5216.0 - Australian National Accounts: Concepts, Sources and Methods, 2000  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 15/11/2000   
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Capital stock

16.4 Capital stock estimates provide information about the stock of capital available in an economy at a particular point in time. Three measures of capital stock can be distinguished: gross, net and productive.

      • The value of an economy's gross capital stock is obtained by valuing each asset in use at the current price of a new asset of the same type, regardless of the age of the asset. It is calculated as the accumulation of past investment flows less retirements, at 30 June each year, before the deduction of any allowances for consumption of fixed capital.
      • Net (or economic) capital stock estimates are the written down values of an economy's gross capital stocks. They represent the net present values of the future capital services to be provided by the assets. The difference between the net and gross value of an asset is accumulated depreciation. Net capital stock is essentially a measure of wealth and is shown in an economy's balance sheet.
      • Productive capital stock estimates are derived by writing down each asset in accordance with its decline in efficiency due to age. If, for example, an asset is 75 per cent as efficient as a new asset of the same type, then the productive value of that asset is 75 per cent of the value of the new asset. Efficiency tends to decline with age, as older assets require more frequent and extensive maintenance and more replacement parts. Productive capital stock estimates are a measure of productive capacity and they form the basis for the measure of capital services required for productivity analyses.

Relationship between productive capital stock and net capital stock

16.5 Although the concepts of productive and economic capital are quite different they are intimately related: for any particular asset, given the real productive capital stock and a suitable discount rate we can determine the real economic (i.e. net) capital stock and, after reflation, the current price economic capital stock. The age-efficiency function (after being multiplied by a suitable scalar) defines how the flow of real capital services from an asset declines over an asset's life. The real economic value of an asset at any time can be calculated - given a discount rate - as the sum of discounted future real flows of capital services. Once the real economic values of an asset are determined over its lifespan an age-price function can be derived. The age-price function defines how the net capital stock of an asset declines as it ages in real terms. Unlike net capital stock, productive capital stock is a concept that is really only applicable to the stock of a single type of asset. It is best aggregated over different types of assets by using rental prices as weights. The resulting aggregate is then used to produce a volume index of capital services (see Chapter 27).

16.6 The scope of capital stock is defined by the coverage of gross fixed capital formation (see Chapter 15).

Consumption of fixed capital and capital services

16.7 Two flow concepts are relevant to capital stocks: consumption of fixed capital and capital services.

      • Consumption of fixed capital (COFC) represents the value of a capital asset that is 'used up' in a particular period. The real consumption of fixed capital of an asset in a period is the difference in the real economic value of the asset at the beginning of the period and at the end of the period. Consumption of fixed capital is based on the concept of the expected economic lifetime of an asset, and is designed to cover the loss in value due to normal wear and tear, foreseen obsolescence, and the normal amount of accidental damage which is not made good by repair. Unforeseen obsolescence is treated as a capital loss rather than as consumption of fixed capital.
      • Capital services reflect the amount of 'service' each asset provides during a period. For each asset, the services provided in a period are directly proportional to the asset's productive capital value in the period. As an asset ages and its efficiency declines so does the productive capital value and the services the asset provides. In equilibrium, the value of capital services is equal to the gross returns (or rentals) to owners of capital, i.e. the sum of COFC during the period and a return on the net capital stock of assets. The relationship between the capital services provided by an asset and the asset's productive value is fixed over the asset's life. However, this relationship varies from asset to asset and it depends on an asset's expected life, the discount rate, and the rate of decline in the asset's efficiency.

Relationship between consumption of fixed capital and the flow of capital services

16.8 Consumption of fixed capital is always less than the value of the capital services, since the return to the owner of the asset must also cover the interest (or capital) cost of holding the asset. That is, the value of the service has not only to cover depreciation but provide a return to the owner of the asset sufficient to cover the interest cost. More explicitly, in any given period, consumption of fixed capital is equal to the value of the capital services provided by the asset, minus the return to the owner of the asset.

