首页    期刊浏览 2024年11月28日 星期四
登录注册

文章基本信息

  • 标题:Empirical studies of depreciation.
  • 作者:Jorgenson, Dale W.
  • 期刊名称:Economic Inquiry
  • 印刷版ISSN:0095-2583
  • 出版年度:1996
  • 期号:January
  • 语种:English
  • 出版社:Western Economic Association International
  • 摘要:Empirical research on constant quality price indices focuses on the relationship between the prices of assets and their characteristics--processing speed and memory capacity in the case of computers. By contrast, empirical research on depreciation centers on the relationship between the price of an asset and its age, so that prices of assets of different ages or vintages must be analyzed. Since the connection between research on constant quality price indices and depreciation is not obvious, I describe Hall's "hedonic" model of asset prices, which comprehends both, in the next section.
  • 关键词:Depreciation

Empirical studies of depreciation.


Jorgenson, Dale W.


The purpose of this paper is to survey empirical research on depreciation and its applications. As a framework for the survey I employ the econometric model of asset prices introduced by Hall [1971] that has been the primary vehicle for this research for the past two decades. Since 1985 research on asset prices has been used successfully to generate constant quality price indices for investment in computers; these indices are included in the U.S. National Income and Product Accounts. The challenge facing economic statisticians now is to employ asset price information effectively while making badly needed revisions in the treatment of depreciation in the national accounts.

Empirical research on constant quality price indices focuses on the relationship between the prices of assets and their characteristics--processing speed and memory capacity in the case of computers. By contrast, empirical research on depreciation centers on the relationship between the price of an asset and its age, so that prices of assets of different ages or vintages must be analyzed. Since the connection between research on constant quality price indices and depreciation is not obvious, I describe Hall's "hedonic" model of asset prices, which comprehends both, in the next section.

My 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. Empirical research has generated the information needed for revising the treatment of depreciation in the U.S. national accounts.

My third objective is to illustrate the use of information on asset prices in constructing an integrated system of income, product, and wealth accounts. For this purpose I describe a system of vintage accounts introduced by Christensen and Jorgenson [1973]. This system includes accumulation equations that generate the perpetual inventory of assets required for the wealth accounts and asset pricing equations that produce the information on depreciation needed for income and product accounts. A system of vintage accounts is the key to the successful integration of measures of income and product with a measure of wealth.

My overall conclusion is that the U.S. National Income and Product Accounts have failed to provide internally consistent measures of capital stocks and depreciation. Top priority should be assigned to improving the national accounts by incorporating information now available from empirical research on depreciation. Fortunately, this task can be facilitated by using concepts and methods already familiar to economic statisticians from their work on constant quality price indices.

The following section outlines Hall's econometric model of asset prices, focusing on the version of this model employed by Hulten and Wykoff. I also consider an alternative version recently introduced by Oliner [1993]. In section II, I summarize empirical research on depreciation, including studies of asset prices and retirements. Studies of both types are required for constructing a system of vintage asset prices. In section III, I outline the role of depreciation in an integrated system of income, product and wealth accounts. The system of vintage accounts originated by Christensen and Jorgenson provides a natural framework for incorporating the results of empirical research on depreciation. Section IV concludes the paper.

I. ECONOMETRIC MODELS

To measure depreciation one needs a set of prices and quantities of investment goods. Investment represents the acquisition of capital goods, for example, a certain number of computers with a given performance. The price of acquisition of a durable good is the unit cost of acquiring it. For instance, the price of acquisition of a computer is the unit cost of purchasing the machine. Implicit in these definitions is the assumption that prices and quantities are measured in units of constant quality.

Capital services are defined in terms of the use of an investment good for a specified period of time. For example, computers 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 associated with the aging of assets. This component can be isolated by comparing prices of assets of different ages. The objective of empirical research on depreciation is to construct a system of asset prices for this purpose.

I begin the description of a system of vintage accounts with quantities of investment goods. I refer to investment goods acquired at different points of time as different vintages of capital. A system of vintage accounts 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 investment. 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 investment good are proportional to the initial investment, the services provided by different vintages at the same point in time are perfect substitutes. Under perfect substitutability the flow of capital services is a weighted sum of past investments; the weights 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 a vintage accounting system. The rental price of capital services is the price of capital input. Under perfect substitut-ability 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 system of vintage accounts containing data on prices of capital goods of every age in every period is required.

Durable goods decline in efficiency with age, and thus require replacement in order to maintain productive capacity. This is the quantity interpretation of the intuitive notion of "maintaining capital intact." 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 used in a system of vintage accounts.(1)

Price and quantity indices of capital services in each period can be constructed for each durable good given a full set of vintage price and quantity data. With less complete information, a simplified set of price and quantity indices can be constructed from empirical estimates of the 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, consider a system of vintage accounts introduced by Christensen and Jorgenson [1973]. This system is based on the assumption that the decline in efficiency of assets with age is geometric.

To construct this simplified accounting system, estimate capital stock at the end of each period [K.sub.t] as a weighted sum of investments of age v at time t {[A.sub.t-v]}

[Mathematical Expression Omitted]

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 [delta], replacement [R.sub.t] is proportional to capital stock:

[R.sub.t]=[delta][K.sub.t-1].

