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Improved Estimates of Fixed Reproducible Tangible Wealth, 1929–95

By Arnold J. Katz and Shelby W. Herman

This article presents revised estimates of the value of fixed reproducible tangible wealth in the United States for 1929–95; these estimates incorporate the definitional and statistical improvements introduced in last year's comprehensive revision of the national income and product accounts (NIPA's)./1/ The most important of these improvements in the wealth estimates, which cover the stock of privately owned and government-owned equipment and structures and durable goods owned by consumers, is the use of an improved methodology for calculating depreciation.

The improved methodology uses empirical evidence on prices of used equipment and structures in resale markets, which have shown that depreciation for most types of assets approximates a geometric pattern. Previously, the depreciation estimates were derived using straight-line depreciation and assumed patterns of retirements./2/ For equipment, the new depreciation rates are faster than the old ones in the early years of an asset's life and slower in the later years. For structures, the new rates are slower throughout an asset's life. As a result, the revisions to depreciation and to the net stocks of equipment are relatively small, and the revisions to depreciation and to the net stocks of structures are relatively large; depreciation is lower and net stocks are higher.

The first section of the article describes the methodology for estimating net stocks and depreciation and provides a table of the new depreciation rates and services lives by type of asset. The second section discusses the effects of the new methodology for depreciation and other improvements to the estimates of net stock. Summary tables of revised estimates of reproducible tangible wealth are presented at the end of the article.

The improved depreciation estimates presented in this article also are incorporated into the revised NIPA estimates of consumption of fixed capital and related series beginning with 1929 that appear elsewhere in this issue of the SURVEY. However, there are two fundamental differences between the two series. First, government consumption of fixed capital in the NIPA's differs from depreciation of fixed tangible reproducible wealth owned by government, because NIPA depreciation does not include the adjustments made to general government capital for natural disasters and war losses. Second, depreciation on purchases of durable goods by consumers are not recorded in the NIPA's, because such purchases are treated as consumption, not as investment.

A complete set of BEA wealth estimates for the years through 1994 will be available in Fixed Reproducible Tangible Wealth in the United States, 1925–94, which will be published later this year. (See the box "Availability of Data.") This publication will present annual estimates of net stocks and depreciation in historical-cost, real-cost, and current-cost valuations for the types of assets shown in tables 1–15 in this article, for private assets by industry and legal form of organization, and for government assets by type of equipment and structures; it will also provide the average age of net stocks, the investment data used to derive the wealth estimates, and a detailed statement of the methodology underlying the estimates.

Methodology for Net Stocks and Depreciation

The primary measure of the value of fixed reproducible tangible wealth is the net stock, that is, the value of the stock adjusted for depreciation. Depreciation is the decline in value due to wear and tear, obsolescence, accidental damage, and aging. For business and government, in addition to its use in calculating net stocks, the same depreciation—consumption of fixed capital—is presented as part of the NIPA's./3/ Consumption of fixed capital is a charge for the using up of fixed capital, and as such, it is, along with compensation of employees and other components of gross domestic income and gross national income, one of the costs incurred and the profits earned in the production of gross domestic product (GDP) and gross national product (GNP). Consumption of fixed capital is deducted from GDP and GNP to derive net domestic product and net national product. In addition, government consumption of fixed capital is a component of government consumption expenditures (and GDP) as a measure of the value of the services of government fixed assets./4/

The net stock estimates in this article are presented in terms of two valuations—current cost and real cost. Current-cost (or "replacement-cost") valuation expresses all assets in the net stock in terms of the prices that prevailed in the period to which the stock estimates refer. For example, the yearend 1995 net stock estimate in current-cost valuation shows the assets that were in the stock at yearend 1995 expressed at the market prices prevailing for those assets at yearend 1995./5/ The real-cost estimates are expressed either as quantity indexes or in "real" dollars, with 1992 as the base period.

Overview of methodology

Estimates of net stock and depreciation—under both the new and old methodologies—are derived using the perpetual inventory method, which is based on the accumulation of investment flows./6/ With this method, both the net stock and depreciation of any given type of asset is a weighted average of past investment in that asset. Specifically, the net stock is calculated as the cumulative value of past gross investment less the cumulative value of past depreciation. The initial calculations are performed in real terms; current-dollar values are estimated by reflation.

