NEW METHODS for MEASURING CAPITAL by Dale W. Jorgenson Abstract

NEW METHODS FOR MEASURING CAPITAL by Dale W. Jorgenson Abstract

In the July 1997 issue of the Survey of Current Business the Bureau of Economic Analysis presented new methods for the measurement of capital in the U.S. National Income and Prod- uct Accounts. This is one of the most important advances in national accounting since the creation of the United Nations (1968) System of National Accounts and presents the critical challenge to members of the Canberra Group. How should the new treatment of capital be incorporated into the United Nations (1993) System of National Accounts? This paper describes the conceptual basis for BEA’s approach, presents the empirical evidence employed in implementing this approach, and outlines the implications for the SNA. (Jour- nal of Economic Literature Classiﬁcation C82.)

The purpose of this paper is to describe the conceptual and empirical basis for new methods for measuring capital recently introduced into the U.S. National Income and Product Accounts. The new methodology was first announced by the Bureau of Economic Analysis (BEA) in its 1995 benchmark revision and is described in detail by Barbara M. Fraumeni (1997), now Chief Economist of BEA. The key innovation in BEA’s approach is the introduction of a perpetual inventory of asset prices that parallels the perpetual inventory of asset quantities traditionally employed in accounting for capital. Since 1986 BEA has employed data on asset prices in generating constant quality price indices for investment in computers and related equipment in the U.S. national accounts. The benchmark revision of these Accounts on October 28, 1999, introduced constant quality price indices for computer software. Empirical research on constant quality price indices focuses on the relationship between the prices of assets and the characteristics of these assets -- processing speed and memory capacity in the case of computers. In July 1997 BEA combined perpetual inventories of asset prices and asset quantities to provide new measures of capital stocks and depreciation for all depreciable assets in the U.S. economy. Like the BEA’s constant quality price indices for investment in computers, BEA’s new measures of depreciation rest on an extensive body of empirical research. This research models the dependence of the price of an asset on its age, holding quality constant. The two applications of asset prices are intertwined and rely on a "hedonic" model of asset prices. Our first objective is to describe this model and show how it is used to construct constant quality price indexes, measures of depreciation and capital stocks, and both in combination. Our second objective is to summarize empirical research on depreciation, beginning with the landmark studies of Hulten and Wykoff (1981a, 1981b, 1981c) for the Office of Tax Analysis of the Department of the Treasury. As a consequence of the rapid assimilation of the results of Hulten and Wykoff, depreciation has been transformed from one of the most contentious and problematic areas in economic measurement to one of the best understood and most useful. This research has generated the information on asset prices incorporated into BEA’s new measures of depreciation and capital stocks. Our third objective is to outline the potential role for BEA’s perpetual inventory of asset prices in the SNA (1993). This is the construction of a production account in an integrated system of income, product, and wealth accounts. For this purpose we describe the system of vintage accounts introduced by Christensen and Jorgenson (1973). This system includes accumulation equations that generate the perpetual inventory of assets required for wealth accounts and asset pricing equations that produce the perpetual inventory of asset prices. The asset prices are used to generate prices of capital inputs for the production account. This is linked to income and expenditure and wealth accounts. Our overall conclusion is that the Canberra Group should recommend BEA’s new methodology for capital accounting for adoption into the SNA (1993). First priority should be given to construction of a production account within a unified system of income, product, and wealth accounts. Christensen and Jorgenson (1973) have designed and implemented a system of this type at the aggregate level for the United States. Fraumeni and Jorgenson (1980) have extended this system to the industry level. Jorgenson (1990) describes the production account for the new system and presents estimates for the U.S. through 1985. These estimates have recently been updated through 1996, using BEA’s estimates of depreciation and capital stocks, and are now available on the internet.1 1. Modeling Asset Prices.

