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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.
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).
Consumption of fixed capital and capital services
16.7 Two flow concepts are relevant to capital stocks: consumption of fixed capital and capital services.
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).
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.
Age-efficiency, age-price and depreciation rate 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.
16.21 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.
16.1 AGE-EFFICIENCY FUNCTIONS
16.2 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.
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).