Accounting for mineral resources: issues and BEA's initial estimates.

Landefeld, J. Steven ; Carson, Carol S.

AMONG NATURAL assets, the characteristics of minerals--oil, gas, coal, and nonfuel minerals--are the most similar to the characteristics of assets included in traditional economic accounting systems. Not surprisingly then, minerals have long been considered as candidates for a treatment that is symmetrical with the treatment given other assets. Such a treatment is at the heart of the integrated economic and environmental satellite accounts (IEESA's), which are the subject of a companion article, beginning on page 33. Failure to account symmetrically for mineral resources as a form of capital has been blamed both for their over- or under-exploitation and for incomplete analysis and policy decisions in areas relating to productivity and budgeting.

The companion article noted three points of asymmetry between the treatment given assets such as structures and equipment in the traditional economic accounts and the treatment given natural assets. First, in traditional economic accounts, there is no entry for additions to the stock of natural resources parallel to the entry for additions to the stock of structures and equipment. Second, there is no explicit entry for the contribution of natural resources to current production, as measured by gross domestic product (GDP), parallel to the entries that capture the value added of structures and equipment. Finally, there is no entry for the using up of the stock of natural resources parallel to the entry for the depreciation of structures and equipment used to arrive at net domestic product (NDP)--which is used by some as a shorthand measure of sustainable product.

This treatment given mineral resources in the traditional economic accounts is anomalous in several respects. First, firms spend large amounts of time and other resources in "proving" mineral reserves, and these reserves, like structures and equipment, yield a flow of services over many years. As firms prove these reserves, they are entered, along with investments in new structures and equipment, in the firms' balance sheets. Additions to these reserves are also recognized by investors and reflected in firms' equity prices. Second, the value added of a resource like coal or oil is included in GDP even though no explicit entry for its contribution is made: Its value added is in a sense "appropriated" by the other factors of production and is included in the rents, royalties, and profits of the owners of invested capital. Finally, although the traditional economic accounts do not include an entry for depletion of natural resources, firms and investors recognize depletion in assessing the value of firms and the sustainability of their current profit levels.

The treatment of natural resources in the mining industry has long been debated in economics literature.(1) While there is a conceptual case for symmetrical treatment of mineral resources and invested capital, the absence of good market prices to value additions, depletion, and stocks has been a stumbling block. Property rights issues, incomplete information, asymmetry in bargaining, and the structure of payments for mineral rights create a situation in which either there are no observable prices or prices are seriously incomplete or unrepresentative. Partly as a result of this situation, traditional economic accounts have treated the value added of mineral resources as free gifts of nature, making entries neither to the flow accounts for additions to, or depletion of, the stock of these resources nor to the wealth accounts.

The omission of explicit entries for mineral resources has import beyond the economic accounts. The absence of an entry, or market price, for depletion may--in combination with common property rights--mean that the accounts do not identify overexploitation. This possibility is particularly important because a large share of the Nation's mineral resources are on public lands. (However, as the current problems in the New England fisheries suggest, the issue clearly has import for a wide range of other resources.) Such omissions have also been cited as the source of problems in productivity analysis. Despite the inclusion of land, labor, and capital in the most elementary production function used in studying productivity, measures of natural resources have generally not been available. Finally, the absence of measures of natural resource stocks and stock changes on Federal lands has been cited as contributing to less-than-optimal Federal budgeting decisions.(2)

As previously mentioned, this article is the second of two articles reporting on the IEESA's. It provides initial estimates of the value of additions, depletion, revaluations, and stocks of mineral resources and on the impact such estimates would have on the estimates of the Nation's production, income, and wealth. This article begins with a summary of the major conceptual and methodological issues in accounting for mineral resources. Next, the article describes alternative methods of valuation that can be used to develop IEESA estimates for minerals, and it then presents estimates for oil, gas, coal, metals, and other minerals using these methods. An appendix provides information on data sources and methods. Tables 1-5 appear at the end of the article: Table 1.1-1.6 present estimates of oil--opening stocks, additions, depletion, and the revaluation adjustment--for 1947-91; tables 2.1-2.6 present estimates of gas for 1947-91; tables 3.1-3.4 present estimates of coal for 1958-91; tables 4.1-4.4 present estimates of metals for 1958-91; and tables 5.1-5.4 Present estimates of other minerals for 1958-91.

Conceptual and Methodological Issues

In addressing conceptual and methodological issues for mineral resources, as for natural resources and the environment more broadly, BEA has attempted to follow two principles. First, the treatment in the satellite accounts should be consistent with the principles of economic theory. Second, the satellite accounts should embody some concepts and definitions that differ from those of the existing accounts in order achieve their purpose of showing the interaction of the economy and the environment, but in other respects they should be consistent with the existing accounts. Satellite accounts provide the flexibility to make changes that are useful in analyzing natural resources and long-term economic growth, but consistency with the existing accounts will allow the satellite accounts covering mineral resources to link to, and build upon, the existing economic accounts, including the input-output and regional accounts.

The conceptual and methodological issues discussed in this section can be divided into two main groups. The first group deals with the accounting treatment for mineral resources. The second group deals with valuation.