Similarly, the price of acquisition of new investment goods [p.sub.A,t] is a weighted sum of the present values of future rentals {[p.sub.K,t]} This is the capital asset pricing equation, relating the asset price to the values of future capital services, needed for a vintage price system. With a constant rate of decline in efficiency the rental price becomes

[p.sub.k,t] = [p.sub.A,t-1][r.sub.t] + [delta][p.sub.A,t]-([p.sub.A,t]-[p.sub.A,t-1]),

where [r.sub.t] is the rate of discount. Depreciation [p.sub.D,t] is proportional to the acquisition price:

[p.sub.D,t]= [delta] [p.sub.A,t]

Finally, the acquisition price of investment goods of age v at time t, say PA t v iS

[p.sub.A,t,v] = [(1 - [delta]).sup.v] [p.sub.A,t]

The vintage price system consists of the acquisition prices {[p.sub.A,t,v]} while the vintage quantity system consists of the quantities of past investments {[A.sub.t-v]}. The price and quantity of capital services can be derived from these two systems of vintage accounts, together with depreciation and replacement of capital goods.(2)

Under the assumption that the decline in efficiency of a durable good is geometric, the vintage price system required for construction of price and quantity indices for capital input depends on the price for acquisition of new capital goods [p.sub.A,t]. At each point in time the prices for acquisition of capital goods of age v, say {[p.sub.A,t,v]}, are proportional to the price for new capital goods. The constants of proportionality decline geometrically at the rate 6. The rate of decline can be treated as an unknown parameter in an econometric model and estimated from a sample of prices for the acquisition of capital goods of different vintages.

I obtain an econometric model for vintage price functions by taking logarithms of the acquisition prices {[p.sub.A,t,V]} and adding a random disturbance term:

ln[p.sub.A,t,v]=ln[p.sub.A,0]+ln(1 -[delta])v + ln (1 + [g]) t + [[epsilon].sub.t,v] =[[alpha].sub.0]+[[beta].sub.v]v+[[beta].sub.t]t+[[epsilon].sub.t,v], (t=1,2...T; v=0,1...),

where the rate of decline in efficiency [delta] and the rate of inflation in the price of the asset [g] are unknown parameters and [[epsilon].sub.t,v] is an unobservable random disturbance.

Assume that the disturbance term has an expected value equal to zero and constant variance, say [[sigma].sup.2], so that (2.) These vintage accounts are used to generate an integrated system of income, product and wealth accounts for the U.S. by Christensen and Jorgenson [1973]. This system is extended to the industry level by Jorgenson [1980] and implemented by Fraumeni and Jorgenson [1980]. Fraumeni and Jorgenson [1986] have incorporated the results of the empirical research on depreciation summarized in section II, below.

E([[epsilon].sub.t,v]) = 0, V([[epsilon].sub.t,v]) = [[sigma].sup.2] (t = 1,2...T; v = 0,1...),

and that disturbances corresponding to distinct observations are uncorrelated:

C([[epsilon].sub.t,v] [[epsilon].sub.t',v]) = 0,(t[not equal to]t', v[not equal to]v')

Under these assumptions the unknown parameters of the econometric model can be estimated by linear regression methods.

The econometric model for vintage price functions 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 [1971] has proposed an analysis of variance model for the vintage price function. In his 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 as

ln[p.sub.A,t,v]=[[alpha].sub.0]+[[beta].sub.v'] [D.sub.v]+[[beta].sub.t'] [D.sub.t]+[[epsilon].sub.t,v'] (t = 1,2...T; v = 0,1...),

where [D.sub.v] is a vector of dummy variables for age v and [D.sub.t] is a vector of dummy variables for time t; [[beta].sub.v] and [[beta].sub.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.

An alternative approach to nonlinearity has been proposed by Hulten and Wykoff [1981b]. They transform the prices of acquisition {[p.sub.A,t,v]}, age v, and time t by means of the Box-Cox transformation, obtaining

[Mathematical Expression Omitted]

where the parameters [[theta].sub.p], [[theta].sub.v], and [[theta].sub.t] can be estimated by nonlinear regression methods from the model for vintage price functions:

[Mathematical Expression Omitted]

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

[[theta].sub.p] = 0, [[theta].sub.v] = 1, [[theta].sub.t] = 1.

A third approach to nonlinearity is taken by Oliner [1993]. He proposes to augment the linear model by introducing polynomials in age and time. For example, a quadratic model can be represented by

ln[p.sub.A,t,v] = [[alpha].sub.0] + [[beta].sub.1,v] + [[beta].sub.2,v] [v.sup.2] +[[beta].sub.1,t] + [[beta].sub.2,t] [t.sup.2] + [[beta].sub.v,t] v t + [[epsilon].sub.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 [1971]. 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:

ln [p.sub.A,0] = [[alpha].sub.0] + [[beta].sub.c]' C,

where C is a vector of characteristics and pc 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 heterogeneity 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.(3)

Cole, Chen, Barquin-Stolleman, Dulberger, Helvacian, and Hodge [1986] reported the results of a joint project conducted by the Bureau of Economic Analysis 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, the Bureau of Economic Analysis [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 Bureau of Economic Analysis-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].(4)

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. Substituting the "hedonic" model of prices of net assets into the econometric model of vintage price functions:

ln[p.sub.A,t,v] = [[alpha].sub.0] + [[beta].sub.v]' [D.sub.v] + [[beta].sub.t]' [D.sub.t] + [[beta].sub.c'] C + [[epsilon].sub.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; 1995a]. 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 [p.sub.A,0] into the econometric model, so that the dependent variable is the difference between the logarithms of new and used assets:

ln[p.sub.,t,v] - ln[p.sub.A,0] = [[alpha].sub.0] + [[beta].sub.v]' [D.sub.v] + [b]t]'[D.sub.t] + [[epsilon].sub.t,v], (t = 1,2...T; v = 0,1...).

This makes it possible to separate the modeling of the vintage price function and the quality-corrected price index of new capital goods. Hulten, Robertson, and Wykoff [1989], Wykoff [1989], and the Office of Tax Analysis [1990; 1991a; 1991b] employ this approach.

A further decomposition of the econometric model of asset prices has been suggested by Biorn [1992b]. 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 [p.sub.A,t] into the econometric model:

ln[p.sub.A,t,v] - ln[p.sub.A,t] = [[alpha].sub.0] + [[beta].sub.v]' [D.sub.v] + [[epsilon].sub.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 [1992a; 1992b].

