NEW METHODS FOR MEASURING CAPITAL by

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 Product 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. (Journal 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. 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 associated 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 primarily on the profile of relative efficiencies of assets of different ages. As the asset ages, the discounted 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 represent 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 independently, 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. 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 consider 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 }: