profits on min-eral assets in the numerator, but exclude thevalue of mineral reserves in the denominator.Gross rates of return for all private capital de-cline from percent per year if mineral reservesare excluded to – percent if mineral reservesare included. does not present net returns,however. Because net post-tax returns on non-financial corporate capital have averaged around

. These findings are presented in Bureau of Economic Analysis (b)and summarized in Table – in Chapter of this report.

percent per year over the last three decades,our estimate of the profitability of American cor-porations would be significantly modified if the– percentage point decline in the gross returncarried over to the net return.

In quantity terms, the physical stock of aggre-gate metal reserves has tended to decline overtime, while the physical stock of coal reserves hasincreased. Quantities of oil, gas, and industrialminerals (“other minerals” in ’s five broadcategories) have remained stable. Revaluationshave tended to be positive primarily because theprices of most subsoil minerals have risen overthe period under investigation.

estimates the value of the nation’s stockof mineral reserves, after deduction of associatedcapital, to be between billion (current rentmethod I) and billion (current rent methodII) for ; this figure amounts to between and percent of the value of produced assets (existingproduced structures, equipment, and invento-ries). Current rent method II yields the higheststock and flow values for all mineral types. Cur-rent rent method I yields the lowest values forcoal, metals, and other minerals, while the trans-action price method yields the lowest value foroil, and the replacement cost method yields thelowest value for gas. (Recall that these last twomethods are used only for oil and gas.) Given thealgebra of the different valuation techniques, it isnot surprising that the replacement cost methodyields lower values than the current rent meth-ods for gas since the replacement cost method isreally current rent method II multiplied by ..

One important question concerns the impact ofincluding subsoil minerals in the overall nationalaccounts. In , the year for which presentsthe asset accounts, the calculated value ofreserve additions roughly offsets reserve deple-tions, so including mineral assets in the forthat year would not substantially alter the esti-mate of the level of net domestic product ().It would, however, increase the level of bybetween and billion (. to . percentof ), depending on the method used to valuereserve additions. The only year in which themineral accounts would have a substantial im-pact on the growth of real or is ,the year Alaskan reserves were added. Box –shows the calculations of real (in prices)with and without mineral additions for that year.The large surge of oil reserves erases the recessionof and leads to a downturn in growth in. While this kind of volatility is unique in theperiod analyzed by , it does indicate that in-

February •

Box –: Growth in Real Gross Domestic Productand Net Domestic Product With and Without

Mineral Additionsa

() ()Conventional with Mineral Additions

. . . . . -.

() ()Conventional with Mineral

Additions and Depletions . . -. . . -.

a Percent per year.Source: Conventional and in prices werecalculated by (U.S. Congress Economic Report ofthe President, ). with mineral additions wascalculated based on data in columns () and () andestimates of mineral additions and depletions fromBureau of Economic Analysis (b:). Mineral addi-tions and depletions in this calculation rely on currentrent method I.

troducing minerals into the accounts might leadto large changes in measured output that wouldreflect primarily changes in mineral reserves.

EVALUATION OF BEA’S APPROACH

This section evaluates the methodology of ’spreliminary approach to accounting for subsoilminerals. We begin with the advantages ofthe approach and then review some issues andconcerns.

Advantages

Feasibility

Phase I of ’s plan for extending the nationalaccounts to include supplemental mineral ac-counts is now complete. In accordance withthe recommendations of the United Nations Sys-tem of National Accounts (), limitedthe focus of Phase I to mineral reserves. Thisis probably the simplest of the natural-resourcesectors to include because the output is com-pletely contained in the current national accountsand involves primarily estimating and valuingreserve changes. The data, although obtainedfrom various sources, are publicly available fromthe (former) Bureau of Mines, the U.S. Geolog-ical Survey, the U.S. Department of Energy, andthe Bureau of the Census. Some minor adjust-ments of the data were needed in cases where thedefinition of reserves changed over time.

began this work in and completed itin April . Given the late start and limitedresources of the U.S. natural-resource account-ing effort, along with the sparsity of observablemarket prices with which to value mineral addi-tions, depletions, and stocks, the progress madeby to date is remarkable. Furthermore, thetask was completed by a group of eight offi-cials working part time on this assignment whilecontinuing with their regular duties. The resultis a partially completed satellite account that fitsinto the current definitions of the U.S. andcan be readily prepared in a short amount oftime. ’s approach is therefore clearly feasibleand relatively inexpensive.

Consistency with Other Valuation andAccounting Frameworks

treats mineral additions in parallel with otherforms of capital formation. In this respect, theU.S. accounts differ from the System of Inte-grated Environmental and Economic Accounting(), an alternative satellite accounting sys-tem proposed by the United Nations. In bothaccounting systems, depletions are treated as de-preciations of the fixed capital stock. Underthe , however, additions are not includedas income and do not appear in the productionaccounts as capital formation.

In calculating , the considers as capitalformation only investments in “made capital”and not mineral finds, treating discoveries asan “off-book” entry. This approach avoids thevolatility associated with mineral finds, which,if included in , makes a volatile se-ries (see Box – ). , on the other hand,treats mineral assets on the same basis as fixedcapital. For example, according to calcula-tions, booking the exceptional Alaskan oil findsin augmented the existing stock of U.S. oilassets by nearly percent, or almost billionin prices, despite exploration investmentson these reserves that were only a fraction ofthis amount. Including the increase in mineralreserves in private investment would have in-creased gross investment by percent in and would have increased net investment by percent. As is seen in Box – , the trend inreal nonminerals growth would have beenseriously distorted, wiping out the reces-sion and causing an apparent recession in .Thus, while including mineral additions as capitalformation treats made and natural capital aug-mentations in a parallel fashion, the aggregate series may become more volatile and may

• February

not accurately reflect movements in productionand employment.

A second concern with treating mineral addi-tions as capital formation is that the two do notnecessarily have the same effect on the economy.In particular, when fixed capital is added to thecapital stock, payments have been made to thefactors of production involved in producing thecapital. Mineral-stock additions, in contrast, re-veal themselves as increases in land value, whichare balance sheet adjustments rather than pay-ments to factors of production. It is for thisreason that the United Nations approachomits additions from net investment in the pro-duction accounts and introduces a reconciliationterm in the asset accounts to capture additions.