Accounting issues

Treatment of additions to reserves.--Symmetrical treatment of proved mineral resources with structures and equipment requires treatment of additions to the stock as capital formation and of deductions as depletion. Capital formation records the initial production of the capital, as well as its addition to the capital stock; depreciation records the reduction in the capital stock associated with its use, as reflected in NDP. Over the life of the asset, depreciation sums to the value of the original investment.

In economic accounting, as in business accounting, what comes off the books must have gone on the books. This business accounting requirement was one of the reasons why estimates of depletion of natural resources have not been included in official estimates of NDP. Beginning in 1942, depletion allowances for minerals and timber were deducted from GDP in the estimates of net national product made by the U.S. Department of Commerce. Discoveries of minerals, however, were not included in capital formation and net product. The depletion allowances were eliminated in 1947 because of this absence of an entry for capital formation.

Despite this accounting requirement for symmetrical treatment of additions and reductions, a number of economists have called for a return to the 1942 treatment--that is, an entry for depletion but not for additions. This position seems to have been based on at least three considerations, each of which is evaluated in the paragraphs that follow.

First, an entry for depletion will respond to at least part of the concern about the treatment of mineral resources in the traditional accounts. If the goal is to produce a measure of NDP that reflects the depletion of mineral resources in GDP, deduction of depletion to arrive at an alternative NDP will provide such a measure. Although it cannot be explicitly identified, as noted previously, the contribution of mineral resources is already included in GDP. Deduction of an estimate of depletion will give a partial measure of sustainability, one that indicates the using up of the existing stock of mineral resources.

What such a partial measure will not do is allow the detailed identification of the contribution of the mineral resource to income, production, consumption, or wealth, either in the aggregate or by sector. Nor will it provide a complete measure of sustainability. Without an entry for additions, deduction of depletion alone to calculate an alternative NDP may produce misleading signals regarding the sustainability of a nation's production and wealth. For example, with only depletion accounted for, a nation adding to its stock of reserves--through exploration and development and through improved recovery techniques--at a rate that more than offsets depletion would nonetheless have an alternative NDP lower than the traditional NDP. The lower NDP would suggest that the country was running down its resources and that the current level of production was at the expense of future production, despite the fact that reserves were actually increasing.

Second, estimates of the value of additions to the resource stocks are quite volatile, uncertain, and, at times, large. Volatility in resource prices, changes in mining technology, and uncertainty about the ultimate recoverability from existing reserves all affect the value of mineral reserves. It is not clear, however, that the volatility introduced by such estimates would be any larger than that already observed in investment, particularly inventory investment, the most volatile component of traditional accounts.

Third, probably the most important reason for the lack of enthusiasm for including additions to reserves as capital formation in GDP is that additions to reserves are so different from additions to capital stock. This difference, in combination with the volatility of additions to reserves, would limit the usefulness of accounts for conventional macroeconomic analysis. The inclusion of large additions to mineral resources in GDP, such as those associated with the North Slope in Alaska and the North Sea in Europe, are important additions to a nation's wealth and have a significant impact on economic activity, but the effect differs from that associated with investment in a new factory. Both add to wealth, but for the factors of production involved in building the factory, payments have been made, and the resources are available for current consumption. In contrast, much of the increase in wealth associated with adding proved reserves accrues to mining companies and landowners in the form of increases in land values and equity prices. To make these resources available for current consumption would require the "producers" of the mine or well to sell their product.

Many of the concerns about volatility and the different nature of additions to mineral reserves can be diffused by placing these values in a satellite account that allows integrated analysis of mineral resources outside the main accounts. This inclusion of natural resources in a satellite account allows researchers the flexibility to experiment without impairing the usefulness of the traditional accounts. In addition, within the IEESA's, the effect of volatility in mineral prices is largely confined to the revaluation account and has a limited effect on the estimates of current income, production, and consumption.

Fixed capital or inventory treatment.--Even when economic theorists have thought of natural resources as a type of capital, they have disagreed about whether the resources should be treated as fixed capital or as inventories.(3) This disagreement may seem a bit strange because proved mineral reserves seem to fit the classic characteristics of fixed capital: Expenditures of materials and labor are needed to produce a productive asset ("roundabout" production), which yields a stream of product over long periods of time. The rent to owners of fixed assets comprises the reduction in the value of the asset due to its use in the current period (depreciation) and a return equal to what the current value of the asset could earn if invested elsewhere. Inventories, on the other hand, are buffer stocks of inputs and final products that help to smooth production and avoid lost sales. As a rule, inventories are sold within a year or one accounting cycle. Although interest or holding costs are a consideration in determining inventory levels, they are much less important than for fixed capital.

Part of the rationale for treating mineral reserves as inventories may arise from the perception that they differ from fixed capital in that they are a set number of units waiting to be used up in production. However, like the output from a new machine, the number of units extracted from a new field or mine is quite uncertain and varies over time with the path of future demand, changes in technology, prices, costs, and returns on alternative investments. In addition, although a piece of machinery may not appear from the exterior to be used up in production, its parts or service life are most certainly "used up" in production; this "using up" is reflected in the decline in its value, or the depreciation on the equipment.