The starting point for the measurement of depreciation is data on the price and quantity of investment goods. Investment represents the acquisition of capital goods, for example, a certain number of computers of a given age with a given performance. The price of acquisition is the unit cost of acquiring a capital good and depends on both the characteristics of the good and its age. As an illustration, the price of acquisition of a new computer is the unit cost of purchasing the machine from a dealer or, increasingly, the manufacturer. Both prices and quantities are measured in units of constant quality, like those for computers presented in the U.S. National Income and Product Accounts. Capital services are defined in terms of the use of an investment good for a specified period of time. For example, a computer with a given set of characteristics and a certain age can be leased for days, months, or years. The rental price of capital services is the unit cost of renting an investment good rather than purchasing it, so that the rental price of a computer is the unit cost of using a machine for a specified period of time. Depreciation is the component of unit cost associ- ated with the aging of assets. This component can be identified by comparing prices of assets of different ages at a given point of time. The second component of unit rental cost is the re valuation of an investment good of a given age between two time periods. For example, the cost of renting a computer includes depreciation due to aging; it also includes revaluation due to the continuing decline in the prices of computers of a given age. Both components of rental cost are essential and both are quantitatively significant. Jorgenson and Stiroh (1999) show that depreciation of computers averages 31.5 percent per year, while prices of new computers have declined at almost 40 percent per year since 1995. The third and final component of unit rental cost is the cost of capital, which is the same for all assets. For the U.S. this averages around five percent per year. It is important to note that this definition of depreciation differs from that in the United Nations (1993) System of National Accounts, paragraph 6.179. This definition identifies capital consumption as the decline "during the course of the accounting period" in the value of an asset. However, this decline has two distinct components, namely, capital consumption or depreciation due to aging and revaluation due to a change in the price of an asset of a given age, which is not part of capital consumption. The first issue to be addressed is, why is it necessary to distinguish the two components of the change in the value of an asset during an accounting period? Depreciation is defined as the decline in the value of an asset with age. This depends pri- marily on the profile of relative efficiencies of assets of different ages. As the asset ages, the dis- counted value of future capital services gradually declines. This decline can be measured at each point of time by observing the age profile of asset prices. The incorporation of this definition of depreciation into the U.S. National Income and Product Accounts is the most important innovation in BEA’s methodology for measuring depreciation and capital stocks. Revaluation is the change in the price of an asset from time period to time period, holding the age of the asset and the quality of the asset constant. For new assets this price change is measured by constructing a constant quality price index, like the one employed for computers in the U.S. national accounts. Hill (1999) points out that the SNA (1993) definition of capital consumption can be traced to Hotelling (1925) and was endorsed by a host of distinguished economists writing in the 1940’s and before. Unfortunately, this definition has become a serious source of confusion. The change in the price of an asset during an accounting period can be identified with depreciation only when the revaluation of assets, as defined above, is zero. When the price of an asset of a given age and quality does not change over time, the SNA definition correctly identifies capital consumption with the aging of an asset during the accounting period. Otherwise, the price of an asset of constant quality changes due to aging and also due to the change in the price of an asset of a given age and quality. Reverting to the example of computers, the rate of depreciation is 31.5 percent per year. This represents the decline in the price of computers across the age profile at each point of time. However, the rate of revaluation has varied from time period to time period. These changes repre- sent the decline in the price of computers of a given age and quality over time. Until 1995 the rate of revaluation for new computers was around 20 percent per year. Since 1995 the rate of revaluation for these computers has been around 40 percent per year. Before 1995 the change in the price of an asset during an accounting period was the rate of depreciation of 31.5 percent plus the change in the price of an asset of constant quality of 20 percent or 51.5 percent per year. Since 1995 the change during an accounting period has been 20 percent higher or 71.5 percent per year. Only the constant depreciation of 31.5 percent per year is included in a measure of capital consumption. Since the two components of change in the prices of assets of a constant quality vary inde- pendently, any attempt to reconcile the SNA (1993) definition with the new definition will lead to inconsistencies in the resulting accounting system. Hill (1999) has proposed the introduction of a concept of "foreseen obsolescence" as a way of reconciling the two definitions. However, there is no role for the concept of "obsolescence" in the new definition, since all asset prices are defined in terms of constant quality price indices, like those employed for computers by BEA. Purchasers of assets anticipate quality change, but this information is included in the prices of assets, so that no separate accounting for obsolescence is required. Accounting for depreciation and capital stocks requires a perpetual inventory of asset prices and quantities. The purpose of empirical research on depreciation is to construct a vintage system of asset prices for this purpose, giving prices of assets of different ages at each point of time. Since the concept of a perpetual inventory of prices may be an unfamiliar one, it may be helpful to be more specific. A perpetual inventory of prices consists of the age profiles of asset prices at each point of time. The price of each asset of every age is expressed in terms of units of constant quality. The data on the asset prices can be represented in the same manner as the more familiar perpetual inventory of asset quantities. As a practical matter, age profiles of asset prices, holding quality constant, are usually represented in terms of a depreciation formula that captures the decline in the price of an asset with age. The novel element in BEA’s methods for depreciation is that the depreciation formulas for each asset are constructed by econometric modeling of asset prices for each category of assets. These asset prices are arrayed in age profiles and, if necessary, adjusted for quality changes so as to assure that prices are expressed in terms of assets of constant quality. In Section 2 below we describe the results of this research in more detail. We refer to investment goods acquired at different points of time as different vintages of capital. A system of vintage accounts for asset quantities can be generated by the perpetual inventory method. This method is based on the assumption that the quantity of capital is proportional to the initial level of inv estment. The constants of proportionality are given by the relative efficiencies of different vintages of capital. An important simplifying assumption is that relative efficiencies of different vintages of an investment good depend only on the age of the investment good and not on the time at which it was acquired. The quantity of capital input is the flow of capital services into production. Since the capital services provided by a given inv estment good are proportional to the initial investment, the services provided by different vintages at the same point of time are perfect substitutes. Under perfect substitutability the flow of capital services is a weighted sum of past investments with weights that correspond to the relative efficiencies of the different vintages of capital. A system of vintage accounts containing data on investments of every age in every period is essential for the measurement of depreciation. We turn next to the price data required for capital accounting. The rental price of capital services is the price of capital input. Under perfect substitutability of capital goods of different vintages, the rental prices for all vintages of capital are proportional to a single rental price with constants of proportionality given by the relative efficiencies of the different vintages. The price of acquisition of a capital good is the sum of present values of future rental prices of capital services, weighted by relative efficiencies of the capital good in future time periods. To measure rental prices a perpetual inventory of prices of capital goods of every age in every period, holding quality constant, is required. At each point of time durable goods decline in efficiency with age, giving rise to needs for replacement in order to maintain productive capacity. This is the quantity interpretation of the intuitive notion of "maintaining capital intact" that underlies the SNA (1993) definition of capital consumption. Similarly, the price of a durable good declines with age, resulting in depreciation that reflects both the current decline in efficiency and the present value of future declines in efficiency. Depreciation provides the price interpretation of "maintaining capital intact." Both concepts are required for a perpetual inventory of asset prices and quantities.2 Price and quantity indices of capital services could be constructed at each point of time for each durable good with a perpetual inventory of both prices and quantities of assets. With less complete information a simplified set of price and quantity indices can be constructed from empirical estimates of relative efficiencies of investment goods of different ages. This is the point at which empirical research on depreciation can be particularly useful. As an illustration, we con- sider the simplified system of vintage accounts introduced by Christensen and Jorgenson (1973) and employed for most assets by Fraumeni (1997) in the U.S. National Income and Product Accounts. The simplified system is based on the empirical fact that the decline in efficiency of most assets with age is geometric. In the construction of a simplified accounting system we estimate capital stock at the end of each period Kt as a weighted sum of investments of age v at time t { At−v }: ∞ v Kt = Σ (1 − δ ) At−v . v=0