Finally, it has been argued by some that mineralstocks are inventory and should be treated as suchin the . chooses to treat mineral stocksas fixed capital, suggesting that, just as with pro-duced fixed capital, expenditures of materials andlabor are needed to produce these mineral assets,which in turn yield a stream of output over an ex-tended period of time. The treatment of mineralstocks then becomes consistent with the treat-ment of traditional capital in the . Of course,the concept of a satellite account allows individ-ual policy researchers to take the information inthese accounts and make their own adjustmentsto the . The approach is just one poten-tial way of treating natural capital formation anddepletion.

In terms of valuation methodology, the approach is consistent with current mineral assetvaluation theory.

Utility

presents an Asset Account and an Product Account that supplement the .Researchers, businesses, and policy makers canuse the satellite accounts to adjust output and in-come measures as they see fit, focusing on anyor all of the five valuation methods used by .Moreover, presents separate entries for fivetypes of mineral assets, including three types offuels, and an aggregate mineral category.

This level of detail makes the satellite accountsuseful to policy makers who wish to focus on par-ticular mineral issues. The data on the value ofmineral stocks, additions, depletions, and reval-uations (the residual) are given annually for the– period for oil and gas (the two mostimportant mineral groupings in terms of totalstock value) and from to for the otherthree mineral groupings. The constant ()

dollar figures for the aggregate mineral stockshow a price-weighted index of the stock, as wellas of additions and depletions to the aggregate,and are useful for determining whether the ag-gregate price-weighted quantity of U.S. mineralreserves is changing over time. One of the im-portant findings from the data is that theindex of the total constant-price stock of mineralassets has been approximately constant from to . This implies that the nation has on aver-age replaced reserve depletions with an equivalentquantity of reserve additions (or, more precisely,quantities of reserve additions and depletions ofdifferent minerals weighted by prices).

Issues and Concerns

’s approach to calculating mineral stock andflow values raises a number of issues related bothto measurement problems and to conceptual con-cerns with the individual valuation techniques.Some of these issues are intrinsic to any ac-counting approach in which data on prices orquantities must be imputed or constructed, whileother issues arise for particular methodologies.The major issues are reviewed here.

Heterogeneity of Reserves

A major problem with most accountingapproaches is that they assume all reserves arehomogeneous in terms of grade and costs. Forexample, under the Hotelling valuation princi-ple, average extraction cost should be calculatedas the average cost of extraction from all reserveclasses. In practice, most techniques use the ex-traction cost of currently extracted reserves. Thereality is that a nation’s reserves are not all in onecost class. It has already been noted that reservesare likely to exist in a number of classes, rangingfrom high quality (low cost) to low quality (highcost). Resource accounting, such as that in thecurrent , generally treats the entire nationalstock as one heterogeneous deposit whose valueis calculated by multiplying the average unit valueof that reserve by the quantity of the reserve.

An example will illustrate the issues raised byresource heterogeneity. Suppose that a nationowns million ounces of subsoil gold reserveswhose total value is billion, for an average unitvalue of per ounce. In a given year, the na-tion extracts million ounces, with no additions,and the value of the remaining reserves with un-changing gold prices is million. Accordingly,the depletion is measured at million, with anaverage value of per ounce extracted. This

February •

pattern is typical of many extraction profiles inwhich the lowest-cost and highest-value resourcesare extracted first.

Note that the correct depletion charge is thevalue of the extracted ore times the quantity ex-tracted, for a total of million. If we wereinstead to use the average value of the ore of per ounce to value depletion, we would be un-derestimating depletion at million rather than million. Moreover, if we used the value of theextracted reserve to value the remaining reservesof million ounces, we would incorrectly valuereserves at x = million, rather thanthe correct million. This example showsthat with reserve heterogeneity, using the averagereserve value to estimate depletion is likely to un-derstate depletion, while using the value of theextracted resource to value remaining reserves islikely to overstate the value of reserves.

This example is useful because common prac-tice in constructing national resource accounts,and one of ’s approaches, uses the averagevalue of the extracted resource to value the en-tire reserve stock. Nor can average costs fromcurrent production be used to calculate the netpresent value of additions. Because of the ran-dom quality of additions, it is not possible todetermine whether additions will be undervaluedor overvalued using these cost data. Heterogene-ity of reserves poses problems for the transactionsapproach because transaction values need not re-flect the average value of the total reserves, asthose parcels of reserves sold in any one periodmay have a quality above or below the average.All these problems of heterogeneity are particu-larly severe for metals, because there is a cleartendency for ore grades to fall over time. Theissue is less clear for petroleum because newfindings may have lower cost than current pro-duction, but the general trend in petroleum hasbeen for lower finding rates per unit drilling.

Putting the point differently, the difficulty invaluing the stocks and flows arises because theprices of reserves are not readily available. Al-though the commodities, such as gold and oil,trade frequently, the underlying assets tend totrade infrequently. There is no organized mar-ket for oil or gold properties, and there is suchgreat heterogeneity in these assets that there isno standard for classifying them as there is foroil or gold (in terms of sulfur content, purity,and the like). When reserves are transacted, theprices are not generally publicly available, whichmeans the reserve prices are generally not ob-servable. A further difficulty is that the tendency

is to observe the value of the total bundle ofassets and liabilities (reserves, associated capital,environmental liabilities, royalty and tax obliga-tions, and so on), so that even if the transactionprice were observed, the price of the mineral re-serve could not readily be determined. All thesecomplications mean that the values of reservestocks, additions, and depletions—which are es-sential for the construction of national accountsfor subsoil assets by and other statisticalagencies—must be estimated using the relevanteconomic and financial theories of valuation.

In principle, the heterogeneity problem couldbe overcome by calculating reserve values for eachreserve class and then aggregating across reserveclasses. This approach is likely to be quite costly,and extraction data may not be available for allreserve classes, particularly those not yet beingexploited. However, since these disaggregatedcalculations are not undertaken by , its esti-mated values for the total reserve stock are likelyto be too high for many of the minerals.