Calculations of net stocks and depreciation are based on real investment data at the type-of-asset level of detail, which generally is the same level of detail as that presented in NIPA tables 5.7, 5.9, and 5.15, and real consumer purchases of durable goods, which generally is the same level of detail presented in NIPA table 2.7. At this detailed level, real investment in a given type of asset is obtained by dividing current-dollar investment in that type by the price index for new assets of that type, expressed as 1992=100, multiplied by 100. (Real investment for higher levels of detail shown in the NIPA tables is calculated using BEA's chain-type annual-weighted indexes.)

Under the new methodology, most assets are assumed to have depreciation patterns that decline geometrically over time. For a given year, the depreciation charges on existing assets are obtained by multiplying the prior year's charge by one minus the annual depreciation rate./7/ For each type of asset, depreciation is cumulated over all vintages, and net stocks are estimated by subtracting cumulative depreciation from cumulative gross investment.

As is the case for real investment, year-to-year growth rates for both depreciation and net stocks on a real-cost basis for higher level aggregates are then computed using the annual-weighted Fisher index. These rates are chained together to obtain cumulative growth rates, which in turn are used to obtain estimates of levels expressed as indexes (1992=100) and as chained (1992) dollars./8/

Current-cost estimates (in dollars) are obtained by "reflating" real estimates at the type-of-asset level. Depreciation is reflated to current cost using indexes that reflect average prices of new assets for the year; net stock is reflated to current cost using indexes of prices of new assets for the current yearend. Current-cost aggregates are obtained by directly summing current-cost estimates for the various types of assets. Finally, estimates by type of asset are adjusted for the net value of assets destroyed in wars and natural disasters.

Investment flows

The investment flows in new equipment and structures by type and the transfers of used assets used to implement the perpetual inventory method come from the revised NIPA's. For privately owned assets, investment by type of asset is distributed by industry and by legal form of organization, primarily through the use of data from BEA's benchmark input-output accounts for 1982 and 1987 and from the 1987 and 1992 Economic Censuses. These flows are modified to account for transfers of used assets between sectors of the economy. (Because of the lack of information, transfers of used assets within sectors are not accounted for in the wealth estimates.)

Depreciation patterns and depreciation profiles

In the perpetual inventory method, the pattern of depreciation charges for a given asset is determined by its "depreciation profile." The new methodology for estimating depreciation uses depreciation profiles that reflect a geometric pattern and that replace the previously used profiles, which were based on straight-line depreciation and on assumed patterns of retirements./9/ The depreciation profile for a given type of asset describes the pattern of how, in the absence of inflation, the price of an asset of that type declines as it ages. Although the profile for a given type of asset is assumed to be constant over time, different vintages of a given type of asset may have profiles that differ from those of other vintages of the same type of asset.

The new net stock and depreciation methodology uses depreciation profiles that are based on empirical evidence on used asset prices. Ideally, the profiles for each type of asset should be estimated using prices for used assets in resale markets, but such studies have only been conducted for some types of assets. However, the available studies suggest that, in general, depreciation profiles are more closely approximated by a geometric pattern of price declines than by a straight-line pattern. Consequently, in the revised estimates, the depreciation profiles for most assets were assumed to be strictly geometric, and the appropriate rate of declining-balance depreciation was taken from empirical studies of similar classes of assets. The depreciation rates for specific types of assets were then determined by dividing the appropriate declining-balance rate for each asset by the asset's assumed service life. For autos and for computers and computer peripheral equipment, two classes of assets for which information on used asset prices makes it possible to estimate the underlying depreciation profiles, the actual empirical profiles were used. For computers and peripheral equipment, the profiles were taken from studies by Stephen Oliner./10/ For missiles and nuclear fuel rods, depreciation was estimated using a straight-line pattern and a Winfrey retirement pattern, which is essentially a bell-shaped curve.