This is the capital accumulation equation, relating the stock of assets to past investments, required for a perpetual inventory of assets. With a constant rate of decline in efﬁciency δ , replacement Rt is proportional to capital stock: Rt = δ Kt−1 .

Similarly, the price of acquisition of new inv estment goods pA,t is a weighted sum of of the present values of future rentals { pK,t }. This is the capital asset pricing equation, relating the asset price to the values of future capital services, needed for a perpetual inventory of asset prices. With a constant rate of decline in efﬁciency the rental price becomes:

pK,t = pA,t−1rt + δ pA,t − (pA,t − pA,t−1), where rt is the rate of discount. Depreciation pD,t is proportional to the acquisition price: pD,t = δ pA,t .

Finally, the acquisition price of investment goods of age v at time t, say pA,t,v is: v pA,t,v = (1 − δ ) pA,t .

The perpetual inventory of asset prices consists of the acquisition prices {pA,t,v} of assets at all ages at all points of time. Similarly, the perpetual inventory of asset quantities consists of the quantities of past investments {At−v}, weighted by the relative efficiencies of assets of each age. The price and quantity of capital services can be derived from these two perpetual inventories, together with depreciation and replacement of capital goods.3 It is important to underline the fact that the perpetual inventories of asset prices and quantities required in accounting for depreciation and capital stocks can be implemented without the simplifying assumption that relative efficiencies of assets decline geometrically. For example, Fraumeni (1997) employs relative efficiencies for computers constructed by Oliner (1993) that are not geometric. While geometrically declining relative efficiencies greatly simplify the implemen- tation of the perpetual inventory method for both asset prices and asset quantities, the perpetual inventories can be constructed for any set of relative efficiencies. This has the important advantage that BEA’s estimates can be revised from time to time to incorporate the results of new empirical research, as in the case of Oliner’s work on computers. Under the assumption that the decline in efficiency of a durable good is geometric, the perpetual inventory of asset prices required for construction of price and quantity indices for capital services depends on the price for acquisition of new capital goods pA,t . At each point of time the prices for acquisition of capital goods of age v, say {pA,t,v}, are proportional to the price for new capital goods. The constants of proportionality decline geometrically at the rate δ . The rate of decline can be treated as an unknown parameter in an econometric model and estimated from a sample of prices for acquisition of capital goods of different vintages. We obtain an econometric model for asset prices by taking logarithms of the acquisition prices {pA,t,v} and adding a random disturbance term: ln pA,t,v = ln pA,0 + ln (1 − δ ) v + ln (1 + γ ) t + ε t,v ,

= α 0 + β v v + β t t + ε t,v ,(t = 1, 2 ...T; v = 0, 1 ...), where the rate of decline in efﬁciency δ and the rate of inﬂation in the price of the asset γ are unknown parameters and ε t,v is an unobservable random disturbance. We assume that the disturbance term has expected value equal to zero and constant variance, say σ 2, so that:

E(ε t,v) = 0, 2 V(ε t,v) = σ ,(t = 1, 2 ...T; v = 0, 1 ...).

We also assume that disturbances corresponding to distinct observations that are uncorrelated: ε ε = ≠ ′ ≠ ′ C( t,v , t′ ,v′ ) 0,(t t , v v ).

Under these assumptions the unknown parameters of the econometric model can be estimated by linear regression methods. The econometric model for asset prices can be generalized in several directions. First, the age of the durable good v and the time period t can enter nonlinearly into the vintage price function. Hall (l97l) has proposed an analysis of variance model for the vintage price function. In this model each age is represented by a dummy variable equal to one for that age and zero otherwise. Similarly, each time period can be represented by a dummy variable equal to one for that time period and zero otherwise. Hall’s analysis of variance model for vintage price functions can be written: = α + β ′ + β ′ + ε ln pA,t,v 0 v Dv t Dt t,v , (t = 1, 2 ...T; v = 0, 1 ...), where Dv is a vector of dummy variables for age v and Dt is a vector of dummy variables for time t; β v and β t are the corresponding vectors of parameters. In the estimation of this model dummy variables for one vintage and one time period can be dropped in order to obtain a matrix of observations on the independent variables of full rank. Hulten and Wykoff (1981b) have proposed an alternative approach to nonlinearity. They transform the prices of acquisition {pA,t,v}, age v, and time t by means of the Box-Cox transformation, obtaining: θ θ θ * = p − θ * = v − θ * = t − θ pA,t,v (pA,t,v 1) / p, v (v 1) v, t (t 1) / t , where the parameters θ p, θ v, and θ t can be estimated by nonlinear regression methods from the model for vintage price functions: * = α + β * + β * + ε = ... = ... pA,t,v 0 v v t t t,v,(t 1, 2 ; v 0, 1 ).