If in fact the lowest-cost and highest-valuereserves are extracted first, the use of extractioncosts from current depletion will provide a biasedestimate of reserve values. All of the valua-tion methods except the transaction cost methoduse an inappropriate measure of reserve valuesbased on the cost of current extraction. Although does not report total mineral asset and min-eral resource values separately, the estimation biasin the asset value will flow through to the calcu-lation of the mineral value that does reportin Table , rows through (Bureau of Eco-nomic Analysis, a). The result will be anupward bias in the mineral-resource values calcu-lated with current rent method II. Whether thisbias carries through to the calculation of mineral-resource values in the other calculation methodsis unknown since, as discussed below, the deduc-tions for capital may be too high or too low withthe other approaches.

A similar problem arises in valuing reserve ad-ditions, since assumes they have the samecharacteristics as current depletions. Conse-quently, if the quantity of additions equals thequantity of depletions, the value of additions willequal the value of depletions, even though thegrade of reserves may be quite different for de-pletions and additions. ’s approach is likelyto overvalue additions. With the best depositsextracted first, additions are likely to be of lessvalue than current depletions. This discrepancywill affect the production account sincewith a lower value for additions, the adjusted

• February

. Kilburn () suggests that the value of metalliferous ores in unex-plored land is Canadian per . hectares. This equates to peracre. Maintaining mineral claims in the United States requires an annualpayment of per acre, which, at a discount rate of percent per year,equates to a net present value of per acre. Hence, unexplored leasedland with some indication of mineral potential would appear to have a mar-ket value of at least acre. If percent of the ,,-acre U.S.land mass is mineable in the future (an obvious overestimate), the currentvalue of subsoil mineral resources other than reserves is on the order of .billion at per acre. Even when allowance is made for energy resourcesand industrial minerals and offshore petroleum potential, the total presentvalue of resources, other than reserves, is unlikely to exceed billion. calculates a current reserve stock value of some billion.

and figures will be lower. The discrepancyalso introduces a downward bias into the reval-uations of minerals because of the overstatementof additions.

Measures of Resource Quantities

Although most of the issues in minerals account-ing involve valuation, issues involving the quan-tity of reserves or resources are also important ina few areas.

The first of these issues relates to thecomprehensiveness of the resource base consid-ered by . In constructing product and assetaccounts, one is concerned with valuing the stockof the nation’s mineral resources and estimat-ing changes in the value of the stock due todepletions, additions, and revaluations. Thesequantities are measured with considerable un-certainty. An important issue here (as it isthroughout the federal statistical system) is de-veloping measures of accuracy, both for satelliteaccounts and the main accounts. Mineral re-sources other than reserves are often unknown ornot well established and thus are also quite dif-ficult to measure with any accuracy. In all cases,even where quantities are known, their value isnot easily calculated. For example, resource classN in Figure – has an average current extractioncost above price; thus, according to the Hotellingvaluation principle, its value is zero. All resourcesother than reserves (classes N and above in Figure– ) are assigned zero value. For both prac-tical and economic reasons, considers onlyreserves in its . Hence, ’s asset accountincludes a blank row for measures of stocks andof additions to and depletions from unprovedsubsoil assets. Yet these nonreserve resources arelikely to have some positive market value becauseof their option value.

A related flaw in the preliminaryaccounting framework is that current additionsto reserves produce no compensating depletionof nonreserve resources. Yet every ton of reservescomes from nonreserve resources. If nonreserveresources have economic value (as they certainlydo in the case of many oil and gas properties),the result will be an upward bias in the currentestimates of net capital formation (additions mi-nus depletions) in mineral resources. The failureto consider nonreserve resources means that ad-ditions to, as well as depletions from, differentcategories of nonreserve mineral assets are ig-nored. For example, adjacent drilling may leadto moving a resource from the speculative tothe hypothetical category or from an inferred

submarginal resource to a demonstrated subeco-nomic resource (see Figure – ). Proven reservequantities sometimes change dramatically be-cause previously uncertain nonreserve resourcesare found to be economic (e.g., Alaskan oil). Be-cause the option values of different grades willdiffer, the overall bias in mineral capital for-mation could be in either direction. The basicproblem again is valuing nonreserve resources. intends ultimately to include unproved re-sources as a part of nonproduced environmentalassets.

It is recognized that current estimates ofmineral capital formation are incomplete andlikely to be biased. correctly notes that anoperational methodology for valuing these non-reserve resources is not yet available. As withreserves, market prices based on resource trans-actions are not widely available, especially outsideof oil and gas, and unit prices must be de-duced using related economic series. Economistsare currently involved in developing methodsfor valuing such resources. However, offi-cial natural-resource accounting procedures havewithout exception omitted nonreserve mineralassets. Fortunately, the omitted value may not begreat.

A final issue is that values only a subsetof U.S. mineral reserves. Omitted are severalheavily mined industrial minerals such as sandand gravel, which may have small scarcity orHotelling rents because of their superabundancebut Ricardian rents because of their location. Inproduction terms, considers minerals thatmade up percent of the value of mineral andenergy production in the United States in ,a year in the middle of the available time series(Bureau of Mines, ). The series is incom-plete, but it values the most important mineralreserves, at least in terms of production value, inthe United States.

Measurement of Associated Capital

Accounting for minerals poses serious issuesof jointness of value of the mineral resource

February •

and the associated capital. Because these arecomplementary factors, dividing the total valuebetween capital and minerals is difficult andinvolves somewhat arbitrary accounting conven-tions. Similarly, when minerals are extracted, thevalue of the existing mineral asset diminishes.Some of the decreased value is depreciation ofcapital, while some is depletion of the mineral re-serve. The total depreciation in asset value due toextraction must be apportioned between the twoin resource accounting. With capital deprecia-tion being determined by guidelines that apply tocapital more generally, the residual loss in valueis then applied to depletion (see Cairns, ).The only rules that apply are that total depletionsover the life of the asset must sum to the value ofthe resource, and the total depreciation over thelife of the asset must sum to the value of installedcapital. Hence in an accounting framework thatmust separate depletion from depreciation on anannual basis, the depletion numbers are basedarbitrarily on the depreciation schedule chosen,being less than the total decrease in the value ofthe asset, but greater than zero. One comfortingfactor, however, is that although the breakdownin value or change in value between the capitalcomponent and the minerals component is some-what arbitrary, this affects only the compositionof the depletion and depreciation values and notthe total asset value.