Valuation of capital stock and consumption of fixed capital

16.9 Capital stock and consumption of fixed capital are presented in the Australian national accounts in current prices and as chain volume measures. The chain volume measures are referenced to the average values in the reference year, which is chosen to be the latest base year.

Capital stock measurement

16.10 There are two broad approaches to the measurement of capital stock: direct measurement and the perpetual inventory method (PIM).

16.11 Direct measurement, as the name implies, involves direct approaches to owners of fixed capital assets to obtain estimates of their capital stock. Such data have not been collected for Australia.

16.12 The PIM involves the compilation of a 'rolling' inventory of capital stocks; in any particular period investment in capital assets is added to stocks, and retired assets are deducted. To apply the PIM, the following are generally required:

      • the average length of asset lives, i.e. average of the length of time they are used in production;
      • the extent to which assets are retired before, on or after the average asset life for that asset - the retirement distribution. Alternatively, retirements can be expressed as a survival function;
      • the age-price function of assets (used to derive net capital stock estimates and estimates of consumption of fixed capital);
      • the age-efficiency function of assets (used to derive productive capital stock estimates);
      • gross fixed capital formation (GFCF) for the period for which the capital stock estimate is required and for periods prior to that period equal to the maximum life of the asset; and
      • price indexes for the entire timespan of GFCF.

Obsolescence and consumption of fixed capital

16.13 Obsolescence occurs when an event occurs which causes an otherwise useful asset to become less useful or useless. Examples include immovable assets at a remote mine site when the mine is worked out, a building that fails to meet new health and safety regulations, or, very commonly, technical innovation. As time passes technical innovation occurs, leading to the availability of assets that are superior in some way to assets previously available that performed a similar function. An example is a new model of computer that has superior performance to previous models, but is not commensurately more expensive. New, desirable software becomes available which only the new computers can support. Demand for the new, superior computers is strong while the demand for older-style computers declines sharply, and the older-style assets in service are retired before they are worn out.

16.14 Obsolescence is time-dependent, not age-dependent. All vintages of an older style asset suffer obsolescence at the same time. For many types of asset there is a history of regular technical innovation that leads purchasers to expect further innovations in the future. Computer equipment is an asset of this type. Purchasers of computer equipment can expect rapid technical innovation to make an asset bought today obsolete in a few years time. While computers might be expected to give relatively trouble free service for many years their economic lives are much shorter. As a consequence the values of assets such as computer equipment fall rapidly and their rate of COFC is high.

16.15 If obsolescence is foreseen then it is factored in by the owner in determining the asset's expected economic life, and hence its expected value and depreciation in future periods. Therefore, when the event causing the foreseen obsolescence occurs there is not an abrupt fall in the value of the asset. Foreseen obsolescence is included in COFC in the national accounts because it is an expected cost of production. If there is a loss in value of an asset due to obsolescence that is not foreseen then it should be recorded in the other changes in the volume of assets account and not in COFC. In general it is assumed in the Australian national accounts that all obsolescence is foreseen.

16.16 If proper account is taken of quality changes in the compilation of price indexes then they will reflect relative price falls when technical innovation occurs. As a consequence, if such price indexes are used to deflate capital formation of a type of asset that undergoes a technical innovation, the resulting volume estimates of older-style and new-style assets will be comparable because the price indexes used to deflate the current price values of the old- and new-style assets reflect the difference in quality between the two.

16.17 The age-price functions referred to above are in real terms; therefore, providing they do not change over time (due to the rate of foreseen obsolescence changing or changes in asset reliability, etc.), the same age-price function is applicable to both different vintages of the same asset type at any particular time or to any particular vintage of an asset type over time. For most asset types it is assumed that the age-price function is constant. There are some exceptions for which slowly changing economic lives are prescribed, and as a result the age-price functions of these asset types change slowly over time. In these cases it is the same suite of age-price functions that is applicable both to different vintages of the same asset type at any particular time and to any particular vintage of an asset type over time. Thus the same suite of age-price functions can be used to permit the aggregation of different vintages of the same asset type at a particular time to obtain estimates of net capital stock, or they can be used to calculate the change in value of assets over time - COFC - in volume terms.