The model giving the logarithm of an asset price as a linear function of age v and time period t is a limiting case of the Hulten-Wykoff model with parameter values:

θ p = 0, θ v = 1, θ t = 1.

A third approach to nonlinearity has been introduced by Oliner (1993). He proposes to aug- ment the linear model by introducing polynomials in age and time. For example, a quadratic model can be represented by: 2 2 ln pA,t,v = α 0 + β 1,v v + β 2,v v + β 1,t t + β 2,t t + β v,t vt+ ε t,v , (t = 1, 2 ...T; v = 0, 1 ...).

This has the advantage of flexibility in the representation of time and age effects, but economizes on the number of unknown parameters. A further generalization of the econometric model of vintage price functions has been proposed by Hall (l97l). This is appropriate for durable goods with a number of different models that are perfect substitutes in production. Each model is characterized by a number of technical characteristics that affect relative efficiency. We can express the price for acquisition of new capital goods at time zero as a function of the characteristics: = α + β ′ ln pA,0 0 cC, where C is a vector of characteristics and β c is the corresponding vector of parameters. An econometric model of prices of new capital goods makes it possible to correct these prices for quality change. Changes in quality can be incorporated into price indices for capital goods by means of the "hedonic technique" originated by Waugh (1929) in dealing with the het- erogeneity of agricultural commodities. This approach was first applied to capital goods in an important study of automobile prices by Court (1939). A seminal article by Griliches (1961) revived the hedonic methodology and applied it to postwar automobile prices. Chow (1967) first applied this methodology to computer prices in research conducted at IBM.4 Cole, Chen, Barquin-Stolleman, Dulberger, Helvacian, and Hodge (1986) reported the results of a joint project conducted by Bureau of Economic Analysis (BEA) of the Department of Commerce and IBM to construct a constant quality price index for computers. Triplett (1986) discussed the economic interpretation of constant quality price indices in an accompanying article. Subsequently, BEA (1986) described the introduction of constant quality price indices for computers into the U.S. National Income and Product Accounts. A more detailed report on the BEA- IBM research on computer processors is presented by Dulberger (1989), who employs speed of processing and main memory as technical characteristics in modeling the prices of processors. An extensive survey of research on hedonic price indices for computers is given by Triplett (1989).5 Hall’s (1971) methodology provides a means for determining both a quality-corrected price index for new capital goods and relative efficiencies for different vintages of capital goods. Sub- stituting the "hedonic" model of prices of net assets into the econometric model of vintage price functions: = α + β ′ + β ′ + β ′ + ε ln pA,t,v 0 v Dv t Dt c C t,v , (t = 1, 2 ...T; v = 0, 1 ...).

The unknown parameters of this model can be estimated by linear regression methods. Hall’s methodology has been applied to prices of mainframe computers and computer peripherals by Oliner (1993, 1996a). In Oliner’s applications the chronological age of assets is replaced by the "model" age, that is, the time that a model has been available from the manufacturer. An alternative approach is to substitute observations on the price of new capital goods pA,0 into the econometric model, so that the dependent variable is the difference between the logarithms of new and used assets: − = α + β ′ + β ′ + ε ′ ln pA,t,v ln pA,0 0 v Dv t Dt t,v (t = 1, 2 ...T; v = 0, 1 ...).

This makes it possible to separate the modeling of asset prices as a function of age and the quality-corrected price index of new capital goods. Hulten, Robertson, and Wykoff (1989), Wykoff (1989), and OTA (1990, 1991a, 1991b) have employed this approach. A further decomposition of the econometric model of asset prices has been suggested by Biorn (1999). In order to isolate the vintage effect from the other determinants of asset prices, Biorn proposes to substitute observations on the prices of new capital goods in each time period pA,t into the econometric model: − = α + β ′ + ε ′ ln pA,t,v ln pA,t 0 v Dv t,v (t = 1, 2 ...T; v = 0, 1 ...).

This decomposition is implicit in the vintage price model originated by Terborgh (1954). The decomposition of vintage price functions is discussed in more detail by Biorn (1999). We conclude that the same concepts and methods for measuring capital are employed in developing constant quality price indices and measuring depreciation in the U.S. National Income and Product Accounts. A constant quality price index requires a cross section of prices on assets with different characteristics. This approach is used in constructing price indices for computers in the U.S. National Income and Product Accounts. Estimates of depreciation employ prices of assets of different vintages to construct a perpetual inventory of asset prices. Hall’s "hedonic" model of asset prices provides a unified framework for modeling asset prices for both purposes. This model is very flexible and can readily be adapted to modeling age profiles, constructing constant quality price indices, or both in combination. 2. Applications.