Once the value of a mineral asset has beencalculated, the value of associated capital must bededucted to produce the mineral-reserve value.Only current rent method II and the transactionprice method deduct associated capital appropri-ately. Because the value of the asset is likely tobe overestimated through use of the Hotellingvaluation principle, current rent method II willnevertheless tend to overvalue the stock of min-eral reserves. Setting aside issues of heterogeneityand assuming that appropriate corrections aremade for associated assets and liabilities, thetransaction price method is the only method thatin principle can provide unbiased estimates of themineral value.

Current rent method I deducts depreciationand the gross return for capital per unit of ex-traction from gross price (see Box – ). Sinceone does not know whether this subtraction ismore or less than the subtraction under cur-rent rent method II, one cannot say whether thecalculated value of mineral-resource value usingcurrent rent method I will be too high or too low,even given its upward bias in the calculation ofthe total asset value due to use of the Hotelling

valuation principle. In the case of the metalscategory, however, current rent method I givesnegative values for the stock of metal reserves inthe s, which are clearly biased downward. Itappears, then, that with current rent method I,the upward bias in measurement of total assetvalue due to use of the Hotelling valuation prin-ciple is outweighed by an excessive deduction forassociated capital.

As noted in the previous section, the method deducts some fraction of the value ofassociated capital. Doing so would make senseonly if the value of the associated capital werethought to be less than its replacement cost. Onaverage, one would expect the value of the asso-ciated capital to equal its replacement cost. Thededuction for capital cost under the replacementcost method (see Box – ) also will generally notreflect the value of associated capital.

includes exploration and finding costs aspart of associated capital and then deducts thesecosts as part of the capital costs when valuingmineral reserves. This practice raises the ques-tion of what is actually trying to value. If, forexample, a gold deposit before the installation ofany development expenditures or physical capitalcan be sold for million dollars, some wouldsuggest this is the value of the mineral reserves. subtracts past exploration costs from thisfigure, and thus would value the mineral com-ponent of the property at less than million.The former approach values the asset as a “giftof nature,” while values it as the product ofprevious human endeavor and charges the stockaccount with the cost of moving the mineral fromthe resource to the reserve category.

Early models of mineral value suggested thatdepletion can be calculated as current net revenueless capital depreciation less a return to capi-tal, and follows this approach with currentrent method I. Subsequent research, however, hasshown that this approach overestimates depletion(Cairns, ; Davis, ). As a result, estimatesof depletion with current rent method I are toohigh, perhaps by as much as half. The deple-tion calculations with each of the other methods,including current rent method II, do not con-form to any known depletion formulations, andthe level or direction of measurement bias cannotbe determined. Nevertheless, the panel’s reviewindicates that the depletion calculations with cur-rent rent method I represent an upper bound ondepletion. Moreover, according to Cairns ()and Davis (), depletion can be appropriatelycalculated if one takes depletion as estimated by

• February

current rent method I (that is, current net rev-enue less capital depreciation less a return tocapital) and subtracts from this amount a returnto the mineral resource.

Production Constraints and the HotellingAssumptions

As noted earlier, current rent methods I and IIcalculate total asset values based on the Hotellingvaluation principle, which assumes that produc-ers face no production constraints and that thenet price rises at the rate of interest. In gen-eral, producers do face production constraints,and net prices rise at less than the rate of interest.The Hotelling principle is used as a valuation toolbecause of its extreme simplicity; yet, as discussedabove, it has been shown both theoretically andempirically to substantially overvalue mineral re-serves. Cairns and Davis (a, b) and Davisand Moore (, ) demonstrate that assetvalues calculated using the Hotelling principletend to be up to twice the market values. Thuscaution is necessary in using this approach toprovide asset or mineral-resource values.

Because of the potential for overvaluation usingthe Hotelling valuation principle, uses the method to adjust the stock estimates fromcurrent rent method II downward. For pur-poses of the present discussion, ’s approachis termed variant I. As shown above in Box–, this method takes the current rent methodII stock values and adjusts them downward by and percent using the two assumed discountrates.

The replacement cost formula is based on amodel that does not require the strict assump-tions of the Hotelling valuation principle andimplicitly takes into account the capital con-straints on oil and gas production (see Cairns andDavis, a ). Therefore, given the appropri-ate value for average costs, the model is likely toyield an accurate estimate of asset values. Therehas been no empirical verification of Adelman’sreplacement cost rule for valuing the associatedcapital, however, so it is not possible to judge theaccuracy of the method for deducting thevalue of associated capital to obtain the value of amineral resource. might, however, consideran alternative approach (termed here replacementcost variant II) that would subtract the replace-ment cost of capital from the asset value as incurrent rent method II, rather than the value ofexploration and development expenditures.

. In mathematical terms, depletionst = [p t − a t − r t K /q t −Dt /q t − rV t /q t ]xq t , where the variables are as defined in Box –.

Royalty and Severance Fees

The transaction price approach has the potentialto yield reasonable mineral-reserve values since itis based on observed market prices that in prin-ciple account for production constraints, marketdiscount rates, actual reserve quality, and otherfactors that affect the value of mineral reserves.As noted elsewhere, however, the market valueof an asset depends on the liabilities attached tothe asset. In the case of minerals, productionoften incurs royalties, severance fees, and taxespayable to third parties as production proceeds.These and other liabilities attached to currentand future production reduce the observed mar-ket value of the reserve and are deducted fromthe asset value by the purchaser during a reservetransaction. Thus, the observed transaction valuedoes not represent the value of the reserves, butthe value of a bundle of financial and real as-sets and liabilities, of which the reserves are oneaspect (a point illustrated above in Box – ).

The treatment of these costs is not clear in accounts. It appears that royalty and severancetaxes are included in the unit costs used to cal-culate net rent in valuation methods other thanthe transaction method for oil and gas. Thistreatment is inconsistent with that under ’stransaction price method, whereby no adjust-ment is made for the present value of taxes androyalties. In both cases, the pre-tax-and-royaltyvalue of the resource will be underestimated by’s methods.

Revaluation

Revaluation effects are an additional element ofnatural-resource accounting and some other aug-mented accounts that are not present in thecurrent U.S. . As discussed earlier, changesin the value of reserves are composed of addi-tions, depletions, and revaluations (see equation. in Box – ).