To emphasize the replaceability of proved reserves, some analysts have chosen to describe these reserves as inventories. This motive notwithstanding, treatment of mineral reserves symmetrically with fixed investment in structures and equipment would serve equally well as a reminder of the "reproducibility" of proved reserves in the IEESA's.

Proved reserves or total resources.--The amount of mineral resources that can be recovered, given current economic conditions, is not certain. Reserves are generally classified by the degree of certainty attached to the estimates. For example, proved petroleum reserves are estimated physical quantities that have been demonstrated by geologic and engineering data to be recoverable under current economic conditions and technology. Reserves whose recovery under current economic conditions is less certain are classified as either "probable" or "possible." Estimates are also available on the total amount of reserves that remain to be discovered--that is, of "undiscovered" reserves. There are a variety of perspectives on which of these measures of reserves should be used in accounting for minerals. Should the accounts be concerned only with "proved" reserves, or should they also account for "probable," "possible," or even "undiscovered" reserves?

Authors who have focused on proved reserves have tended to do so because of the large uncertainty associated with the other measures. As noted in the companion article, BEA ultimately intends to include unproved reserves as part of "nonproduced/environmental" assets, but the mineral reserve estimates presented here are restricted to proved reserves.

One means of dealing with the uncertainty in valuing unproved reserves may be the use of "option" values. Unproved reserves are clearly bought and sold, and the values or options that could be used in these transactions might be used to develop average option values to be used in valuing the entire stock of a nation's reserves. An operational methodology for making such estimates has not yet been identified.

Valuation issues

The absence of complete data on mineral resource prices has meant that the value and contribution of mineral resources to income, production, consumption, and wealth have usually had to be based on methodologies that produce proxy estimates of their market price. There are two elements to making such estimates. The first is separating the contribution of the resource in the ground--which is implicitly included in the price of a marketed mineral product--from that of other factors of production. The second is determining the appropriate per-unit value for estimating the value of the stock of the resource and the value of changes in the stock, including additions, depletion, and revaluations.

In addition, it is useful to identify several terms at the outset. First, "rent" refers to the concept of the return to factors of production after deduction of variable costs. More empirically, "gross rent" is simply gross revenues less expenditures on intermediate goods and employee compensation. (Rent in these situations is not to be confused with "rental income of persons" found in the national income and product accounts.) Second, "invested capital" refers to the structures and equipment in which the firm or industry has invested.

Identifying the return to the resource.--The price of a unit of the resource--for example, a barrel of oil--reflects, in addition to the cost of goods and services used in its production, a return to labor, a return to invested capital, and a return to the resource. The first step in identifying the value of a barrel in the ground is to determine the rent, in this case the rent to the resource and the capitalized value of investments in mining. In industries such as petroleum mining, good data are generally available on the variable costs, so arriving at gross rent is, at least conceptually, relatively simple. The next step is to determine the share of gross rent that accrues to the invested capital and the share that accrues to the resource.

In theory, the rent to owners of both the invested capital and the oil in the ground should equal the reduction in the value of each asset due to its use in the current period (depreciation and depletion, respectively) plus a return equal to what the current value of the well (the invested capital and the oil in the ground) could earn if invested elsewhere. The desirable way to measure the rent would be to observe market prices for these transactions; however, often there is no transaction, and the observable transactions that take place are often not representative of the full value of the oil. As a result, the various methods described in the next section use indirect techniques to estimate the market value of the return to invested capital, and they derive the return to the oil in the ground as a residual.

Valuing the resource stock and depletion.--Valuing the stock of a resource and valuing the decline in the stock's value associated with extraction are complicated because the extraction takes place over a long period of time. Unless the price, or value, of that resource rises enough to offset the income that could have been earned on alternative investments (including an inflation premium), resources extracted in the future will be worth less, in real terms, than those extracted today. In theory, the market value of the stock should be equal to the present discounted value of the future stream of rent from the stock, whereas depletion is the decline in the value of the stock associated with extraction in the current period. Translating the current per-unit rent of a resource into a per-unit value appropriate for valuing the stock and depletion requires information about the future path of extraction, prices, and interest rates. Unfortunately, such information is generally not available. In the absence of market prices, estimation of the current value of the resource requires either resort to economic theory, use of a set of explicit assumptions, or empirical estimation.

Empirical estimation of the factors required for computing the present discounted value of the resource is fraught with difficulties, in part because of the volatility of mineral markets. Simplistic assumptions do at least as well as econometric forecasts in tests of their predictive accuracy, and the assumptions are relatively easy to understand.

Alternative Methods of Valuing Mineral Resources

BEA has prepared estimates using four methods of valuing resource stocks and changes--depletion, additions, and revaluations--in the stocks.(4) These methods rely on estimates of three variables: (1) The normal return to invested capital, based on some average rate of return to all investment in the economy; (2) the return to capital based on the market value of the capital stock in the oil industry; and (3) the per-unit capital cost of additions to the stock of proved reserves. The use of these variables as described in the following paragraphs represents BEA's assessment of the best estimates given existing source data and frameworks. The accompanying box provides an algebraic description of the methods.