The concepts and methods employed in developing constant quality price indices for the U.S. National Income and Product Accounts can also be used in measuring depreciation. A constant quality price index can be constructed by focusing on 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. Alternatively, prices of assets of different vintages can be analyzed to obtain estimates of depreciation suitable for introduction into the U.S. national accounts. Finally, these two objectives can be combined in Hall's "hedonic" model of asset prices. This model provides a unified framework for modeling asset prices for these different purposes.

II. STUDIES OF DEPRECIATION

To illustrate the econometric modeling of vintage price functions I present a model implemented by Hulten and Wykoff [1981b] 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 1977 investment expenditures on these categories amounted to 55 percent of spending on producers' durable equipment and 42 percent of spending on nonresidential structures.(5)

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 [1981b] multiply the prices of surviving assets of each vintage by the probability of survival, expressed as a function of age.

Vintage price functions for commercial and industrial buildings are summarized in Table I. For each class of assets the rate of economic depreciation is tabulated as a function of the age of the asset. The natural logarithm of the price is regressed on age and time to obtain an average rate of depreciation, which Hulten and WyRoff refer to as the best geometric rate. The square of the multiple correlation coefficient (R2) is given as a measure of the goodness of fit of the geometric approximation to the fitted vintage price function for each asset. Vintage price functions are estimated with and without the correction for censored sample bias.

The first conclusion that emerges from Table I is that a correction for censored sample bias is extremely important in the estimation of vintage price functions. The Hulten-Wykoff study is the first to employ such a correction. The second conclusion reached by Hulten and Wykoff [1981b, 387] is that "a constant rate of depreciation can serve as a reasonable 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 dramatically at both aggregate and sectoral levels. Baily [1981] attributes 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] test the stability of vintage price functions during the 1970s. Wykoff [1989] analyzes 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, 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."

Table II presents rates of economic depreciation derived from the best geometric approximations of Hulten and Wykoff [1981b] for thirty-four categories of nonresidential business assets and one category of residential assets. These rates were extended to include public utility and residential property by Jorgenson and Sullivan [1981]. Hulten and Wykoff compare the best geometric depreciation rates presented in Table 1 with depreciation rates employed by the Bureau of Economic Analysis [1977] in estimating capital stock. The Hulten-Wykoff rate for equipment averages 0.133, while the Bureau's rate averages 0.141, so that the two rates are very similar. The Hulten-Wykoff rate for structures is 0.037, while the Bureau's rate is 0.060, so that these rates are substantially different.
Table 1
Rates of Economic Depreciation

 Without Censored Without Censored
 Sample Correction Sample Correction
Age Commercial Industrial Commercial Industrial

 5 2.85 2.99 2.66 2.02
10 2.64 3.01 1.84 1.68
15 2.43 3.04 1.48 1.50
20 2.30 3.07 1.27 1.39
30 2.15 3.15 1.02 1.25
40 2.08 3.24 0.88 1.17
50 2.04 3.34 0.79 1.11
60 2.02 3.45 0.72 1.06
70 2.02 3.57 0.66 1.03
Best Geometric
 Rate 2.47 3.61 1.05 1.28
[R.sup.2] 0.985 0.997 0.971 0.995

Source: Hulten and Wykoff [1981], Table 5, p. 387; commercial corresponds to
office, industrial corresponds to factory.




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 Bureau of Economic Analysis [1977] lifetimes. These lifetimes are taken, in turn, from Bulletin F, compiled by the Internal Revenue Service and published in 1942. Between 1971 and 1931 the Office of Industrial Economics conducted forty-six studies of survival probabilities, based on vintage accounts for assets reported under the Asset Depreciation Range System introduced in 1962. The results of twenty-seven 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 research on vintage price functions is to incorporate information from the Office of Industrial Studies research into corrections for sample selection bias.

Before 1981 the tax law 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.(6) Under the 1986 Act the Office of Tax Analysis was mandated by the Congress to undertake empirical studies of economic depreciation, including "the anticipated decline in value over time,"(7) 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 the Office of Tax Analysis [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 [1995b] conducts 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 Bureau of Economic Analysis's 1987 Capital Stock Study. Oliner's study, like those of the Office of Tax Analysis, 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] collects and analyzes used asset prices for IBM mainframe computers and estimates constant-quality price change and economic depreciation simultaneously. Previous studies of computer prices, such as the studies surveyed by Triplett [1989], were 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 were obtained from data on the installed stock of IBM computers tabulated by the International Data Corporation. Oliner [1995a] conducts 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 the Computer Price Guide and estimates of retirement patterns are inferred from the duration of price listings.

An alternative to the vintage price approach is to employ rental prices rather than prices of acquisition to estimate the pattern of decline in efficiency.(8) This approach is employed by Malpezzi, Ozanne, and Thibodeau [1987] to analyze rental price data on residential structures and by Taubman and Rasche [1969] 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 pattern 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 [1957] is to analyze investment for replacement purposes. Coen [1980] 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 [1981c, 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 are employed by Pakes and Griliches [1984] and Doms [1994]. Pakes and Griliches relate profits for U.S. manufacturing firms to past investment expenditures. The weights on investments of different ages can be interpreted as the relative efficiencies of these assets. Doms includes 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 efficiencies of assets. While Pakes and Griliches find patterns of relative efficiencies that rise and then decline, Doms obtains relative efficiencies that decline geometrically.

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 the Office of Tax Analysis [1990; 1991a; 1991b] and Oliner [1993; 1995a; 1995b]. Finally, estimates of retirement distributions required for correcting sample selection bias have been completed by the Office of Industrial Economics and summarized by Brazell, Dworin, and Walsh [1989]. Taken together, these empirical studies of depreciation provide the information needed to revise the treatment of depreciation in the national accounts.