The new geometric depreciation rates and the associated declining-balance depreciation rates and service lives used by BEA to derive the new estimates of net stocks and depreciation are shown in table A. Except as previously noted, BEA's depreciation rate equals the declining-balance rate divided by the service life. The rate of declining-balance depreciation is the multiple of the comparable straight-line rate used to calculate the geometric rate of depreciation. For example, a 1.65 declining-balance depreciation rate refers to a geometric rate of depreciation of 1.65/L, where L is the service life of the asset in years and 1/L is the straight-line rate. Separate service lives are used for each type of asset and for the estimates of fixed private capital; separate service lives are also used in different industries for certain types of assets. Most of the service lives are held constant over time because the information necessary to estimate changes in them is not available. The lives themselves are based on a wide variety of sources and for most types of assets, are the same as those used for the previously published estimates./11/

Comparison With the Previous Methodology

The new methodology for net stocks and depreciation differs from the previous one in several important respects. As noted earlier, depreciation patterns had previously been assumed to follow a straight-line pattern with service lives distributed about the mean of assumed retirement patterns. Destruction of government assets in wars and natural disasters has been accounted for differently. In addition, estimates of gross stocks of fixed capital are no longer prepared, and aggregate series are now prepared using BEA's newly featured chain-type annual-weighted indexes rather than fixed-weighted (Laspeyres) indexes.

The remainder of this section provides additional information on these changes in methodology and describes the revisions to net stocks of private and government assets.

Depreciation profiles

Previously, all assets were assumed to have depreciation profiles that declined to zero in a straight-line manner. However, all assets of a given type were not assumed to have the same life. Instead, each vintage of a given type of asset was divided into several dozen cohorts, each of which was assumed to have a different service life. These lives were assumed to be distributed about the mean according to one of several Winfrey retirement patterns. Consequently, the net stock of an entire vintage of assets of a given type declined over time in a manner that was somewhat more accelerated than that given by the simple straight-line pattern.

The differences between the typical depreciation profiles used in the previous and new methodologies are illustrated in charts 1 and 2. The comparison is made for a typical type of equipment in chart 1 and for a typical type of structure in chart 2; both charts are for an entire vintage of investment in these types. In chart 1, the equipment is assumed to have a mean service life of 15 years. (All three of the depreciation profiles shown on the chart assume this mean life, though the profile for strict straight-line depreciation would be appropriate only if all assets in the vintage had a 15-year life.) Because of the use of the Winfrey pattern, the depreciation profile in the previous methodology is seen to be slightly more accelerated than the curve for strict straight-line depreciation (that is, below it) except in the last few years of the asset's life. A depreciation profile is also shown on chart 1 for 1.65 declining-balance depreciation, a declining-balance rate that is used for many types of equipment in the new methodology. In the first 10 years of the profile, this depreciation profile is more accelerated than the one in the previous methodology. In later years, the profile in the new methodology yields higher values of the vintage.

For structures, the differences between the previous and new depreciation profiles are substantial in all years. Chart 2 illustrates the aggregate depreciation profile for a vintage of structures that has an average service life of 36 years and that in the new methodology is depreciated using a 0.9 declining-balance depreciation rate. With the previous methodology, 56 years after the initial investment, the entire vintage has been fully depreciated and has a value of zero. With the new methodology, after 56 years, the vintage retains 25 percent of its initial value, and after 112 years, it retains more than 5 percent of its initial value. Thus, for example, nearly all the office buildings that were constructed in 1887 have been torn down or otherwise destroyed (their average service life is 36 years), but the new depreciation pattern assumes that about 6 percent of the initial value of all such construction is still in the net stock. However, the effect of this assumption is minimal: Because of the substantial growth in investment in office buildings, the value of this vintage of construction constitutes less than 0.01 percent of the total value of the current net stock of office buildings.

Gross stock estimates

The previous methodology used to calculate net stocks and depreciation allowed BEA to prepare two other "wealth" measures—gross stocks and discards. Gross stocks are the cumulative value, not adjusted for depreciation, of past investment still in existence—that is, the value of past investments less the cumulative value of investment that has been discarded or retired. The estimation of gross stocks and discards requires a methodology that assigns a specific service life to each of the assets distributed around the mean service life used by BEA. The new methodology uses a depreciation profile that is applied to all investment in a given cohort, and thus consistent data are not available on discards for each of the discrete service lives for investment within the cohort. As a result, BEA is no longer producing estimates of gross stock and discards.