For a simple gold-reserve case, revaluationsenter the equation when reserve values adjustduring the accounting period to reflect unex-pected price changes. For example, suppose theaverage price of the existing gold-reserve stock is per ounce at the start of the year, then jumpsto an average of per ounce on December .The revaluation equation becomes: revaluations( billion) = closing stock value (. billion)− opening stock value ( billion) − additions( million) + depletions ( million). This ex-ample shows that revaluations are calculated asa residual—the change in the value of the stock

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through price changes that are not taken into ac-count in the depletion and addition calculations.Given the volatile nature of mineral prices, therevaluation component is substantial, often largerthan additions or depletions. Yet the revaluationterm is not directly calculated; it will include anyerrors in calculating additions, depletions, andopening and closing stock values.

Mineral-stock revaluations caused by unex-pected changes in unit prices for reserves are cal-culated by as a residual, and therefore are alsoaffected by the capital depreciation schedule cho-sen. In the data, mineral-stock revaluationsare usually greater than either reserve additionsor depletions, implying that most mineral wealthcreation or loss comes not from additions to ordepletions of the mineral-reserve base, but fromlarge mineral price changes. Several resourceeconomists have suggested that these revaluationsare important indicators of economic welfare andshould be considered equivalent to investment(gross domestic capital formation). For exam-ple, a small nation could in principle sell itsmineral assets to a foreign producer, and hencean upward revaluation of its assets would createwealth and higher sustainable consumption forthe nation. does not include revaluations inthe gross domestic capital formation column ofits Production Account and thereby ignoresthis aspect of sustainable national income.

Short-Run Volatility in Price

Where the value of a mineral asset is a function ofthe current extracted mineral price, as in currentrent methods I and II, the method, and thereplacement cost method, short-run volatility inmineral commodity prices makes the value of thestock of mineral assets itself a volatile series. Tothe extent that price movements are temporaryexcursions from long-run levels, these changes instock value will show up as revaluations. Cur-rent measures of national saving do not includerevaluation effects, but future measures might doso. It should be noted that the revaluation ef-fects in mineral assets pale in comparison withthe revaluation effects from security markets.

In addition, the depletion calculations dependin part on current prices and will also be af-fected by price volatility. For example, consideran economy that is running down its mineralreserves at a constant rate, with no reserve addi-tions. Depletion values will depend on current

. The issue of inclusion of revaluation in income is considered inChapter .

mineral prices. If nominal mineral prices in-crease sharply in a given year, the depletioncharge will also rise sharply.

The dependence of additions and depletionson current mineral prices will affect the currentvalue or nominal value of augmented if min-erals are included. Sharp changes in mineralprices could also lead to a significant change inthe augmented- deflator or chain-weightedprice index. The volatility of prices would notlead to volatility in the constant-price or chain-weighted indexes of real output under currentconcepts applied in the U.S. national accounts,but it would affect those measures of sustain-able income that include elements of revaluation.These effects will necessitate considerable care ininterpreting movements in and its compo-nents if additions and depletions are to be addedto the core accounts.

mitigates problems of price volatility byarbitrarily using annual prices averaged over years. In addition, quantity additions and de-pletions are in most years nearly offsetting; thus,given ’s approach of valuing additions at thesame unit price as depletions, price fluctuationswill have little impact on adjusted figures.Price fluctuations do impact the stock revalua-tions column, but these data are not currentlyused in current accounting measures.

Scarcity and Long-Run Price Trends

One possible use of a series showing the changein quantity and value of a nation’s stock of min-erals is for assessing trends in mineral scarcity.In quantity terms, increasing scarcity might bereflected in a declining constant-dollar stock ofmineral resources or of some component of min-eral resources. On this front, is developinga constant--price series for mineral stocks,shown in Figure –, that is equivalent to a phys-ical quantity series, aggregated across differentmineral types on the basis of mineral prices.This graph shows that the stock of mineral as-sets as a whole has been roughly constant overthe – period. This finding might be in-terpreted as indicating that additions have offsetdepletions and that concerns about the UnitedStates running out of oil and other minerals areunfounded. Figure – shows the value of stocksand changes in current prices (from Bureau ofEconomic Analysis, b).

The constant-price stock has limited utility asan indicator of natural-resource scarcity, how-ever. Depletion of a physical resource indicatesnothing about scarcity if that commodity is

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becoming worthless to society, since its disap-pearance will have no economic consequences.(In this respect, even chain-price indexes willnot produce improved indicators.) Stock meas-ures are particularly questionable indicators forcommodities that are heavily involved in inter-national trade, which includes all major mineralcommodities. For example, many countries haveseen the economic value of their domestic coalstocks decline, primarily because of the availabil-ity of low-cost coal on the world market, but thisis not taken as an indicator of coal scarcity.

Relative price is usually a better index ofeconomic scarcity, with increasing relative prices

indicating that a unit of the particular asset isbecoming more valuable to society, and hencemore scarce, relative to other assets. Thus amineral reserve’s unit price is an indicator of itsvalue to society. Increasing scarcity would be in-dicated by rising average reserve prices relativeto other prices; for example, one might comparethe relative prices of reserves and consumptiongoods and services or the ratio of reserve pricesto the prices of other inputs, such as wage rates.These scarcity indices are not currently presentedin satellite accounts. does not report unitprices for reserves, and thus it is difficult to de-termine the implications of its findings for trendsin mineral scarcity. If scarcity indicators are de-sired, deflated per unit prices for each type ofmineral reserve should be presented.

Data Availability Issues

Although ’s valuation methods require lim-ited data, all may suffer from potentially signifi-cant measurement error. For example, while thereplacement cost method of valuing oil and gasreserves is conceptually appropriate, it requiresan estimate of the value of associated capitalthat cannot be measured directly and must beestimated through current exploration and devel-opment expenditures. There is no indication thatthis estimate, as proposed by , has any empir-ical validity. The transaction price method is alsoconceptually correct, but one must make adjust-ments to the transactions, as listed in Box –,to obtain the reserve value. The necessary datamay not be available for each transaction, caus-ing the method to lose its appeal. The currentrent methods, once correctly formulated to takeproduction constraints into account, will requireaverage cost data that are not always observablein markets.