III. APPLICATIONS

The measurement of depreciation has been an important objective of research at the Bureau of Economic Analysis for several decades. National income, net of depreciation, is included in the U.S. National Income and Product Accounts. Stocks of depreciable assets are estimated as a component of national wealth. The culmination of this research was the magisterial Bureau of Economic Analysis's [1987] study, Fixed Reproducible Tangible Wealth in the United States, 1925-85, updated in 1993 to cover the period 1925-89. Perhaps surprisingly, the Bureau's estimates of capital stocks and depreciation do not incorporate the results of the extensive empirical literature on vintage price functions that has been summarized in section II.(9)

The Bureau employs measures of capital stocks for equipment and structures with relative efficiencies that are constant over the lifetime of each capital good. This produces a measure of gross capital stock. Depreciation based on the straight-line method is used to produce a measure of net capital stock. The first issue is whether the Bureau's [1987; 1993] studies are internally consistent. This issue arises because patterns of decline in efficiency of assets are used in estimating both depreciation and capital stocks, but these patterns can be the same or different. Obviously, internal consistency requires that the same relative efficiencies be used in both sets of estimates.(10)

If we consider economic depreciation under the assumption that assets do not decline in efficiency until the end of their useful lives, we can simplify the analysis by assuming that rates of return {[r.sub.t+s]} and prices of capital services {[p.sub.k,t+[tau]]} are constant to obtain depreciation on an asset of age v:

[TABULAR DATA OMITTED]

Under the Bureau's assumption that relative efficiencies of assets of different ages are constant over the lifetimes of assets, economic depreciation declines geometrically. This reflects the time discounting of the retirement of an asset.

The Bureau's straight-line estimates of depreciation obviously reflect a different pattern of relative efficiencies than that employed in estimating capital stock, so that its measurements of depreciation and capital stock are internally inconsistent. This issue was first analyzed in detail by Jorgenson and Griliches [1972a, esp. pp. 81-87]. Denison [1972, esp. pp. 101-109] defends the Bureau's use of straight-line depreciation. However, he fails to respond to the criticism that straight-line depreciation is inconsistent with the relative efficiencies of capital goods of different ages that the Bureau employs in measuring capital stock.

The logical inconsistencies in the Bureau's methodology arise from the definition of depreciation. Denison's [1972, 104-105] defense of the straight-line formula is based on the "capital input definition" of depreciation that he originally introduced in 1957. This definition was subsequently adopted in the U.S. National Income and Product Accounts. The capital input definition is described by Young and Musgrave [1980, 32] as follows: "Depreciation is the cost of the asset allocated over its service life in proportion to its estimated service at each date." Within the vintage accounting framework presented in section I, Denison's capital input definition of depreciation allocates the cost of an asset over its lifetime in proportion to the relative efficiencies of capital goods of different ages.(11)

Young and Musgrave [1980, 33-37] contrast the Denison definition with the "discounted value definition" employed in the vintage accounting system outlined in section I. Among the advantages for the capital input definition claimed by Denison [1957, 240] and by Young and Musgrave [1980, 33] is that this definition avoids discounting of future capital services. In fact, discounting can be avoided in the measurement of depreciation only if the decline in the efficiency of capital goods is geometric. The Bureau of Economic Analysis's assumption that efficiency is constant over the lifetime of an asset requires discounting, as I have already demonstrated. Only if relative efficiencies decline geometrically does economic depreciation coincide with Denison's capital input definition. But this definition then implies declining balance rather than straight-line depreciation.

The second issue that arises in the measurement of depreciation is the incorporation of up-to-date information from empirical studies like those summarized in section II. The available empirical evidence on efficiency functions for different classes of assets, growing out of the work of Hulten and Wykoff [1981a; 1981b; 1981c], is very extensive. This evidence includes the results of econometric modeling of vintage price functions, like those of Hulten, Wykoff, and Robertson [1989], Wykoff [1989], Office of Tax Analysis [1990; 1991a; 1991b], and Oliner [1993; 1995a; 1995b]. It also includes studies of retirement patterns like those developed by the Office of Industrial Economics and summarized by Brazell, Dworin, and Walsh [1989]. Both types of information are needed for the measurement of depreciation.

The Bureau of Economic Analysis [1987; 1993] employs only information about retirements in measuring depreciation. This is a consequence of applying the "capital input definition" of depreciation under the assumption that relative efficiencies of assets are constant over the lifetime of each capital good. This assumption is contradicted by the empirical evidence on depreciation I have reviewed in section II. The incorporation of this evidence into the U.S. National Income and Product Accounts requires that the Bureau's definition of depreciation be replaced by the "discounted value definition" presented in section I.

A vintage accounting system for prices and quantities of investment goods, such as that originated by Christensen and Jorgenson [1973], provides an internally consistent framework for measuring capital stocks and depreciation. Christensen and Jorgenson use this framework in constructing an integrated system of income, product and wealth accounts. They distinguish between two alternative measures of economic performance, identifying the production approach with the production possibility frontier employed by Jorgenson and Griliches [1967]. This approach is implemented by means of a production account with an accounting identity between the values of outputs and inputs. These data are used to allocate the growth of output between the growth of capital and labor inputs and productivity growth.

Christensen and Jorgenson have also described a welfare approach to the measurement of economic performance, based on a social welfare function like that employed by Jorgenson and Yun [1991a]. This approach can be implemented by means of an income and expenditure account with an accounting identity between income net of depreciation and the sum of saving and consumption. Data from this account can be 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 are essential components of the U.S. National Income and Product Accounts and accounting systems that employ the United Nations [1968] System of National Accounts.