Current rent estimates

The simplest assumption that can be used is based on Harold Hotelling's observation that in equilibrium, the price of the marginal unit of a nonrenewable natural resource net of extraction costs (the current per-unit rent to the resource) should increase over time at a rate equal to the nominal rate of interest.(5) At any rate of increase in the per-unit rent above (below) the rate of return on alternative investments, entry (exit) and increases (decreases) in the rate of extraction will combine to reestablish the equilibrium rate of increase in the resource rent. If this observation holds, the value of the stock of the resource is independent of when it is extracted and is equal to the current per-unit rent to the resource times the number of units of the resource.(6)

The following two methods assume that over time the rent per unit will increase at the rate of interest; they simply use the current per-unit rent to value the resource and depletion.

The first method, current rent method I, utilizes an estimate of a normal, or average, rate of return to investment to estimate the rent to the associated capital invested in the mining industry and then derives the resource rent as a residual. This method applies this average, economywide rate of return to investment to an estimate of the replacement cost, or market value, of the net stock of associated capital invested in mining and then adds depreciation to estimate a "normal" rent to invested capital. The rate of return used is 6 percent, approximately the 45-year average real rate of return to investment in corporate bonds and equities for the period ending in 1991, which is an estimate of the rate of return available on alternative investments. The steps in estimating the rent to and value of the resource are as follows: 1. Gross rent is calculated as total revenue less

current operating expenditures. (Current

operating expenditures are those associated

with bringing the mineral from the deposit

to the wellhead or mine gate.) 2. The resource rent is obtained by subtracting

the rent to capital (both depreciation and a

normal rate of return for capital) from the

gross rent. 3. The per-unit rent to the resource equals the

resource rent divided by the physical quantity

extracted. 4. The value of the resource equals the per-unit

rent times the physical quantity of reserves.

Additions and depletion are valued at rent

per unit times the physical quantities of

added and extracted reserves. 5. Revaluations--the effect of price changes-are

computed as a residual: The value of the

resource at the end of the current year less

its value at the end of the preceding year,

plus depletion during the year, less additions

during the year.

The advantage of this method is that it is relatively straightforward and requires few assumptions. The main disadvantage is that an explicit assumption must be made regarding the appropriate rate of return. In addition to the conceptual and empirical problems in identifying an appropriate rate, prespecification of a rate does not allow for relatively low or high rates of return in the mining industry due to conditions specific to the industry.

An alternative method, current rent method II, derives resource rent by removing the market value of capital, both physical and capitalized expenditures, from the value of the resource reserve. The steps to deriving the per-unit rent are as follows: 1. Gross rent per unit is derived by dividing

gross rent by the physical quantity of

extraction. 2. The total value of the mineral reserve (the

resource and the associated invested capital)

equals the gross rent per unit times the

quantity of reserves. 3. The value of the resource equals the total

value of reserves less the current replacement

value of the net stock of invested capital. 4. Resource rent per unit equals the value of the

resource divided by the quantity of reserves.

The advantage of this method is that it does not require an explicit assumption about the return to invested capital associated with the resource.

Present discounted value estimates

If it is assumed that rent to the resource does not rise enough to compensate the owners of the resource for the nominal interest they could earn on alternative investments, then the stream of future rents must be discounted by the difference between the rate of increase in resource rent and the nominal interest rate. As noted previously, with discounting, identical dollar values during different time periods have different present values, so valuation by present discounted values requires--in addition to an assumed discount rate--a number of assumptions about the stream of future rents.

In BEA's implementation of this method, three simplifying assumptions were made so that each cohort of additions to reserves did not have to be tracked separately throughout its economic life. First, extraction resulting from additions to proved reserves was assumed to be constant in each year of a field's life, and depletions were assumed to result equally from all cohorts still in the stock. Second, new reserves were assumed to be extracted at constant rates over the same time-frame used for depreciating wells and mines in the NIPA's: 16 years until 1972 and 12 years thereafter. Finally, extractions were assumed to occur at midyear and were valued using the per-unit rents described for current rent method II.

Two real rates of discount--3 percent and 10 percent--were chosen to illustrate the effects of a broad range of rates on the values of additions, depletion, and stocks of reserves. Thus, the relatively high and relatively low rates chosen encompass many of the alternatives that have been used in discounting.(7) The 3-percent discount rate has often been used to approximate the rate of time preference. The 10-percent rate has often been used to approximate the long-term real rate of return to business investment.

The steps for estimating the present discounted value estimate of the resource rent per unit are as follows: 1. A discount factor was derived using an estimate

of the real rate of discount--the

nominal interest rate less the rate of increase

in the resource rent--and the NIPA estimates

of the lifespans of mineshafts and wells. 2. The rent per unit equals the discount factor

times the gross rent per unit derived

from the current rent method that is based

on the value of capital stock in the mineral

industry.(8)

Replacement-cost estimates

The replacement-cost method subtracts from gross rent the cost per unit of adding new reserves, thereby identifying the resource rent as a residual. It uses the per-unit cost of proving new reserves to represent invested capital's share of the gross rent. The value of a unit of resource in the ground is estimated; the cost to replace it by investment is subtracted from that in-ground value, and the residual is the resource rent. This method uses current rates of extraction to estimate future production and uses an assumed discount rate of 6 percent.9 Because of the lack of production cost data, transactions data for the sale of reserves, and techniques to estimate those market values for all other minerals, the replacement-cost method is used only for oil and gas. The steps for deriving the per-unit resource rent are as follows:

1. The barrel factor-which is used to calculate

the value of a barrel of oil in the ground--is

equal to the depletion rate of the reserves

divided by the sum of the real discount rate

and the depletion rate.(10)

2. The per-unit resource rent is calculated by

multiplying the gross rent per unit by the

barrel factor and subtracting the per-unit

exploration and development cost.