Destruction of assets

In the new net stock estimates, the value of assets in the general government sector is written down to reflect the destruction of military assets during wars. (As previously noted, these write-downs are included in depreciation in the wealth estimates but excluded from the consumption of fixed capital in the NIPA's in order to avoid increasing the value of the output of government services, which is measured by consumption of fixed capital, when there is war damage. In the previous methodology, service lives of military equipment were shortened during wars to account for their destruction.)

Calculation of real estimates

BEA's improved method of calculating real output and prices also improves the measures of aggregate stocks and depreciation. Before the recent comprehensive revision, BEA featured estimates of real GDP and its components valued in terms of a single base period (fixed weights), which resulted in "constant-dollar" estimates. Now, BEA features estimates derived using chain-type annual-weighted indexes; these indexes also are used for the improved estimates of real net stocks and depreciation./12/

The new chain-type measures allow for the effects of changes in relative prices and in the composition of output over time and thereby eliminate a major source of bias in the previously featured fixed-weighted, or Laspeyres, measures of real GDP and prices. As described in the article "BEA's Chain Indexes, Time Series, and Measures of Long-Term Economic Growth" in this issue, the new indexes are more accurate, but they are also computationally more complex than the fixed-weighted indexes that converted to "constant-dollar" estimates that were additive and therefore easily manipulated. The new indexes have been converted to "chained (1992) dollar" estimates; however, as BEA pointed out when these estimates were introduced, they are not additive and may work well only for periods close to the base period. Moreover, calculations of contributions to the growth of aggregate measures, such as total private nonresidential net stock, may produce increasingly misleading results as one moves away from the base year. Consequently, BEA will present chained (1992) dollar estimates of selected aggregate measures (see table 15) beginning with 1929 and chained (1992) dollar estimates for all measures beginning with 1982. (Chain indexes will be presented for all periods.) For users who rely on chained (1992) dollar estimates, a note accompanying the chain-index article demonstrates how to prepare close approximations of contributions to real growth or relative changes for any period.

Comparison with previously published estimates

The overall effects of the changes in methodology can be gauged by comparing the new estimates of the major components of fixed reproducible tangible wealth with the previously published estimates. In table B, this comparison is made for growth rates of the "real" measures of net stock. Except for the growth rate for government net stock, which is revised up from an average annual increase of 3.1 percent to 3.5 percent, the changes in methodology resulted in relatively small revisions to growth rates for 1929–94.

In table C, current-dollar levels are compared for selected years. The revisions to the levels of producers' durable equipment and consumer durable goods were relatively small (revisions to consumer durable goods were largely due to revisions to the depreciation rates for autos). The revisions to the levels of net stocks of nonresidential structures, residential capital, and government capital were large. For example, the revisions raised the levels of these three aggregates 44.3 percent, 26.6 percent, and 35.2 percent, respectively, over the previously published levels for 1994. These large increases primarily reflect the new depreciation patterns for structures.

Presentation of the revised estimates

Tables 1–15 present the revised estimates of fixed reproducible tangible wealth. The odd-numbered tables (except table 15) present current-cost estimates in dollars and the even-numbered tables present real-cost estimates in terms of chain-type annual-weighted quantity indexes that are set equal to 100 in 1992. Tables 1 and 2 present estimates for total fixed reproducible tangible wealth and its major components for 1929–95. Tables 3 and 4 present estimates for fixed private capital by detailed type of asset for 1959–95. For the period 1985–95, estimates for fixed private capital are shown in tables 5 and 6; fixed nonresidential private capital, in tables 7 and 8; residential capital, in tables 9 and 10; government-owned capital, in tables 11 and 12; and durable goods owned by consumers, in tables 13 and 14. Table 15 presents the same chained (1992) dollar estimates for total fixed reproducible tangible wealth and its major components comparable as in table 2.