16.18 It is evident from the foregoing that volume estimation is an essential first step in estimating capital services, net capital stock and COFC.

Age-efficiency, age-price and depreciation rate functions

Age-efficiency functions

16.19 There is a lack of empirical data about the shape of age-efficiency functions, and the choice is a matter of judgement. Although capital stock levels are sensitive to the shape of the age-efficiency function, average growth rates are not. (In fact, if real GFCF is held constant over time, the choice would have no impact on the capital stock growth rate, but it would affect the capital stock level.) The ABS has chosen to use hyperbolic functions, the same approach as that used by the US Bureau of Labor Statistics (BLS). That is, the efficiency of the asset declines by small amounts at first and the rate of decline increases as the asset ages.

16.20 Hyperbolic decline has the form:

Et =M - At
M - bAt
whereEt is the efficiency of the asset at time t (as a ratio of the asset's efficiency when new).

M is the asset life as per the Winfrey distribution (discussed below).

At is the age of the asset at time t.

b is the efficiency reduction parameter.

16.21 The efficiency reduction parameter b is set to 0.5 for machinery and equipment, and 0.75 for structures - the same parameter values as used by the BLS. The higher value for other buildings and structures redistributes efficiency decline to occur later in the asset's life, relative to machinery and equipment, the efficiency decline of which is distributed more evenly throughout the asset's life. For computer software, b is set to 0.5. For livestock, b is also set to 0.5. Clearly, a more accurate age-efficiency function and age-price function could be assumed by recognising that livestock are immature for a number of years before they begin service as mature animals. However such improvements compromise model simplicity and, as mentioned in paragraph 16.19, the improvements from doing so would be quite small. For mineral exploration b is set to 1, implying that there is no efficiency decline in exploration knowledge. The opposite is the case for artistic originals, where b is set to 0, implying straight-line efficiency decline.

16.22 Graphs 16.1 and 16.2 below show (i) the main types of age-efficiency functions and (ii) the age-price functions relating to each of the age-efficiency functions. When the hyperbolic functions for each of the possible lives of an asset are weighted together (as per the Winfrey distribution), the resulting average age-efficiency function resembles a logistic function with a point of inflection towards the end of its maximum life.



Age-price functions

16.23 Age-price functions are calculated using average age-efficiency functions and a real discount rate. The age-efficiency function describes the decline in the flow of capital services of an asset as it ages. Using the discount rate, the net present value of future capital services can be readily calculated. For instance, when multiplied by a suitable scalar, the first value of the age-price function represents the present discounted value of the capital services provided by an asset over its entire life. The second value of the age-price function represents the present discounted value of the capital services provided by an asset from the end of its first year until the end of its life. The third value represents the present discounted value of the capital services provided by an asset from the end of its second year until the end of its life, and so on. Age-price functions are normalised and adjusted for mid-year purchase, to allow for some consumption of fixed capital occurring in the first year. The ABS has chosen a real discount rate of 4 per cent, the same as that used by the BLS and which approximates the average real 10 year Australian bond rate.

16.24 When the net present values of the different assets are aggregated for a particular period, they form the net capital stock for that period.

Depreciation rate functions

16.25 In real terms, depreciation (or COFC) is the difference between the real economic value of the asset at the beginning of the period and at the end of the period. The depreciation rate function is calculated as the decline in the age-price function between assets of consecutive ages. When multiplied by a suitable scalar, it shows the pattern of real economic depreciation or COFC over an asset's life. Consumption of fixed capital for each vintage of each asset type is then aggregated to form the total consumption of fixed capital for that period. It can also be calculated as GFCF less the net increase in the net capital stock (i.e. GFCF less the difference between the net capital stock at the end of the period and at the beginning of the period).

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