To illustrate the econometric modeling for the purpose of generating a perpetual inventory of asset prices we describe a model that has been implemented by Hulten and Wykoff (l98lb) for eight categories of assets in the United States. Their study includes tractors, construction machinery, metalworking machinery, general industrial equipment, trucks, autos, industrial buildings, and commercial buildings. In l977 investment expenditures on these categories amounted to fifty- five percent of spending on producers’ durable equipment and forty-two percent of spending on nonresidential structures.6 In the estimation of econometric models of vintage price functions, the sample of used asset prices is "censored" by the retirement of assets. The price of acquisition for assets that have been retired is equal to zero. If only observations on surviving assets are included in a sample of used asset prices, estimates of depreciation are biased by excluding observations on assets that have been retired. In order to correct this bias Hulten and Wykoff (l98lb) multiply the prices of surviving assets of each vintage by the probability of survival, expressed as a function of age. For each class of assets Hulten and Wykoff tabulate the rate of economic depreciation as a function of the age of the asset. The natural logarithm of the price is expressed as a function of age and time to obtain an average rate of depreciation, which Hulten and Wykoff refer to as the best geometric rate (BGA). The square of the multiple correlation coefficient (R2) is giv en as a measure of the goodness of fit of the geometric approximation to the fitted vintage price function for each asset. The first conclusion that emerges from the work of Hulten and Wykoff is that a correction for censored sample bias is extremely important in the modeling of asset prices. The Hulten- Wykoff study was the first to employ such a correction. The second conclusion reached by Hul- ten and Wykoff (l98lb, p. 387) is that "... a constant rate of depreciation can serve as a reason- able statistical approximation to the underlying Box-Cox rates even though the latter are not geometric. [ Their italics.] This result, in turn, supports those who use the single parameter depreciation approach in calculating capital stocks using the perpetual inventory method." After 1973 energy prices increased sharply and productivity growth rates declined dramati- cally at both aggregate and sectoral levels. Baily (1981) attributed part of the slowdown in economic growth to a decline in relative efficiencies of older capital goods resulting from higher energy prices. Hulten, Robertson, and Wykoff (1989) have tested the stability of vintage price functions during the 1970s. Wykoff (1989) has analyzed price data for four models of business- use automobiles collected from a large leasing company, applying the Hulten-Wykoff methodology. Hulten, Robertson, and Wykoff (1989, p. 255) have carefully documented the fact that the relative efficiency functions for nine types of producers’ durable equipment were unaffected by higher energy prices: "While depreciation almost certainly varies from year to year in response to a variety of factors, we have found that a major event like the energy crises, which had the potential of significantly increasing the rate of obsolescence, did not in fact result in a systematic change in age-price profiles." They also conclude that "the use of a single number to characterize the process of economic depreciation [of a given type of asset] seems justified in light of the results ... " The distribution of retirements used by Hulten and Wykoff (1981b) to correct for censored sample bias are based on the Winfrey (1935) S-3 curve with BEA (1977) lifetimes. These lifetimes are taken, in turn, from Bulletin F, compiled by the Internal Revenue Service and published in 1942. Between 1971 and 1981 the Office of Industrial Economics (OIE) conducted 46 studies of survival probabilities, based on vintage accounts for assets reported under the Asset Deprecia- tion Range System introduced in 1962. The results of 27 of these studies have been summarized by Brazell, Dworin, and Walsh (1989). These results provide estimates of the distribution of useful lives based on the actual retention periods for the assets examined. A very important objective for future empirical research on asset prices is to incorporate information from the OIE studies into corrections for sample selection bias. Before 1981 tax law had linked tax depreciation to retirement of assets. Between 1981 and 1986 the Accelerated Cost Recovery System severed the link between tax depreciation and economic depreciation altogether. The Tax Reform Act of 1986 re-instituted tax depreciation based on economic depreciation.7 Under the 1986 Act the Office of Tax Analysis (OTA) was mandated by the Congress to undertake empirical studies of economic depreciation, including "the antici- pated decline in value over time",8 and report the results in the form of a useful life. This is the lifetime for straight-line depreciation that yields the same present value as economic depreciation. For this purpose OTA (1990, 1991a, 1991b) conducted major surveys of used asset prices and retirements for scientific instruments, business-use passenger cars, and business-use light trucks and analyzed the results. Oliner (1996b) has conducted an extensive survey of used asset prices and retirement patterns for machine tools with the assistance of the Machinery Dealers National Association. He compares his results with those from previous empirical studies of economic depreciation for this industry, including those of Beidleman (1976) and Hulten and Wykoff (1981b). Finally, he compares estimates of depreciation and capital stock with those of the BEA (1987) Capital Stock Study. Oliner’s study, like those of OTA, combines information on used asset prices and retirements for the same or similar populations of assets. This is an important advance over previous studies based on the vintage price approach. Oliner (1993) has collected and analyzed used asset prices for IBM mainframe computers and has estimated constant-quality price change and economic depreciation simultaneously. Pre- vious studies of computer prices, such as the studies surveyed by Triplett (1989), had been limited to constant-quality price change. The primary data source for computer prices used by Oliner is the Computer Price Guide, published by Computer Merchants, Inc. The data on retirement patterns are obtained from data on the installed stock of IBM computers tabulated by the Interna- tional Data Corporation. Oliner (1996a) has conducted a similar study of computer peripherals -- large and intermediate disk drives, printers, displays, and card readers and punches. The prices of used assets are based on Computer Price Guide and estimates of retirement patterns are inferred from the duration of price listings. An alternative to estimating patterns of decline in relative efficiency from asset prices is to model rental prices.9 This approach has been employed by Malpezzi, Ozanne, and Thibodeau (l987) to analyze rental price data on residential structures and by Taubman and Rasche (l969) to study rental price data on commercial structures. While leases on residential property are very frequently one year or less in duration, leases on commercial property are typically for much longer periods of time. Since the rental prices are constant over the period of the lease, estimates based on annual rental prices for commercial property are biased toward the one-hoss shay pat- tern found by Taubman and Rasche; Malpezzi, Ozanne, and Thibodeau find rental price profiles for residential property that decline with age. A second alternative to the vintage price approach originated by Meyer and Kuh (l957) is to analyze investment for replacement purposes. Coen (l980) compares the explanatory power of alternative patterns of decline in efficiency in a model of investment behavior that also includes the price of capital services. For equipment he finds that eleven of twenty-one two-digit manufacturing industries are characterized by geometric decline in efficiency, three by sum of the years’ digits and seven by straight-line. For structures he finds that fourteen industries are characterized by geometric decline, five by straight-line and two by one-hoss-shay patterns. Hulten and Wykoff (l98lc, p. 110) conclude that: "The weight of Coen’s study is evidently on the side of the geometric and near-geometric forms of depreciation." Alternative approaches for analyzing investment for replacement purposes have been introduced to Pakes and Griliches (1984) and Doms (1996). Pakes and Griliches have related profits for U.S. manufacturing firms to past investment expenditures. The weights on investments of different ages can be interpreted as relative efficiencies of these assets. Doms has included a weighted average of past investment expenditures in a production function. Treating the weights as unknown parameters to be estimated, he obtains estimates of relative efficiences of assets. While Pakes and Griliches find patterns of relative efficiencies that rise and then decline, Doms obtains relative efficiencies that decline geometrically. We conclude that empirical research on depreciation is now available for the principal categories of assets included in the U.S. National Income and Product Accounts. The most extensive body of research is that of Hulten and Wykoff (1981a, 1981b, 1981c), Hulten, Robertson, and Wykoff (1989), and Wykoff (1989). However, important additional studies have been completed by OTA (1990, 1991a, 1991b) and Oliner (1993, 1994a, 1994b). Finally, estimates of retirement distributions required for correcting sample selection bias have been completed by OIE and summarized by Brazell, Dworin, and Walsh (1989). These empirical studies of depreciation have provided the information employed by the Fraumeni (1997) in revising BEA’s measures of depreciation and capital stocks. The measurement of depreciation has been an important objective of research at the Bureau of Economic Analysis (BEA) for several decades. The culmination of this research was the mag- isterial BEA (1987) study, Fixed Reproducible Tangible Wealth in the United States, 1925-85. This study presented a perpetual inventory of quantities for all depreciable assets in the U.S. capital stock. Since 1995 BEA’s estimates of capital stocks and depreciation have incorporated a perpetual inventory of asset prices, based on the empirical literature on depreciation we have summarized.10 A system of perpetual inventories for asset prices and quantities like that originated by Christensen and Jorgenson (1973) provides an internally consistent framework for measuring capital stocks and depreciation. Christensen and Jorgenson have used this framework in implementing an integrated system of income, product and wealth accounts. They construct a production account on the basis of the production possibility frontier employed by Jorgenson and Griliches (1967). This approach incorporates an accounting identity between the values of outputs and inputs. The prices and quantities of outputs and inputs are used to allocate the growth of output between the growth of capital and labor inputs and productivity growth. Christensen and Jorgenson have also constructed an income and expenditure account, based on a social welfare function like that employed by Jorgenson and Yun (1991a). This income and expenditure account incorporates an accounting identity between income net of depreciation and the sum of saving and consumption. Data from this account are used to allocate growth of income between the growth of current consumption and the growth of future consumption through saving. Both production and income and expenditure accounts can be incorporated into the U.S. National Income and Product Accounts and the SNA (1993). Saving is linked to the asset side of the wealth account through capital accumulation equations for each asset like those we have presented in Section 1. These equations provide a perpetual inventory of assets accumulated at different points of time. A perpetual inventory of asset prices for different vintages of investment goods are linked to the prices of capital services through a parallel set of asset pricing equations, like those we have presented in Section 1. At each point of time the perpetual inventories of asset prices and asset quantities give stocks of assets of each age and the corresponding asset prices. The stocks can be cumulated to obtain quantities of assets, while the prices can be used to value the stocks and derive rental prices for capital services and measures of depreciation. Hulten (1992) has formalized the welfare and production approaches to economic performance by means of a model of optimal economic growth. This model includes a production function with output as a function of capital and labor inputs. Output is divided between consumption, which contributes to the welfare of a representative consumer, and saving, which contributes to future consumption through capital accumulation. Income net of depreciation measures the welfare resulting from intertemporal optimization of consumption in Hulten’s model of growth, as in a similar model proposed by Weitzman (1976). This measure of welfare summarizes the stream of present and future consumption. Hulten shows that gross product is the measure of output appropriate for separating the growth of output between productivity growth and the growth of capital and labor inputs, while national income net of depreciation is appropriate for allocating the growth of income between consumption growth and contributions to the growth of future consumption through saving. A complete system of accounts includes a production account, an income and expenditure account, and a wealth account. Measures of depreciation employed in all three accounts can be generated in an internally consistent way from the system of vintage accounts for assets we have outlined in Section 1. Hulten (1992) points out that the Haig-Simons definition of taxable income requires that capital cost recovery for tax purposes must equal economic depreciation. Capital cost recovery for tax purposes has differed from economic depreciation whenever capital consumption allowances and the investment tax credit have been used to provide tax incentives for private investment, as in the Accelerated Cost Recovery System during the period 1981-1986. Under U.S. tax law capital recovery is based on the original acquisition price of an asset rather than current replacement cost. During periods of high inflation, the original acquisition price and the current replacement cost have div erged substantially. The production account of an integrated system of income, product, and wealth accounts can be used in measuring productivity. Jorgenson (1990) provides estimates of capital stocks and rental prices, classified by four asset classes -- producers’ durable equipment, nonresidential construction, inventories, and land -- and three legal forms of organization -- corporate and noncorpo- rate business and nonprofit enterprises. This study is based on annual data for the period 1947-1985 for an average of as many as 156 components of capital services for each of 35 industries. These data incorporate investment data from the BEA (1987) study of U.S. national wealth and depreciation rates from Jorgenson and Yun (1991b). In constructing data on capital input for each of the 35 industrial sectors Jorgenson (1990) combines price and quantity data for different classes of assets and legal forms of organization by expressing sectoral capital services, say {Ki}, as a translog function of its 156 individual components, say {Kki}. The corresponding index of sectoral capital services is a translog quantity index of individual capital services: − − = i − − ln Ki(T) ln Ki(T 1) Σ vKk [ln Kki(T) ln Kki(T 1)], (i = 1, 2 ... n), where weights are given by average shares of each component in the value of sectoral property compensation: 1 vi = [vi (T) + vi (T − 1)], (i = 1, 2 ... n; k = 1, 2 ... p), Kk 2 Kk Kk and i i = pKk Kki = ... = ... vKk i ,(i 1, 2 n; k 1, 2 p). Σ pKk Kki