Saving is linked to the asset side of the wealth account through capital accumulation equations for each asset like those presented in section I. These equations provide a perpetual inventory of assets accumulated at different points in time. 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 presented in section I. The complete system of vintage accounts gives stocks of assets of each age and the corresponding asset prices for each period. 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 services of the assets 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 outlined in section I.

The income account of an integrated system of national accounts can be used in measuring welfare. 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 diverged substantially.

Making use of the asset classification scheme of the Bureau of Economic Affairs's [1987] capital stock study for individual industries, Jorgenson and Yun [1991b] map the economic depreciation rates for the thirty-five asset categories given in Table II, into the Bureau's 1987 asset classification scheme to incorporate additional information about asset lives. Jorgenson and Yun [1991b] employ data on economic depreciation and capital cost recovery under U.S. tax law to summarize the tax burden on capital income. For this purpose they employ the marginal effective tax rate introduced by Auerbach and Jorgenson [1980]. An effective tax rate represents the complex provisions of tax law in terms of a single ad valorem rate.
TABLE II
Rates of Economic Depreciation: Business Assets
 Asset Depreciation Rate
Producer Durable Equipment
1. Furniture and fixtures 0.1100
2. Fabricated metal products 0.0917
3. Engines and turbines 0.0786
4. Tractors 0.1633
5. Agricultural machinery 0.0971
6. Construction machinery 0.1722
7. Mining and oil field machinery 0.1650
8. Metalworking machinery 0.1225
9. Special industry machinery 0.1031
10. General industrial equipment 0.1225
11. Office, computing and accounting machinery 0.2729
12. Service industry machinery 0.1650
13. Electrical machinery 0.1179
14. Trucks, buses and truck trailers 0.2537
15. Autos 0.3333
16. Aircraft 0.1833
17. Ships and boats 0.0750
18. Railroad equipment 0.0660
19. Instruments 0.1500
20. Other equipment 0.1500

Nonresidential Structures
21. Industrial buildings 0.0361
22. Commercial buildings 0.0247
23. Religious buildings 0.0188
24. Educational buildings 0.0188
25. Hospital and institutional buildings 0.0233
26. Other nonfarm buildings 0.0454
27. Railroad structures 0.0176
28. Telephone and telegraph structures 0.0333
29. Electric light and power structures 0.0300
30. Gas structures 0.0300
31. Other public utility structures 0.0450
32. Farm structures 0.0237
33. Mining exploration, shaft and wells 0.0563
34. Other nonbuilding structures 0.0290

Residential Structures
35. Residential structures 0.0130
Source: Jorgenson and Sullivan [1981], Table I.




The production account of an integrated system of income, product, and wealth accounts can be used in measuring productivity. The estimates of depreciation by Jorgenson and Yun [1991b] have been incorporated into price and quantity indices of capital services for productivity measurement by Jorgenson [1990]. The underlying estimates of capital stocks and rental prices are classified by four asset classes--producers' durable equipment, nonresidential construction, inventories, and land--and three legal forms of organization--corporate and noncorporate 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 thirty-five industries. These data incorporate investment data from the Bureau of Economic Analysis's [1987] study of U.S. national wealth.

In constructing data on capital input for each of the thirty-five 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 {[K.sub.i]}, as a translog function of its 156 individual components, say {[K.sub.ki]}. The corresponding index of sectoral capital services is a translog quantity index of individual capital services:

[Mathematical Expression Omitted] where weights are given by average shares of each component in the value of sectoral property compensation:

[Mathematical Expression Omitted]

(i = 1,2 ... n; k = 1,2 ... p),

and

[Mathematical Expression Omitted]

(i = 1,2...n; k = 1,2...p).

The value shares are computed from data on capital services {[K.sub.ki]}and the rental price of capital services {[Mathematical Expression Omitted]}, cross-classified by asset class and legal form of organization.

Internal consistency of a measure of capital input requires that the same pattern of relative efficiency is employed in measuring both capital stock and the rental price of capital services. The decline in efficiency affects both the level of capital stock and the depreciation component of the corresponding rental price. Estimates of capital stocks and rental prices that underlie the data presented by Jorgenson [1990] are based on geometrically declining relative efficiencies. The same patterns of decline in efficiency are used for both capital stock and depreciation, so that the requirement for internal consistency of price and quantity indices of capital services is met.

The Bureau of Labor Statistics [1983, 57-59] also employs relative efficiency functions estimated by Hulten and Wykoff. However, the Bureau of Labor Statistics does not utilize the geometric relative efficiency functions fitted by Hulten and Wykoff. Instead, it has fitted a set of hyperbolic functions to Hulten and Wykoff's relative efficiency functions. 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. The Bureau of Labor Statistics [1983, 57-59] shows that measures of capital services based on hyperbolic and geometric relative efficiency functions are very similar.

The Bureau of Labor Statistics [1991] expands annual productivity estimates reported for private business, private nonfarm business, and manufacturing to include measures of capital services that differ among fifty-seven industries. For each industry, capital service prices and quantities are estimated for seventy-two types of depreciable assets. The Economic Research Service [1991] publishes 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 the Bureau of Labor Statistics. 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].(12)

I conclude that the U.S. National Income and Product Accounts fail to provide internally consistent measures of capital stocks and depreciation. Top priority should be given to replacing the "capital input definition" of depreciation by the "discounted value definition" presented in section I. This has important implications for improving the income, product, and wealth measures now included in the U.S. national accounts. Second, estimates of depreciation should be enhanced by incorporating the information from studies of vintage price functions that are summarized in section II. These two tasks can be accomplished by utilizing concepts and methods already familiar to economic statisticians as a result of the introduction of constant quality prices for computers into the national accounts.