Transactions-price estimates

When oil and gas firms seek to replace the reserves that have been depleted as a result of their production, they face a "make or buy" decision. They can either make new reserves by financing exploration and development efforts, or they can buy reserves that have already been proved by others. This article refers to the purchase price of proved reserves as a "transactions price" because it represents a price that was paid in an actual transaction. The costs of acquiring new reserves by financing exploration and development efforts are termed "finding costs." In equilibrium, and ignoring the different tax treatment of purchasing and drilling for oil, the finding costs should be equal to the transactions price.

If available, transactions prices are ideal for valuing reserves. As it turns out, such transactions are relatively infrequent because companies generally develop their own reserves. As a result, the few transactions that occur are not easily generalized for estimating the total value of reserves.

The estimates of resource values for off and natural gas presented here are derived from transactions prices constructed from publicly available data on the activities of large energy-producing firms. The derivation of per-unit resource rent is as follows:

1. The per-unit gross rent for the resource and

its associated invested capital is obtained by

dividing aggregate expenditures for the purchase

of the rights to proved reserves by the

quantity of purchased reserves.

2. The per-unit resource rent equals the per-unit

gross rent less the per-unit net stock of

associated capital invested in the oil and gas

industry.

Estimates for Mineral Resources

The value of resource reserves and changes in reserves were estimated for the period 1958-91 for major mineral resources using the four valuation methods just discussed.(11) The minerals valued include the fuels (petroleum, natural gas, coal, and uranium), the metals (iron ore, copper, lead, zinc, gold, silver, and molybdenum), and other minerals (phosphate rock, sulfur, boron, diatomite, gypsum, and potash). Petroleum and gas account for the lion's share of mineral production. The other minerals were selected because, of the minerals that have scarcity value, their value of production was relatively high.

The picture that emerges from the various estimates of the value of U.S. mineral stocks is broadly similar, regardless of which methodology is used:

* The value of additions has tended to exceed

depletions; since 1958, the value of the stocks

of proved mineral reserves in the aggregate

has grown in current dollars, while showing

little change in constant (1987) dollars

(charts 1 and 2 and table A).

[TABULAR DATA A 1-4 OMITTED]

* Changes in the stocks of these productive assets

over time have largely reflected changes

in their resource rents. Increases in resource

rents have been accompanied by greater

investment in exploration and enhanced recovery

technology, and decreases in rents for

some resources have been accompanied by

reduced exploration activity and the closing

of marginal fields and mines.

* Proved mineral reserves constitute a significant

share of the economy's stock of

productive resources. Addition of the value

of the stock of these mineral resources to

the value of structures, equipment, and inventories

for 1991 would raise the total by

$471-$916 billion, or 3-7 percent, depending

on the valuation method used.

* The stocks of proved mineral resources are

worth much more than the stocks of invested

structures and equipment associated with the

resources. In 1991, the value of the stock of

subsoil assets was 2 to 4 times as large as

the value of the associated stock of invested

structures and equipment and inventories.

* Valuing the effect of depletion and additions,

as well as including the value of resource

stocks, provides a significantly different picture

of returns. Compared with rates of

return calculated using income and capital

stock as measured in the existing accounts,

the IEESA-based average rates of return on

capital in the mining industry for 1958-91 are

lower--4-5 percent rather than 23 percent

(table B). Rates of return for all private capital

slip from 16 percent using measures in

the existing accounts to 14-15 percent using

IEESA measures for the mining industries. Table B.-Alternative Rates of Return, Averages for 1958-91 [Percent] IEESA based NIPA Current I Current II PDV 3% rate PDV 10% rate based Mining industries 23.1 5.2 3.5 4.0 5.0 Total private capital 16.1 14.9 14.1 14.4 14.8

NOTE.-In general, rates of return are some measure of income divided by some measure of capital stock. For the Nipa-based estimates, income is defined as property-type income (profits, rents, net interest plus indirect business taxes), and capital stock is defined as structures, equipment, and inventories. In the alternative IEESA methods, income is also defined as property-type income, but depletion is subtracted from profits, and the value of additions is added; IEESA capital stock is defined as structures, equipment, and inventories plus the value of mineral resources.

PDV Present discounted value

* Although the trends that emerge from the

alternative methods are similar, the range

of estimates is large. The highest estimates

of stocks, depletion, and additions were obtained

from the current rent estimates based

on capital stock values, and the lowest were

from the current rent estimates based on

average rates of return to capital.