The value shares are computed from data on capital services {K } and the rental price of capital i ki services {pKk }, cross-classified by asset class and legal form of organization. BLS (1983, pp. 57-59) also employs relative efficiency functions estimated by Hulten and Wykoff. Howev er, BLS does not utilize the geometric relative efficiency functions fitted by Hul- ten and Wykoff. Instead, BLS has fitted a set of hyperbolic functions to the relative efficiency functions estimated by Hulten and Wykoff. Consistency is preserved between the resulting estimates of capital stocks and rental prices by implementing a system of vintage price accounts for each class of assets. This set of accounts includes asset prices and quantities of investment goods of all ages at each point of time. BLS (1983, pp. 57-59) shows that measures of capital services based on hyperbolic and geometric relative efficiency functions are very similar. BLS (1991) has expanded annual productivity estimates reported for private business, private nonfarm business, and manufacturing to include measures of capital services that differ among 57 industries. For each industry capital service prices and quantities are estimated for 72 types of depreciable assets. The Economic Research Service (1991) has published official productivity estimates for agriculture that include prices and quantities of capital services, based on the approach of Ball (1985). The methodology for depreciable assets, except for breeding livestock, is similar to that employed by BLS. Data on prices and quantities of capital services for breeding livestock have been constructed by the vintage accounting approach developed by Ball and Harper (1990).11 3. Conclusion.