IV. CONCLUSION

Hall's [1971] "hedonic" model of vintage asset prices, outlined in section I, has proved to be an indispensable guide to empirical research. The applications surveyed here are based on the pioneering studies of Hulten and Wykoff [1981a; 1981b; 1981c], who have constructed vintage price functions 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.

I conclude that the results of empirical research on depreciation should be incorporated into the U.S. National Income and Product Accounts. The research of Hulten and Wykoff has been used successfully in two important applications of depreciation--the empirical description of the U.S. tax system for depreciable assets by Jorgenson and Yun [1991b] and the measurement of capital services and rental prices for studies of productivity by Jorgenson [1990] and the Bureau of Labor Statistics [1991]. Information from the research summarized in section II should be combined with the detailed data on investment flows by class of asset and industry produced by the Bureau of Economic Analysis [1987; 1993] to improve measures of U.S. national income, product and wealth.

While the Bureau of Economic Analysis [1987; 1993] provides estimates of capital stocks and economic depreciation, the two sets of estimates are logically inconsistent since they are based, implicitly, on different assumptions about the relative efficiencies of assets of different ages. Gross capital stocks are based on unchanging efficiencies throughout the lifetime of an asset. This implies a declining balance method of depreciation that reflects the time discounting of retirements. However, the Bureau of Economic Analysis's measures of depreciation are based on the straightline method. The first step toward removing these inconsistencies is to adopt the discounted value definition of depreciation presented in section I.

My overall conclusion is that top priority in future applications of empirical studies of depreciation should be assigned to developing internally consistent measures of national income and wealth. An equally important priority is to utilize the results of empirical studies of depreciation growing out of the work of Hulten and Wykoff. The appropriate conceptual framework for both of these important tasks is provided by the system of vintage price and quantity accounts introduced by Christensen and Jorgenson. This vintage accounting system is the key to integrating income and product accounts with wealth accounts and incorporating relative efficiencies of assets of different ages based on econometric estimates of vintage price functions.

(1.) The system of vintage accounts summarized here is discussed in greater generality by Christensen and Jorgenson [1973] and Jorgenson [1980]. The model of capital as a factor of production that underlies this system is discussed by Diewert [1980], Hulten [1990], Jorgenson [1973; 1980; 1989], and Triplett [1995]. (3.) Surveys of the hedonic technique are given by Triplett [1975;1987; 1990]. (4.) Gordon [1989] has presented an alternative constant quality price index for computers. This was incorporated into Gordon's [1990] study of constant quality price indices for all components of producers' durable equipment in the U.S. national accounts. (5.) Hulten and Wykoff [1981b] 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 1972 and were published in Business Building Statistics [1975]. They estimated vintage price functions for equipment from prices of machine tools collected by Beidleman [1976] and prices of other types of equipment collected from used equipment dealers and auction reports of the U.S. General Services Administration. (6.) Detailed histories of U.S. tax policy for capital recovery are presented by Brazell, Dworin, and Walsh 11989] and Jorgenson and Yun [1991b]. (7.) Joint Committee on Taxation [1986,103]. (8.) Hulten and Wykoff [1981c] summarize studies of economic depreciation completed prior to their own study Vintage price functions have provided the most common methodology for such studies. (9.) The methodology for constructing estimates of depreciation and the corresponding capital stocks is described by the Bureau of Economic Analysis [1987; 1993]. (10.) The Bureau's methodology is discussed in greater detail by Hulten and Wykoff [1981c] and Wykoff [1989]. The incorporation of retirement patterns described in section II, below, results in a decline m efficiency with age after retirements begin. However, this does not affect my conclusion that the Bureau's methodology is internally inconsistent. (11.) The capital input definition has been categorically rejected by economists outside the Bureau of Economic Analysis. See the comments on Denison [1957] by Kuznets [1957] comments on Denison [1972] by Jorgenson and Griliches [1972b], and comments on Young and Musgrave [1980] by Faucett [1980]. (12.) Boskin et al. [1989a, 1989b] 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] apply this approach to the measurement of stocks and depreciation of human capital.

REFERENCES

Auerbach, A. J., and D. W. Jorgenson. "Inflation-Proof Depreciation of Assets." Harvard Business Review September-October 1980, 113-18.

Baily, M. N. "Productivity and the Services of Capital and Labor." Brookings Papers on Economic Activity, vol. 1, 1981, 1-50.

Ball, V. E. "Output, Input, and Productivity Measurement in U.S. Agriculture, 1948-70." American Journal of Agricultural Economics, August 1985, 475-86.

Ball, V. E., and M. J. Harper. "Neoclassical Capital Measures Using Vintage Data: An Application to Breeding Livestock." Washington, D.C.: Economic Research Service, U.S. Department of Agriculture, 1990.

Beidleman, C. R. "Economic Depreciation in a Capital Goods Industry." National Tax Journal, December 1976, 379-90.

Biorn, E. "Concave Survival and Efficiency Curves for Capital and the Form of Age-Price Profiles." Oslo: Department of Economics, University of Oslo, February 1992a.

--. "Survival Curves and Efficiency Curves for Capital and the Behavior of Vintage Prices." Oslo: Department of Economics, University of Oslo, February 1992b.

Boskin, M. J., M. S. Robinson, and A. M. Huber. "Government Saving, Capital Formation, and Wealth in the United States, 1947-1985," in The Measurement of Saving, Investment, and Wealth, edited by R. E. Lipsey and H. S. Tice. Chicago: University of Chicago Press, 1989a, 287-353.

Boskin, M. J., M. S. Robinson, and J. M. Roberts. "New Estimates of Federal Government Tangible Capital and Investment," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 1989b, 451-83.

Brazell, D. W., L. Dworin, and M. Walsh. "A History of Federal Depreciation Policy." Washington, D.C.: Office of Tax Analysis, U.S. Department of the Treasury, 1989.