The stock of proved reserves increased from 103-$182 billion in 1958 to $471-$916 billion in 1991. In constant dollars, the stock rose somewhat and then fell, but over the period showed little change: From 544-$1,077 billion in 1958, the real stock slipped only slightly to 530-$I,030 billion in 1991. The patterns vary by type of mineral and reflect the effects of prices and costs of production, the volatility in international minerals prices, increasing environmental regulation, and the effect of strikes and other factors specific to each industry.

For petroleum, despite periodic concerns that the United States was running out of oil, additions have offset depletion throughout the period as oil companies have responded to higher net returns by stepping up exploration and improved recovery techniques to produce stocks of proved reserves sufficient to meet current and intermediate-term needs in light of current prices, costs, and interest rates. The one spike in the constant-dollar oil and gas series was in 1970, the year of the Alaskan oil strike.

For coal, additions have exceeded depletions, resulting in a generally rising constant-dollar value of stocks over time. For other minerals, the stock patterns have varied, with declining stocks in metals reflecting large declines in the returns to metals.

The 1991 stock of mineral reserves would add 3-7 percent to the 1991 value of reproducible tangible wealth Of $13,637 billion, of which private nonresidential structures and equipment were $5,440 billion. Over time, the mineral reserves share of an expanded estimate of national wealth has fallen; in 1958, mineral reserves would have added 9-17 percent to reproducible tangible wealth. This decline appears to reflect several factors, including the economy's increased reliance on foreign resources and the increased efficiency in the use of fuels and other minerals.

Although industry makes large investments in exploring and developing mineral resources, the value of the invested capital associated with oil-fields and mines is small relative to the value of the mineral reserves themselves. In 1991, the value of subsoil assets was 2-4 times as large as the associated capital invested in mining. Addition of these stocks of productive natural assets provides a more comprehensive picture of both the assets and the returns in the mineral industries.

Treatment of natural resources symmetrically with investments in equipment and structures provides a very different picture of rates of return to mining. Rates of return in the mineral industries calculated using income and capital stock as measured in the existing accounts--specifically, by dividing property--type income by the replacement value of structures, equipment, and inventories--averaged 23.1 percent for 1958-91. The more complete IEESA estimate deducts depletion and adds additions to property-type income, and it adds the value of resource stocks to the value of structures, equipment, and inventories. Depending on the valuation method used, the IEESA rate of return would be 3.5-5.2 percent. The effects of including mining resources are so large that the rate of return to all private capital is reduced from i6.1 percent to 14.1-14.9 percent. These IEESA rates of return provide a significantly different picture of the social rate of return to investments in the mining industries and the sustainability of the industries' output.(12)

As noted, the highest estimates of resource reserves are from the current rent method based on the value of capital stock invested in the industry.(13) The value of subsoil assets using this method was $916 billion in 1991. The lowest value in 1991, $471 billion, was obtained from the current rent method based on a normal return to invested capital. The present discounted value estimates fell somewhere in between--$638-$812 billion.

The replacement-cost and transactions-price estimates were computed only for oil and gas. The transactions-price estimates, despite considerable smoothing, were quite volatile and erratic. The replacement-cost estimates produced the lowest values among all the estimates for gas. The transactions-price estimates produced the lowest values for oil.

For some of the subsoil asset estimates, especially those employing the current rent method based on a normal return to invested capital, the resource stock values and stock changes are quite low. In certain industries, especially the metals industries, the estimates were negative (indicated with an asterisk in the tables). These negative values indicate that the gross rents in these industries are so low that any procedure that assumes a normal return to capital in that industry must attribute a negative residual rent to the resource if total factor returns are to add up to market output. One can imagine an alternative procedure that assumes a normal return plus a depletion allowance and derives a negative residual for the invested capital associated with the resource.

APPENDIX: Data Sources and Methods

Current-dollar Estimates

Petroleum and natural gas

Prices and quantities.--The basic commodity prices used are the average wellhead prices for oil and gas from the American Petroleum Institute (API). The wellhead price for gas includes rents attributable to natural gas liquids (NGL) that, depending on market conditions, may be separated downstream. Oil production quantities are from API and the Department of Energy (DOE) and include both crude production and lease condensate production, both in millions of barrels. Natural gas production is marketed production from API and DOE. Marketed production has not yet undergone the extraction Of NGL. Total revenue for oil and gas production is calculated as price times quantity produced.

Reserve estimates are from API and DOE for crude oil and dry gas. The reserve volumes for oil and gas were augmented for reserves Of NGL, which are reported separately. Additions were set equal to additions from DOE and API plus any residual change in stocks not accounted for by reported flows. The residual arises out of discontinuities in the estimates caused by the different reserve estimation methods used over the last 40 years.

The basic commodity price data used are yearly average prices. The large fluctuation in commodity prices, however, makes them unstable and thus unsuitable for estimating the average or expected returns that investors presumably have in mind in determining the appropriate price for long-lived assets such as mineral reserves. In order to smooth the estimates, a 3-year lagged average of the yearly average prices is used as the midyear market price.