The challenge confronting the Canberra Group how to incorporate BEA’s new methodology for measuring capital into the SNA (1993). The difficulties that confront the Group can be illustrated by considering the two models of capital services presented by Blades (1999). The first model is given in Paragraph 1 of Chapter 7 of his monograph. This ignores the distinction we have made between depreciation and revaluation; it also neglects the issue of holding quality constant in the measurement of both prices and quantities. The second model of the price of capital services presented by Blades (1999) is given in Paragraph 18 of Chapter 7 and is based the "user cost of capital." Formally, this appears to be the same as the formula for the price of capital services we have derived from the asset pricing equation in Section 1. However, Blades gives an interpretation in Paragraph 19 that is totally at odds with the framework of Section 1. According to Blades the term that we define as re valuation of assets due to a change in the price of an asset of a given age and given quality has two components. The first is obsolescence. However, holding the quality of an asset constant, there is no role for obsolescence. The second component, according to Blades, is the "underlying inflation rate." However, there is no role for the underlying inflation rate in the framework we have presented in Section 1. For example, a constant quality index of computer prices declined around 20 percent per year before 1995, but has declined at almost 40 percent per year since 1995. The underlying inflation rate plays no role in either of these measures of revaluation. What is the relationship between the approach to the measurement of capital in the U.S. National Income and Product Accounts and that recommended by Blades (1999)? Blades has summarized the BEA approach to capital measurement in Paragraphs 71-74 of Chapter 4 of his monograph. He presents the BEA approach as an alternative method for implementing a perpetual inventory of asset quantities. This overlooks the most important innovation in the BEA approach, which is the introduction of a perpetual inventory of asset prices as well. Blades also neglects the important role of constant quality price and quantity indices in the BEA approach. It is important to emphasize that the BEA approach is simpler and more straightforward than the traditional approach to capital measurement summarized by Blades. The BEA methodology makes it possible to dispense with the concepts as gross and net capital stock. These are superseded by the concepts of capital stock and capital services we have outlined in Section 1. The BEA methodology also makes it possible to dispense with the concept of obsolescence, which is required only if the quality of assets is not held constant. Finally, there is no role in the BEA methodology for the underlying inflation rate. The concept of revaluation accounts for asset- specific price increases to decreases and no other inflation measures are required. Fortunately, the necessary revisions in Blades’ draft are relatively straightforward. At the outset it is important to adopt the convention that prices and quantities of investment goods are expressed in units of constant quality. This is the subject of a separate project, conducted under the auspices of the OECD by Triplett, so that the details can be left to Triplett’s monograph. Blades should point out that this convention makes it possible to dispense with the idea of obsolescence. In Section 1 we have emphasized the importance of revaluing assets of a given age and quality as these prices change over time. However, revaluation depends only on the change in the price of the asset and not on the underlying rate of inflation. Blades’ monograph should incorporate a perpetual inventory of asset prices of constant quality, as well as the perpetual inventory of asset quantities that he describes. The monograph should also outline the methodology for constructing the perpetual inventory of asset prices that we have presented in Section 1. The definition of depreciation is the change in the price of an asset of a given quality with age at a given point of time. Depreciation formulas are used to describe age profiles of prices of assets of different ages. The selection of an appropriate formula relies on empirical evidence obtained from the age profiles for each asset. Blades’ exposition of capital measurement in Chapters 2-5 can be greatly simplified, since the concepts of gross and net capital stock are no long necessary. Only the concepts of capital stocks and capital services introduced in Chapter 2 are needed. Perpetual inventories of prices and quantities of assets should be introduced in Chapter 2. The model of capital services presented in Paragraphs 29-35 should be replaced by the model outlined in Section 1 above. The definition of capital consumption in Chapter 3 should be replaced by the change in prices of an asset of given quality with age at a given point of time. This leads naturally to the appropriate definition of the price of capital services in terms of the user cost formula for Chapter 5, correctly interpreted. Finally, it would be useful to outline the application of the new methods for capital measurement in systems of national accounts. For this purpose the SNA (1993) must be revised and updated to incorporate the new methodology. This can best be illustrated by outlining the application of the new methods in developing a production account. The description of the BLS approach already given in Chapter 7 could be used for this purpose. However, this has the disadvantage that the BLS does not take advantage of the simplifications resulting from geometric decline in efficiency of assets with age. An alternative approach would be to use the simplified accounting system in Section 1; Christensen and Jorgenson (1973) show how to extend this simplified system to an integrated system of income, product, and wealth accounts for the U.S. We hav enow completed a survey of the new methods for capital measurement introduced by BEA and their applications in national accounting. The applications we have surveyed are based on the pioneering studies of Hulten and Wykoff (1981a, 1981b, 1981c), who have constructed the data required for perpetual inventories of asset prices covering a sizable proportion of U.S. investment expenditures. Alternative methodologies, such as the rental price approach and the modeling of investment for replacement purposes, have been superseded by the vintage price approach with a correction for sample bias originated by Hulten and Wykoff. Jorgenson (1990) and BLS (1991) have incorporated the empirical research of Hulten and Wykoff into measures of the prices and quantities of capital services. Both studies generate aggregate production accounts suitable for incorporation into the U.S. National Income and Product Accounts. Jorgenson (1990) has also provided industry-level production accounts that can be integrated with the U.S. national accounts and the inter-industry transactions accounts constructed by BEA. Fraumeni (1997) has combined the perpetual inventory data for asset prices generated by Hulten and Wykoff with perpetual inventory data on asset quantities by class of asset and industry generated by BEA (1987) to improve BEA’s measures of U.S. capital stocks and depreciation. Our overall conclusion is that first priority should be assigned to developing production accounts consistent with the perpetual inventory of asset prices growing out of the work of Hulten and Wykoff and the perpetual inventory of asset quantities arising from the research of BEA (1987). The appropriate conceptual framework for this important task is provided by the system of perpetual inventories of prices and quantities of assets introduced by Christensen and Jorgen- son (1973). This vintage accounting system is employed to generate prices and quantities of capital services required for a production account. It is also the key to integrating production and income and expenditure accounts with wealth accounts. FOOTNOTES