Bureau of Economic Analysis. The National Income and Product Accounts of the United States, 1929-1974: Statistical Tables, A Supplement to the Survey of Current Business. Washington, D.C.: U.S. Department of Commerce, 1977.

--. "Improved Deflation of Purchases of Computers." Survey of Current Business, March 1986, 7-9.

--. Fixed Reproducible Tangible Wealth in the United States, 1925-85. Washington, D.C.: U.S. Government Printing Office, 1987.

--. Fixed Reproducible Tangible Wealth of the United States, 1925 89, Washington, D.C.: U.S. Government Printing Office, 1993.

Bureau of Labor Statistics. Trends in Multifactor Productivity, 1948-81. Bulletin 2178, Washington, D.C.: U.S. Department of Labor, 1983.

--. "Multifactor Productivity Measures, 1988 and 1989." Washington, D.C.: U.S. Department of Labor, March 26, 1991.

Chow, G. C. "Technological Change and the Demand for Computers." American Economic Review, December 1967, 1117-30.

Christensen, L. R., and D. W. Jorgenson. "Measuring the Performance of the Private Sector of the U.S. Economy, 1929-1969," in Measuring Economic and Social Performance, edited by M. Moss. New York: Columbia University Press, 1973, 233-351.

Coen, R. "Depreciation, Profits, and Rates of Return in Manufacturing Industries," m The Measurement of Capital, edited by D. Usher. Chicago: University of Chicago Press, 1980, 121-52.

Cole, R., Y. C. Chen, J. A. Barquin-Stolleman, E. Dulberger, N. Helvacian, and J. H. Hodge. "Quality-Adjusted Price Indexes for Computer Processors and Selected Peripheral Equipment." Survey of Current Business, January 1986, 41-50.

Computer Merchants, Inc. Computer Price Guide. Chappaque, New York: Computer Merchants, Inc., various quarterly issues.

Court, A. T. "Hedonic Price Indexes with Automotive Examples," in The Dynamics of Automobile Demand. New York: General Motors Corporation, 1939, 99-117.

Denison, E. F. "Theoretical Aspects of Quality Change, Capital Consumption, and Net Capital Formation," in Problems of Capital Formation. Princeton: Princeton University Press, Conference on Research in Income and Wealth, 1957.

--. "Final Comments." Survey of Current Business, May 1972, 95-110.

Diewert, W. E. "Aggregation Problems in the Measurement of Capital," in The Measurement of Capital, D. Usher. Chicago: University of Chicago Press, 1980, 433-528.

Doms, M. E. "Estimating Capital Efficiency Schedules . within Production Functions." Economic Inquiry, January 1996, 78-92.

Dulberger, E. "The Application of a Hedonic Model to a Quality-Adjusted Price Index for Computer Processors," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 37-76.

Economic Research Service. "Production and Efficiency Statistics, 1989." Washington, D.C.: Economic Research Service, U.S. Department of Agriculture, April 1991.

Faucett, J. G. "Comment," in The Measurement of capital, edited by D. Usher. Chicago: University of Chicago Press, 1980, 68-81.

Fraumeni, B. M., and D. W. Jorgenson. "The Role of Capital in U.S. Economic Growth, 1948-1976," in Capital Efficiency and Growth, edited by G. von Furstenberg. Cambridge: Ballinger, 1980, 9-250.

--. "The Role of Capital in U.S. Economic Growth, 1948-1979," in Measurement Issues and Behavior of Productivity Variables, edited by A. Dogramaci. Boston: Martinus Nijhoff, 1986, 161-244.

Gordon, R. J. "The Postwar Evolution of Computer Prices," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 1989, 77-126.

--. The Measurement of Durable Goods Prices. Chicago: University of Chicago Press, 1990.

Griliches, Z. "Hedonic Price Indexes for Automobiles: An Econometric Analysis of Quality Change," in The Price Statistics of the Federal Government. New York: National Bureau of Economic Research, 1961, 137-96.

Hall, R. E. "The Measurement of Quality Changes from Vintage Price Data," in Price Indexes and Quality Change, edited by Z. Griliches. Cambridge, Mass.: Harvard University Press, 1971, 240-71.

Hulten, C. R. "The Measurement of Capital," in Fifty Years of Economic Measurement, edited by E. R. Berndt and J. E. Triplett. Chicago: University of Chicago Press, 1990, 119-52.

--. "Accounting for the Wealth of Nations: The Net versus Gross Output Controversy and its Ramifications." Scandinavian Journal of Economics, vol. 94, Supplement, 1992, 9-24.

Hulten, C. R., J. W. Robertson, and E C. Wykoff. "Energy, Obsolescence, and the Productivity Slowdown," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 1989, 225-58.

Hulten C. R., and E C. Wykoff. "Economic Depreciation and the Taxation of Structures in United States Manufacturing Industries: An Empirical Analysis," in The Measurement of Capital, edited by D. Usher. Chicago: University of Chicago Press, 1981a, 83-120.

--. "The Estimation of Economic Depreciation Using Vintage Asset Prices: An Application of the Box-Cox Power Transformation." Journal of Econometrics, April 1981b, 367-96.

--. "The Measurement of Economic Depreciation," in Depreciation, Inflation, and the Taxation of Income from Capital, edited by C. R. Hulten. Washington: D.C., The Urban Institute Press, 1981c, 81-125.

International Data Corporation, Joint Committee on Taxation. General Explanation of the Tax Reform Act of 1986, Washington, U.S. Government Printing Office, 1987, various issues.

Jorgenson, D. W. "The Economic Theory of Replacement and Depreciation," in Econometrics and Economic Theory, edited by W. Sellekaerts. New York: Macmillan, 1973, 189-221.

--. "Accounting for Capital," in Capital Efficiency and Growth, edited by G. von Furstenberg. Cambridge: Ballinger, 1980, 251-319.