Costs.--Data on current production expenditures and ad valorem and windfall profits taxes are from API's Survey of Oil and Gas Expenditures (SOGE) and, for 1972-81, the Census Bureau's Annual Survey of Oil and Gas (ASOG). "Finding costs" are obtained as a 3-year moving average of development expenditures per unit of reserve added; the source data are from the SOGE and the ASOG. For years not covered by the SOGE, estimates of costs were interpolated using an indicator series.

Capital stock.--The capital stock, depreciation, and investment estimates are from BEA. BEA defines investment and capital for mining industries differently from standard industry practice. BEA investment includes capital equipment, structures, and all exploration and development expenditures, even those expenditures that are treated as current expenses by operators. NIPA capital and investment estimates are available as an aggregate for oil and gas extraction (Sic 13). The portion of capital for four-digit sic industry 1321, natural gas liquids, was removed from this series, as this capital is not used in the extraction of oil or gas. Rather, natural gas liquids, a small piece of sic 13, is a downstream process. The capital stock of the other four-digit components of SIC is considered a part of the capital required for the extraction of oil and gas; for example, off and gas field exploration services, sic industry 1382, is used as inputs for oil and gas extraction.

The NIPA investment series for oil and gas extraction from 1959-91 was desegregated into oil extraction and gas extraction using the ratio of expenditures for successful oil wells drilled to expenditures for successful gas wells drilled. For 1947-58, expenditure ratios for on wells and gas wells were estimated using the number of successful off wells and gas wells drilled. These two investment series were then used to generate current- and constant-dollar capital stock and depreciation estimates for oil extraction and for gas extraction.

Other minerals

Inconsistencies in data and a paucity of data for nonbenchmark years present substantial difficulties in making estimates for other minerals. The data that do exist are often classified incongruendy, or the definitions for series change over time. For example, Census Bureau data--which are the only comprehensive data available on production, costs, and revenues--are on an sic basis; BEA data on capital stocks are on an sic basis but at a more aggregate level than the Census data; and Bureau of Mines and DOE data on reserves, production quantities, and prices are on a commodity basis.

Prices and quantities.--For most minerals, the basic commodity prices used are 3-year lagged averages of the value of production divided by the quantity produced for metals and other minerals from the Bureau of Mines or DOE. For other minerals, a combination of available data on prices, quantities produced, or value of production is used to derive missing data on prices or value of production. Total revenue from current production is equal to the average price times the quantity produced.

Changing definitions for mineral reserve quantities present significant problems for the construction of consistent time series for mineral reserves. Prior to 1978, reserves were defined by the Bureau of Mines as economic reserves, both demonstrated and inferred; between 1979 and 1986, reserve base was the preferred definition, and this comprised demonstrated (but not inferred) economic reserves, marginal economic reserves, and part of subeconomic reserves; since 1987, only demonstrated economic reserves are included in the definition of reserves. Only the last definition is roughly consistent with proved reserves in oil and gas. The published estimates showed such large year-to-year changes--even within subperiods in which reserve definitions were unchanged--that BEA has attempted to develop a consistent, or at least smoothed, time series for these minerals. The BEA series use a weighted average that is based on a constant output-to-reserve ratio and on a judgmentally scaled moving average of published reserves. (Uranium reserves are based on a different method that splices DOE'S forward-cost categories to construct a consistent time series.)

Costs.--Consistent data on production expenditures-current variable costs of extraction, including purchased services--were derived from the Census Bureau's minerals industries data and from BEA'S benchmark input-output data.

Capital stock.--For census years between 1958 and 1991, data on investment in plant, equipment, and exploration and development were derived from the Census Bureau's Census of Mineral Industries. These investment data were then used to construct industry-specific capital stock estimates for mineral industries at a level of detail greater than that at which BEA normally produces estimates.

Constant-Dollar Estimates

Constant-dollar estimates for petroleum, natural gas, and other minerals use i987 as the base year. The base-year estimate for resource rent was used to calculate constant-dollar series for the following methods: Current rent, present discounted value, and, for a shorter period, transactions price. For each method, the 1987 per-unit resource rent for the value of depletion was multiplied by the physical volume of depletion and additions to derive the value of depletion and additions, respectively. The constant-dollar value of the resource stock is the product of the 1987 per-unit resource rent and the end-of-year volume of reserves.

Tables 1.1 through 5.4 follow.

Algebraic Description of the Alternative Methods of Valuing Mineral Resources

Current rent method I (Based on average return to capital): GR = TR - COE RR = GR - (rNS + DEP)

[delta]r = RR/QE

VR = [delta]r (QRES)

DEPL = [delta]r (QE)

VA = [delta]r (QADD)

REVAL = VA (t) - VA (t - 1) + DEPL - VA Current rent method II (Based on value of capital stock): [delta]GR = GR/QE V = [delta]R(QRES) VR = V - NS

[delta]r = VR/QRES Net present discounted value: (*)

[Mathematical Expression Omitted] Replacement cost: (*)

bf = [(QE/QRES)/((QE/QRES)+r)]

[delta]r] = bf[(TR-COE)/Q]-($ADD/Q) Transaction price: (*)

[delta]GR = (TV/TQ)

[delta]r = [delta]GR - (NS/QRES)

Definitions.