Other Issues

Whenever asset valuation requires discounting offuture cash flows, as is the case in the valuationof mineral stocks, questions arise as to the appro-priate discount rate. Finance theory offers sometheoretical guidelines, but practical implementa-tion is difficult. The popularity of the formulabased on the Hotelling valuation principle derivesin part from the fact that it does not require a dis-count rate, but this advantage comes at the costof an implausible assumption about the increasein net mineral rents. In constructing present

. Measures of resource scarcity are reviewed in Fisher (: Ch. ).

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method of pricing reserve stocks or flows.

value estimates, it is difficult to justify the ex-tremely low real discount rate of percent peryear used by if the purpose of the estimatesis to determine the market value of the reserves.

All techniques, which include both currentrent methods and the replacement cost method,omit asset value that is created by managerialflexibility (see Davis, ). With mineral assets,the ability to alter extraction as prices move upor down can create significant option value, es-pecially for marginal deposits. Of the valuationtechniques used by , only the transaction ap-proach includes these option values, since theywill be included in the observed asset price.

’s results show clearly the potential marginfor error among the various techniques, for theyyield widely different estimates. In some cases,the net change in the value of reserves (additionsminus depletions) even has a different sign underdifferent valuation techniques. All of this sug-gests that correctly accounting for mineral stocksand flows in a set of satellite accounts will be

just as intensive an accounting exercise as currentaccounting for the stocks and flows of producedcapital in the .

OTHER APPROACHES ANDMETHODOLOGIES

Efforts in Other Countries

Mineral accounts are currently constructed bymany countries. The current rent and discountedpresent value valuation approaches used by to calculate resource stock and flow values aresimilar to those employed in other countries,with current rent method I being used mostwidely. The shortcomings of this approach werediscussed earlier. Other countries assume that thecurrent rent, after a return to capital is deducted,represents the current unit price of all reserves;they then calculate the present value by discount-ing the projected rent using an arbitrary discountrate. Again, as noted above, this is an unrealistic

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Although estimates only a set of monetaryaccounts, most other countries compute bothphysical and monetary accounts for reserves. InEurope the most important minerals are oil andgas under the North Sea. Indeed, the discov-ery of these resources and the economic-policyproblems they created led Norway to pioneerthe development of resource accounting in thes. Most other minerals appear to have a mar-ket value barely in excess of production costs,and hence the valuations applied to subsoil assetsresult in a very small value for the stocks and de-pletion. In Canada and Australia, however, otherminerals have a significant economic value.

Coverage

The types of minerals covered in studies forother countries are similar to those covered inthe . Most countries tend toward a slightlybroader definition of reserves: instead of the“proven” reserves included by (those that arecurrently known to be commercially exploitableat today’s prices and technology), other coun-tries often include “probable” reserves (definedas those having a better than percent chanceof being commercially exploitable in the future).Canada and Norway distinguish between “devel-oped” or “established” and undeveloped reserves.This distinction is useful for assessing options forthe future schedule of extraction. The distinc-tion is also necessary when applying current rentmethod II, under which the value of associatedfixed capital is deducted from the value of the re-serve, and which therefore applies properly onlyto those reserves for which all fixed capital neededto extract the reserves is already in place.

The minerals covered by studies for othercountries include oil and gas, coal, and a selectionof metal ores, depending on what appears impor-tant in a given country. Hence Canada includesabout basic metals, while Australia values nearly minerals, including precious metals and gold.In Europe, however, most minerals other thanNorth Sea oil and gas appear to have a very smallvalue, and efforts have not focused on them.

Valuation

The valuation methods used by other countriesare generally the same as those reviewed earlier.As in the work, total resource values are asmall fraction of national wealth. The startingpoint is physical data on the stock and annual useof the minerals. As noted early in this chapter,the simplest valuation techniques are current rent

methods I and II, which derive a resource rent forthe current period as the difference between theextraction costs and the wellhead or surface priceof the mineral. Often this margin is relativelysmall and can be highly volatile when the sellingprice of the mineral fluctuates while extractioncosts undergo little change. In some cases, suchas coal extraction in many parts of Europe, theminemouth price of coal is consistently less thanextraction costs, and extraction continues onlybecause of subsidies. A negative asset value inthis case may actually be realistic.

Most countries assume that the Hotelling hy-pothesis is inadequate and instead use the presentdiscounted value of the expected future incomestream from extracting mineral reserves. The fu-ture schedule of extraction is often assumed tobe constant, or it may actually be determinedby contracts with purchasers of the mineral. Inthe absence of other knowledge, prices are as-sumed to rise with expected future inflation. Thediscount rate used tends to be the historical aver-age interest rate on government bonds (typicallyaround percent), which is taken to representthe opportunity cost of funds. Normal rates ofreturn for industry generally, or the mining in-dustry specifically, have also been tested. Becausethese returns include a risk premium, they arehigher than government interest rates. An in-teresting and quite different valuation methodadopted in The Netherlands is described in thenext section.

Practice in Selected Countries

Australia. The Australian Bureau of Statisticspublishes values of reserves and changes in re-serves for nearly minerals, including oil andgas, uranium, and gold. The valuation methodused is essentially ’s current rent methodI. Even in resource-rich Australia, the reportedvalue of subsoil assets is only one-tenth the valueof the fixed capital in structures and equipment.The Australian Bureau of Statistics notes thateconomically exploitable reserves are only a verysmall proportion of the total resource. It alsopoints out that its valuation techniques can givea misleading impression both of the value of re-serves and of year-to-year changes in reservesbecause mineral prices fluctuate considerably.

Canada. Statistics Canada has estimated thevalue of reserves of oil, gas, coal, and eightmetals using both current rent methods I andII, although its preferred valuation technique isthe latter. Current rent method I sometimesproduces negative values for mineral reserves.

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Because Canada is concerned with regional de-pletion issues, it produces monetary and physicalaccounts for each province.

The Netherlands. Statistics Netherlands esti-mates the value of gas under the North Sea,the country’s principal natural resource, by anunusual method. In all North Sea operations,governments (United Kingdom, Norway, TheNetherlands) attempt to appropriate most of theresource rent through royalties and taxes. Insteadof estimating the resource rent indirectly by themethods employed elsewhere, the Dutch estimatethe resource rent directly from known govern-ment receipts. Tests by other countries haveshown this method performs reasonably well forthe North Sea fields, where governments take percent or more of the resource rent.