1. Consult the web site: http://kuznets.harvard.edu/˜djorgens/ Click on "data sets". Detailed documentation is available in Jorgenson (1990), reprinted as Chap- ter 1 in Jorgenson (1995a). 2. Christensen and Jorgenson (1973) and Jorgenson (1980) discuss the system of perpetual inventories for asset prices and quantities in greater generality. The model of capital as a factor of production that underlies this system has been discussed by Diewert (l980), Hulten (1990), Jor- genson (l973, l980, 1989), and Triplett (1996). 3. Christensen and Jorgenson (1973) have used the system of perpetual inventories of asset prices and quantities to generate an integrated system of income, product and wealth accounts for the U.S. This system was extended to the industry level by Jorgenson (l980) and implemented by Fraumeni and Jorgenson (1980). Fraumeni and Jorgenson (1986) incorporated the results of empirical research on depreciation summarized in Section 2, below. 4. Surveys of the hedonic technique have been given by Triplett (l975, 1987, 1990). 5. Gordon (1989) has presented an alternative constant quality price index for computers. This has been incorporated into Gordon’s (1990) study of constant quality price indices for all components of producers’ durable equipment in the U.S. national accounts. 6. Hulten and Wykoff (1981b) have estimated vintage price functions for structures from a sample of 8066 observations on market transactions in used structures. These data were collected by the Ofﬁce of Industrial Economics of the U.S. Department of the Treasury in l972 and were published in Business Building Statistics (l975). They hav eestimated vintage price functions for equipment from prices of machine tools collected by Beidleman (l976) and prices of other types of equipment collected from used equipment dealers and auction reports of the U.S. General Ser- vices Administration. 7. Detailed histories of U.S. tax policy for capital recovery are presented by Brazell, Dworin, and Walsh (1989) and Jorgenson and Yun (1991b). 8. Joint Committee on Taxation (1986), p. 103. 9. Hulten and Wykoff (l98lc) have summarized studies of economic depreciation completed prior to their own study. Vintage price functions have provided the most common methodology for such studies. 10. The methodology for constructing a perpetual inventory of asset quantities is described by the BEA (1987, 1993). The methodology for constructing a perpetual inventory of asset prices is given by Fraumeni (1997). 11. Boskin (1989a, 1989b) and his associates have successfully employed the vintage accounting approach in measuring capital stocks and depreciation for the government sector of the U.S. economy. Jorgenson and Fraumeni (1989) have applied this approach to the measurement of stocks and depreciation of human capital. REFERENCES

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