Future Work

The release of these improved estimates of net stock and depreciation represents a major step forward, but much work remains. As noted in BEA's Mid-Decade Strategic Review, BEA plans to conduct empirical studies of used asset prices for more assets./13/ In addition, such studies will be conducted so that information on the quality differences between vintages of assets reflected in BEA's prices of investment goods is accounted for in estimating depreciation profiles, as reflected in the profiles for computers. In addition, BEA plans to update service lives and to develop depreciation rates that are appropriate for government assets.


1. The previously published estimates of fixed reproducible tangible wealth ending in 1989 appeared in Fixed Reproducible Tangible Wealth in the United States, 1925–89. (Washington DC: U.S. Government Printing Office, 1993). Revised estimates for the periods 1990–92 and 1991–93 appeared in the September 1993 and August 1994 issues, respectively, of the SURVEY OF CURRENT BUSINESS.

2. The improved methodology for depreciation was summarized in Robert P. Parker and Jack E. Triplett, "Preview of the Comprehensive Revision of the National Income and Product Accounts: Recognition of Government Investment and Incorporation of a New Methodology for Calculating Depreciation," SURVEY 75 (September 1995). The empirical and theoretical literature supporting BEA's use of geometric patterns and the selection of specific depreciation rates will be described in a forthcoming SURVEY article by Barbara Fraumeni, Professor of Economics at Northeastern University, who served as a consultant to BEA for this project. The previously used methodology was described in Fixed Reproducible Tangible Wealth.

3. Prior to the recent comprehensive revision, government purchases of fixed assets were not classified as investment in the NIPA's; all such government purchases were classified as consumption expenditures. Consequently, the NIPA's did not include depreciation of government assets.

4. It should be noted that consumption of fixed capital does not provide an estimate of the full value of the services of government fixed assets, because the net rate of return on these assets is assumed to be zero. See Parker and Triplett, "Preview of the Comprehensive Revision," 36.

5. The yearend price for a given type of asset is estimated as the average of the price for the fourth quarter of the given year and the price for the first quarter of the subsequent year. For periods prior to 1959, yearend prices are estimated as the average of the price for the given year and the price for the subsequent year.

6. An alternative to the perpetual inventory method is to use data on the number of units of each type of asset in the net stock. This method was used for autos because the number of units in the stock of each vintage is available from registration data. For all other assets, methods based on direct measurement of the capital stock were not used because of the limited availability of the required data. Stock data are usually stated as book values, which do not provide the detailed information about the vintages or types of assets necessary to derive stock estimates on a current-cost and a real-cost basis.

7. New assets are assumed, on average, to be placed in service at midyear, so that depreciation on them is equal to one-half the new investment times the depreciation rate.

8. For a discussion of BEA's chain-type measures of output and prices, see "BEA's Chain Indexes, Time Series, and Measures of Long-Term Economic Growth" in this issue.

9. For a description of the previously used methodology, see Fixed Reproducible Tangible Wealth.

10. A general description of this work appears in Stephen D. Oliner, "Price Change, Depreciation, and Retirement of Mainframe Computers," in Price Measurements and Their Uses, Studies in Income and Wealth vol. 57, edited by Murray F. Foss, Marilyn E. Manser, and Allan H. Young (Chicago: University of Chicago Press, for the National Bureau of Economic Research, 1993): 19–61. The depreciation profiles used by BEA were taken from that article and from unpublished detail provided by Oliner.

11. In the new estimates, State and local government equipment are assigned the same service lives as those assigned to privately owned assets of the same type. Previously, all State and local government equipment was assigned a single service life. Using information obtained from the Department of Defense, service lives for military equipment are also assigned at a finer level of detail than in the past. For a complete description of the data sources previously used to estimate service lives, see Fixed Reproducible Tangible Wealth, M-16 to M-18.

12. Estimates will no longer be published in fixed-weighted dollars, but will be made available on the Department of Commerce's Economic Bulletin Board.

13. For a detailed description of the strategic plan, see "Mid-Decade Strategic Review of BEA's Economic Accounts: An Update" in the April 1995 SURVEY.