--. "Capital as a Factor of Production," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 1989, 1-36.

--. "Productivity and Economic Growth," in Fifty Years of Economic Measurement, edited by E. Berndt and J. Triplett. Chicago: University of Chicago Press, 1990, 19-118.

Jorgenson, D. W., and B. M. Fraumeni. "The Accumulation of Human and Nonhuman Capital," in The Measurement of Saving, Investment, and Wealth, edited by R. E. Lipsey and H. S. Tice. Chicago: University of Chicago Press, 1989, 227-82.

Jorgenson, D. W., and Z. Griliches. "The Explanation of Productivity Change." Review of Economic Studies, July 1967, 249-83.

--. "Issues in Growth Accounting: A Reply to Edward F Denison." Survey of Current Business, May 1972a, 65-94.

--. "Issues in Growth Accounting: Final Reply." Survey of Current Business, May 1972b, 111.

Jorgenson, D. W., and M. A. Sullivan. "Inflation and Corporate Capital Recovery," in Depreciation, Inflation, and the Taxation of Income from Capital, edited by C. R. Hulten. Washington: Urban Institute Press, 1981, 171-238, 311-13.

Jorgenson, D. W., and K.-Y. Yun. "The Excess Burden of U.S. Taxation." Journal of Accounting, Auditing, and Finance, Fall 1991a, 487-509.

--. Tax Reform and the Cost of Capital. Oxford: Oxford University Press, 1991b.

Kuznets, S. "Comment," in Problems of Capital Formation. Princeton: Princeton University Press, Conference on Research in Income and Wealth, 1957, 271-80.

Malpezzi, S., L. Ozanne, and T. Thibodeau. "Microeconomic Estimates of Housing Depreciation." Land Economics, November 1987, 372-85.

Meyer, J., and E. Kuh. The Investment Decision. Cambridge: Harvard University Press, 1957.

Office of Industrial Economics. Business Building Statistics. Washington, D.C.: U.S. Department of the Treasury, 1975.

Office of Tax Analysis. "Depreciation of Scientific Instruments." Washington, D.C.: Office of Tax Analysis, U.S. Department of the Treasury, March 1990.

--. "Depreciation of Business-Use Light Trucks," Washington, Office of Tax Analysis, U.S. Department of the Treasury, September 1991a.

--. "Depreciation of Business-Use Passenger Cars," Washington, Office of Tax Analysis, U.S. Department of the Treasury, April 1991b.

Oliner, S. D. "Constant-Quality Price Change, Depreciation, and Retirement of Mainframe Computers," in Price Measurements and Their Uses, edited by M. E Foss, M. E. Manser, and A. H. Young. Chicago: University of Chicago Press, 1993, 19

--. "Estimates of Depreciation and Retirement for Computer Peripheral Equipment." Economic Inquiry, January 1996a, 62-63.

--. "New Evidence on the Retirement and Depreciation of Machine Tools." Economic Inquiry, January 1996b, 57-77.

Pakes, A., and Z. Griliches. "Estimating Distributed Lags m Short Panels with an Application to the Specification of Depreciation Patterns and Capital Stock Constructs." Review of Economic Studies, April 1984, 243-62.

United Nations, Statistical Office of the United Nations. A System of National Accounts. Studies in Methods, Series F, No. 2, Rev. 3. New York, Department of Economic and Social Affairs, United Nations, 1968.

Taubman, P., and R. Rasche. "Economic and Tax Depreciation of Office Buildings." National Tax Journal, September 1969, 334-46.

Terborgh, G. Realistic Depreciation Policy. Washington, D.C.: Machinery and Allied Products Institute, 1954.

Triplett, J. E. "The Measurement of Inflation: A Survey of Research on the Accuracy of Price Indexes," in Analysis of Inflation, edited by R H. Earl. Lexington: Heath, 1975, 19-82.

--. "The Economic Interpretation of Hedonic Methods." Survey of Current Business, January 1986, 36-40.

--. "Hedonic Functions and Hedonic Indexes," in The New Palgrave, vol. 2, edited by J. Eatwell, M. Milgate, and R Newman. New York: Stockton, 1987, 630-34.

--. "Price and Technological Change in a Capital Good: Survey of Research on Computers," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 1989, 127-213.

--. "Hedonic Methods in Statistical Agency Environments: An Intellectual Biopsy," in Fifty Years of Economic Measurement, edited by E. R. Berndt and J. E. Triplett. 1990, 207-38.

--. "Measuring the Capital Stock: A Review of Concepts and Data Needs." Presented at the Conference on Research in Income and Wealth, Washington, D.C., June 1992.

--. "Depreciation in Production Analysis and in Income and Wealth Accounts: Resolution of an Old Debate." Economic Inquiry, January 1996, 93-115.

Waugh, E V. Quality as a Determinant of Vegetable Prices. New York: Columbia University Press, 1929.

Weitzman, M. L. "On the Welfare Significance of National Product in a Dynamic Economy." Quarterly Journal of Economics, February 1976, 156-62.

Winfrey, R. C. Statistical Analyses of Industrial Property Retirements, Ames, Iowa: Engineering Experiment Station, Bulletin 125, 1935.

Wykoff, F. C. "Economic Depreciation and the User Cost of Business-leased Automobiles," in Technology and Capital Formation, edited by D. W. Jorgenson and R. Landau. Cambridge: MIT Press, 1989, 259-92.

Young, A., and J. C. Musgrave. "Estimation of Capital Stock in the United States," in The Measurement of Capital, edited by D. Usher. Chicago: University of Chicago Press, 1980, 23-58.

DALE W. JORGENSON, Frederic Eaton Abbe Professor of Economics, Harvard University.
联系我们|关于我们|网站声明
国家哲学社会科学文献中心版权所有