Aggregate value measures:

TR = total revenue

CO = other extraction expenses, including compensation of employees, materials consumed, and overhead cost allocated to current production

GR = gross rent

RR = resource rent

NS = net stock of capital valued at current replacement cost

TV = value of purchased reserves during the year

V = value of the proved reserves (resource and fixed capital values)

VR = value of the resource stock

VA = value of the annual additions

DEP = depreciation DEPL = value of the annual depletions REVAL = the effect of price changes on the value of the stock $ADD = the annual exploration and development expenditures for drilling oil and gas wells in fields of proven reserves (including overhead costs allocated to development)

[phi] = Net discounted present value factor

Quantity measures:

QE = quantity of the resource extracted during the year QRES = stock of reserves QADD = Quantity of resources added to reserves during the year

(through new discoveries, extensions of existing sites, or

revisions in estimated reserves)

TQ = quantity of proved reserves purchased during the year

Per unit measures: [delta]GR = gross rent per unit (GR/Q) [delta]r = resource rent per unit

Rates and other items: r = real rate of interest, or discount rate N = Life span of a resource (e.g., well or mine), R / Q j = current year T = life of asset (NIPA convention) a = reserve decline rate, Q/R bf = barrel factor (*) DEPL, VA, REVAL for all methods are computed using the same formulas as presented for current rent method I. (1.) Business accounting has also long debated issues in accounting for minerals; further, there was a resurgence in interest after the "energy crisis" in the mid-1970's. Since then, the Financial Accounting Standards Board has issued five new standards to improve accounting for mineral resources. (2.) See, for example, Gavin Wright [35] and Michael J. Roskin, Marc S. Robinson, Terrance O'Reilly, and Praveen Kumar [4]. (3.) Part of the debate over the treatment of minerals as inventories or as fixed capital may reflect the view that depletion should be counted as a reduction in the highly visible measure, rather than in the less well known NDP. If natural resources are treated like fixed capital, the depletion of the resources in the production process would be treated like depreciation. Because NDP is defined as GDP less depreciation, with this treatment any depletion charge would affect NDP not GDP (as noted earlier, conventional GDP implicitly includes depletion). On the other hand, the change in business inventories is a component of both GDP and NDP. Consequently, some have argued that if depletion were viewed as a net decline in inventories, it would result in a subtraction from both GDP and NDP. (4.) Among the methods that have not been used is one suggested by Salah El Serafy. The approach essentially calculates the amount that must be invested in a "sinking fund" to create an income stream sufficient to replace that produced by the natural resource, The approach, although frequently mentioned in the resource accounting literature, is not included largely because it is inconsistent with the concepts embodied in traditional national accounts and the IEESA's. In traditional accounts, the value of an asset is determined by its market price, or proxy thereof. El Serafy's approach, a welfare-oriented measure, is not intended to estimate the market value of the mineral resource. (5.) In other words, the real price of the resource should increase at the real rate of interest, and there is no need for discounting. (6.) As discussed later, it may be true that over long periods, the rent per unit for mineral resources--like most tangible assets held for investment purposes--will rise at a rate equal to the nominal discount rate; however, periods of disequilibrium may be quite long. Nevertheless, given the problems in forecasting volatile minerals prices, technology, etc., this simple assumption may yield results as good as or better than other methods. (7.) Although these real rates--3 percent and 10 percent--are often used to discount future returns, both are probably high for an appreciating tangible asset for a number of reasons: (i) Mineral prices do rise, at least partly, if not fully offsetting the effect of discounting; (2) as Many authors have argued, decisions with intergenerational effects should be valued at lower discount rates than other transactions; and (3) a real rate of 10 percent, which is often cited and has been used by the Office of Management and Budget as an estimate of the real rate of return to private capital, is biased upwards. The 10-percent return is based on estimates of the before-tax return to reproducible capital, which is computed as all property-type income divided by the replacement-cost value of reproducible assets. Some authors have attempted to adjust the return to reflect the fact that property-type income is a return to land and other factors as well as to the reproducible capital; nevertheless, to the extent that these other factors are excluded from the denominator, the computed return to capital is too high. (8.) Because of the simplifying assumptions used, somewhat different discount-extraction factors are applied to stocks and flows; for most years, the difference are very small. (9.) The method outlined here is based on the approach used by M.A. Adelman, which has been modified to estimate the resource rent and hence the depletion and the value of oil and gas resources. (10) Note that if the resource appreciates at a rate equal to the nominal interest rate, the real discount rate (nominal rate less the increase in prices) is zero, and the barrel factor has a value of one; in this case, the current rent is used to value reserves and depletion. (11.) The transactions-price and replacement-cost methods are used for the period 1947-91 and only for oil and gas. (12) Given the effect of tax laws, transfer pricing, and excluded assets, Comparison of rates of return across methods is difficult at best. Many of the mining industries have relatively little invested capital fixed or inventory) associated with the resources, and hence the computed returns to reproducible capital are overstated relative to those that mining companies, which do count the value of property, have on their books. (13) Over the period of this analysis, the current rent per unit for all the resources increased at an annual rate of 4-8 percent. Based on a real time

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