Norway. The first work on resource valuationwas done in Norway in the s, when NorthSea oil suddenly appeared as a major influence onthe Norwegian economy. The Norwegians werepioneers in natural-resource accounting, begin-ning with oil, but later extending to other assets,such as forests. Their studies have had a consider-able effect on subsequent work in other countries.The s was, however, a period of massivechanges in world oil prices that produced hugeswings in the apparent value of this resource; as aresult, many Norwegians concluded that their es-timates had serious shortcomings. A number ofNorwegian analysts concluded that physical dataon resources were more useful. Norway recentlyresumed valuing natural resources to completethe balance sheets of national wealth for national accounts.

Sweden. For its national accounts balancesheets, Statistics Sweden has calculated reservesand depletion of subsoil assets, in particularmetal ores. The reserves covered are proven re-serves, which are valued by ’s current rentmethod I. Because prices of metals are volatile,the calculated resource rents occasionally turnnegative, a problem reduced but not removedby adopting a moving average of prices. As aresult of a fall in world copper prices, a propor-tion of the country’s mineral stock has ceasedto be economically exploitable and therefore maydisappear from proven reserves.

United Kingdom. Estimates of the depletion ofU.K. oil and gas in the North Sea were publishedin for several successively broader categoriesof resources—proven, probable, possible, andundiscovered but inferred from geological evi-dence. Several valuation techniques were tested,including current rent methods similar to those

of and the present value of the future incomestream. Significant differences were observed inthe estimates derived with the various techniques.

Other countries. Valuation studies by de-veloping nations including Brazil, China, andZimbabwe have produced other important find-ings (see Smil and Yshi, ; Young and Seroada Motta, ; and Crowards, ).

Alternative Methodologies

One quite different methodology has not beenemployed by —that of relying on financialinformation for individual firms. At the level ofthe firm, the value of mineral reserves can beimputed from data on financial balance sheets.Figure – indicates the calculations required.This method calculates a nation’s mineral wealthby aggregating the values of the domestic min-eral resources held by all resident mineral firms.This is a laborious process that requires assess-ing the balance sheets of both listed and unlistedcompanies. It also provides only private reservevalues, since the owners of the reserve implicitlydeduct the value of any taxes, royalties, and otherpayments on the mineral assets when attaching avalue to equity capital. Finally, as with any cal-culation of the value of the reserve stock, it isdifficult to apportion changes in total values ofthe mineral reserves among additions, depletions,and revaluations.

A much simpler approach entails empiricallybased modifications to current rent method II.Cairns and Davis (a, b) have found thatmultiplying the total asset value as calculated us-ing current rent method II by a fixed fraction caneliminate the upward bias in total reserve valueand produce estimates that are closely alignedwith the observed market values of mineral as-sets. The fraction used, which lies between zeroand one, varies by commodity. Cairns and Davis’work suggests a fraction of . for gold reserves.Work by Adelman suggests a fraction of .for oil and gas reserves. For other mineral re-serves, the appropriate fractions have yet to bedetermined, but are likely in most instances tobe around . according to Cairns and Davis(b). To estimate the value of the mineral re-serves, the value of associated capital must stillbe deducted from the total asset value. This canbe done in the same manner as in current rentmethod II. The mathematical formulation of thismodified reserve valuation approach is shown inBox – .

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deduct an additional term that reflects a return

Additions are simply the value of new reserves,which can be calculated with the same formulaused for valuing total reserves, except that ex-ploration and development expenditures, ratherthan existing associated capital, are deducted.The formula for valuing additions is given inBox – .

Depletion calculations have been studied byCairns () and Davis (), who suggest amodification to the depletion calculations(see Box – ). Cairns and Davis take the de-pletion calculation of current rent method I and

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to the mineral. This modification lowers thedepletion calculation of current rent method I.

The discussion thus far has been aimed at es-timating the value of the reserve stock and thevalue of depletions from and additions to thatreserve stock. The discussion is guided by thenotion that produced capital and natural capitalare currently treated asymmetrically in nationalaccounting and that this discrepancy should becorrected. There are yet other approaches thattake a “sustainability” perspective. El Serafy() has devised an alternative approach to ad-justing to account for mineral depletion.As currently measured, is temporarily aug-mented during mineral extraction. El Serafywould convert the temporary revenue streamfrom mineral extraction into the equivalent in-finite income stream, likening this latter streamto permanent income from the mineral asset.He thus advocates deducting an amount fromthe conventionally measured during the ex-traction period to create an adjusted sustainable. It may be noted that the production ofsatellite accounts is intended to address just thistype of concern, since those who prefer El Ser-afy’s concept of sustainability to other accountingconventions can make their own adjustments tonational output using the information containedin satellite accounts.

CONCLUSIONS ANDRECOMMENDATIONS ON

ACCOUNTING FOR SUBSOIL MINERALRESOURCES

Appraisal of Efforts

. should be commended for its initial effortsto value mineral subsoil assets in the United States.

At very limited cost, has produced usefuland well-documented estimates of the value ofmineral reserves. These efforts reflect a seriousand professional attempt to value subsoil mineralassets and assess their contribution to the U.S.economy. The methods employed by arewidely accepted and used by other countries thatare extending their national income accounts.

. The panel recommends that work on devel-oping and improving estimates of subsoil mineralaccounts resume immediately.

As a result of the congressional mandate, was forced to curtail its work on subsoil as-

. The deduction proposed by El Serafy is R/( 1 + r) n +1 where R isthe current depletion, r is an appropriate discount rate, and n is the numberof years of mineral reserves remaining assuming a constant extraction path.See also Hartwick and Hageman () and Bartelmus () .

Box –: Modified Formulas for the Calculation ofReserve Stocks, Additions, and Depletions


[ p t − a t − Kt /R t ]×Rtadditionst = [ p t − a t − Zt /A t ]×At

depletionst = [p t − a t − rK t /q t −Dt /q t−rV t /q t ]×qt

where is an empirically estimated adjustment coeffi-cient with a value between zero and one, and all othervariables are as defined in Boxes – and –.

sets. Its estimates of subsoil mineral assets areobjective, represent state-of-the-art methodology,and will be useful for policy makers and analystsin the private sector.

. Because of the preliminary nature of the estimates, as well as the potential volatility intro-duced by the inclusion of mineral accounts, thepanel recommends that continue to presentsubsoil mineral accounts in the form of satelliteaccounts for the near term.

Once the accounting procedures used for themineral accounts have been sufficiently studiedand found to be comparable in quality to thoseused for the rest of the accounts, it would be bestto consider including the mineral accounts in thecore accounts. It is appropriate that assess-ments of changes in subsoil assets be presentedon an annual basis, as has done in its initialefforts.

. The panel does not recommend that a singleapproach to mineral accounting be selected at thistime.

No single valuation method has been shown tobe free of problems. Thus should continueto employ a variety of valuation methods, mod-ifying them as warranted by new developmentsin the field.

. The panel has identified a number of short-comings in current valuation approaches, and itrecommends that consider modifying or elim-inating some of its procedures in light of thesefindings.

The panel has identified problems involvingappropriate adjustment of asset values for associ-ated capital and other assets and liabilities, as wellas potential overestimation of the value of assets,additions, and depletions by use of the Hotellingvaluation technique. should consider suchfindings in refining its techniques. Empiricallybased modifications to the Hotelling valuation

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technique along the lines suggested above shouldbe examined.

. The derivation of accurate and parsimoniousvaluation is an area of intensive current research,and should follow new developments in thisarea.

The panel has identified a number of promisingresearch efforts that may reduce the uncertain-ties among various approaches to valuing mineralresources. Most of the shortcomings of ’sapproaches identified in this chapter reflect datalimitations and inherent problems that arise inestimating quantities and values that are notreflected in market transactions. Given the un-certainties involved, as well as the small share oftotal wealth represented by subsoil assets in theUnited States, a major commitment to data gen-eration for these assets does not appear to bejustified at this time. should therefore em-phasize valuation methods that rely on readilyavailable data.

. The most important open issues for fur-ther study are () the value of mineral resourcesthat are not reserves, () the impact of ore-reserveheterogeneity on valuation calculations, () the dis-tortions resulting from the constraints imposed onmineral production by associated capital and otherfactors, () the volatility in the value of mineralassets introduced by short-run price fluctuations,and () the differences between the market andsocial values of subsoil mineral assets.

One of ’s most important contributionshas been to stimulate discussion and research onresource-valuation methodologies. ’s actualfindings regarding the value of reserves—stocks,depletions, and additions—should be consideredpreliminary and tentative until there is a betterunderstanding of the magnitude of the distor-tions introduced by the various techniques. Itis recommended that close attention be paid tothese five important open issues.

Implications for Measuring SustainableEconomic Growth

. The initial estimates of the subsoil min-eral accounts have important implications forunderstanding sustainable economic growth.

In one sense, the major results of the initial es-timates are negative. Perhaps the most importantfinding is that subsoil assets constitute a rela-tively small portion of the total U.S. wealth andthat mineral wealth has remained roughly con-stant over time. According to the results,the value of mineral resources is between and

percent of the tangible capital stock of the coun-try. If other assets, particularly human capital,were considered, mineral value would be an evensmaller fraction of the country’s wealth. This isan important and interesting result that was notwell established before developed its subsoilmineral accounts.

. Alternative measures, along with measuresof sustainability from a broader set of natural-resource and environmental assets, will be neces-sary to obtain useful measures of the impact ofnatural and environmental resources on long-termeconomic growth.

The mineral accounts as currently constructedare of limited value in determining the threat tosustainable economic growth posed by mineraldepletion. The value of subsoil mineral assetsin the United States could fall because muchcheaper sources of supply are available abroad.Conversely, the value could rise because seriousdepletion problems are driving mineral pricesup. The real prices of individual mineral com-modities provide a more direct and appropriatemeasure of recent trends in resource scarcity thanis offered by the total values of specific mineralsin the mineral accounts.

. The panel recommends that maintaina significant effort in the area of accounting fordomestic mineral assets.

While subsoil assets currently account for onlya small share of total wealth in the United Statesand do not appear to pose a threat to sustainableeconomic growth at present, this situation couldchange in the future. A good system of accountscould address the widespread concern that theUnited States is depleting its mineral wealth andshortchanging future generations. By properlymonitoring trends in resource values, volumes,and unit prices, the national accounts could iden-tify the state of important natural resources, notonly at the national level, but also at the re-gional and state levels. Better measures wouldalso allow policy makers to determine whetheradditions to reserves and capital formation inother areas are offsetting depletion of valuableminerals. Development of reserve prices and unitvalues would help in assessing trends in resourcescarcity. Comprehensive mineral accounts wouldprovide the information needed for sound pub-lic policies addressing public concerns related tomineral resources.

. Efforts to develop better mineral accountingprocedures domestically and with other countrieswould have substantial economic benefit for theUnited States.

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Other countries and international organiza-tions are continuing to develop accounts thatinclude subsoil assets and other natural and en-vironmental resources. The United States hashistorically played a leading role in developingsound accounting techniques, exploring differentmethodologies, and introducing new approaches.A significant investment in this area would helpimprove such accounts in the broader worldeconomy. Unfortunately, the United States haslagged behind other countries in developing en-vironmental and natural-resource accounts, par-ticularly since the congressional mandatesuspending those efforts.

. To the extent that the United States de-pends heavily on imports of fuels and mineralsfrom other countries, it would benefit from bet-ter mineral accounts abroad because the reliabilityand cost of imports can be forecast more accuratelywhen data from other countries are accurate andwell designed.

International development of sound natural-resource accounts would be particularly usefulfor those sectors in which international trade isimportant. Indeed, as has been learned from cat-aclysmic events in financial markets such as theMexican peso crisis of – or the finan-cial crises of East Asian countries in –,the United States suffers when foreign account-ing standards are poor and is a direct beneficiaryof better accounting and reporting abroad. Bet-ter international mineral accounts would help thenation understand the extent of resources abroadand the likelihood of major increases in pricesof oil and other minerals such as those of thes. Improved accounts both at home andabroad would help government and the privatesector better predict and cope with the importanttransitions in energy and materials use that arelikely to occur in the decades ahead.

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