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Sources and methods The perpetual inventory method (PIM) 16.26 The steps involved in applying the PIM are summarised in diagram 16.3 below. 16.3 THE PIM PROCESS 16.27 The PIM is applied to volume estimates of GFCF at a detailed level (i.e. for a particular asset type for a particular industry in a particular institutional sector). Volume estimates of net and productive capital stock and consumption of fixed capital are compiled using vector multiplication. The product of two vectors results in a value for a particular period. The first vector represents the age-efficiency or age-price or COFC pattern from when the fixed asset is new to the end of its life. The second vector is always the GFCF series. Shifting the second vector (GFCF) one year at a time before multiplying with the first vector results in a time series of values of capital stock or consumption of fixed capital, depending on the vector used. 16.28 For instance, gross capital stock at the end of period t is the product of the survival function and GFCF vectors. The first element of the GFCF vector is the value for period t, the second element is the value is for period t-1, the third is for period t-2, and so on. The final element is the value for period t-m, where m is the maximum possible life of the asset. A survival function represents the probability that a fixed asset is still in service and is derived from the asset life distribution. When the asset is new, the survival probability is equal to 1, but as it ages the survival probability declines, until it reaches zero. At the end of its life the asset is assumed to have a zero scrap value (in practice, it is recognised that positive and negative scrap values can occur. However, no attempt has been made to quantify the net effect of these). The survival function can be constructed by subtracting, for each period, the probability of retirement in that period. 16.29 Productive capital stock is the product of the average age-efficiency function (AAE) and GFCF vectors. The AAE for a particular asset age is calculated as a weighted average of the efficiency functions for each possible length of life, using the probability of retirement as weights. 16.30 Net capital stock is the product of the age-price function and GFCF vectors. Age-price functions are calculated using the AAE and a real discount rate in the following way. The present discounted value of the future stream of capital services from when the asset is new until the end of its life gives the first value of an age-price function, the present discounted value of the future stream of capital services from when the asset is one year old until the end of its life gives the second value, and so on. Age-price functions are normalised and adjusted on the assumption that all of GFCF in a year occurs mid-year. 16.31 Consumption of fixed capital is the product of the depreciation rate function and GFCF vectors. The depreciation rate function is calculated as the decline in the age-price function between assets of consecutive ages. 16.32 Current price estimates at the most detailed level of estimation of gross capital stock, net capital stock and consumption of fixed capital are obtained by reflating the volume estimates. The price indexes used to reflate the volume estimates are the same as those initially employed to deflate GFCF, except that for capital stocks they are adjusted to an end year basis by averaging consecutive values of the price indexes. For reflated consumption of fixed capital, which is a flow concept, the price indexes are not adjusted to an end of year basis. The resulting elemental series at current prices are aggregated to the level published, while elemental volume measures are aggregated to form chain volume measures at the level published. Elemental estimates of capital stock satisfy the following identities:
16.33 Average age of the gross capital stock at the end of each year is another output of the PIM. Average age is the age at 30 June of past years' GFCF weighted by their proportions of the surviving gross capital stock. These calculations assume an average mid-year purchase. Current price gross fixed capital formation (GFCF) 16.34 The GFCF data required as input into the PIM are consistent with those published in Cat. no. 5204.0. A detailed description of definitions, sources and methods used for these estimates is presented in Chapter 15. The discussion is briefly reiterated in this section, and extended to include industry and institutional sector details. Machinery and equipment 16.42 Data on gross fixed capital formation for machinery and equipment are broken down by kind of economic activity, at the ANZSIC Division level, and into six major classes of machinery and equipment, namely:
16.43 Gross fixed capital formation on each of the six classes of machinery and equipment is estimated for each industry (or purpose category in the case of general government) in each institutional sector. The estimation procedure has two stages. In the first stage various data sources are used to make initial estimates of the breakdown of equipment expenditure for each industry in each sector. Chief among the data sources are the Survey of Private New Capital Expenditure (SPNCE) during 1997 for the above six categories, a survey of private new capital expenditure by detailed category in respect of 1987-88, data for the six categories from the Economic Activity Survey (which covers the whole economy except the general government sector) for every year from 1998-99, a survey of general government capital formation for the six categories in respect of 1994-95, quarterly estimates of the supply of imported and domestically-produced capital goods, and from 1994-95 the annual supply and use tables. In the second stage the initial estimates are adjusted to ensure consistency with both annual GFCF totals and total supply of the six categories of machinery and equipment. The adjustment is done using the RAS procedure (a residual allocation system - see Chapter 12 for further details). 16.44 In the case of computers and peripherals it has been assumed that there is no expenditure on this class of equipment before 1960, and that expenditure on computers rose gradually after that time until the first data observation for imports in 1978-79. Livestock 16.45 Estimates of the value of sheep and cattle that are used repeatedly or continuously to produce products such as milk and wool, or are used as breeding stock, are included in gross fixed capital formation. The scope of livestock and its data sources are discussed in more detail in Chapter 15. The main source of data on volumes is the ABS annual agricultural census, the results of which are published in Agriculture, Australia (Cat. no. 7113.0). Calculation of sheep and cattle numbers also relies on slaughtering and exports data from Livestock Products, Australia (Cat. no. 7215.0). Data on prices of animals are more difficult to obtain and a wide range of sources, including industry publications and direct sources are used. Intangible fixed assets Mineral exploration 16.47 Mineral exploration covers expenditure on exploration for petroleum, metallic minerals, construction materials, gemstones, and other non-metallic minerals, but not expenditure on successful bids for offshore petroleum leases. The scope of exploration activity in Australia is further discussed in Chapter 15. Data on mineral exploration expenditure are obtained from Mineral and Petroleum Exploration, Australia (Cat. no. 8412.0), while data for expenditure on successful bids for offshore petroleum leases are obtained from the Department of Industry, Science and Resources. The latter data are subtracted from the former. Data on exploration by commodity (other than for petroleum) for the period 1948-49 to 1965 are largely based on data compiled by the Bureau of Resource Sciences. 16.49 Estimates for the three components of computer software gross fixed capital formation, namely software developed in-house, purchases of customised software, and purchased 'off the shelf' software, are described in more detail in Chapter 15. 16.53 This item covers the production of originals of: films; television programs, both by television stations (own-account) and independent producers; music products, both by recording companies and music publishers; and books by publishers. Separate estimates are prepared for Film and independent television, Television (own-account), Music record companies, Music publishing, and Literary works. The scope of these items, along with their data sources, is described in more detail in Chapter 15. Ownership transfer costs 16.57 For the stamp duties and other government charges components of ownership transfer costs, estimates are derived using direct data on stamp duties available from each State government. Estimates for the lawyers' and real estate agents' fees components are based on taxation statistics and the results from the periodic surveys published in Real Estate Agents Industry, Australia (Cat. No. 8663.0) and Legal Accounting Services, Australia (Cat. No.8678.0). Price Indexes 16.58 The price indexes used in the PIM are essentially the same as those used in the preparation of chain volume estimates of gross fixed capital formation in the gross domestic product account (described in Chapter 15). However the latter, with the exception of intangible fixed estimates, are only compiled as chain volume estimates back to 1985-86. They are then linked to previously compiled constant price estimates at base years generally five years apart. In contrast, the volume estimates derived as a means of estimating the capital stock related statistics are compiled all in one piece. The same is true for the reflation to derive current price estimates and chain volume estimates. This process requires the compilation of continuous price indexes going much further back in time than those required for the gross domestic product account.
16.60 As with the GFCF data, the poorer quality of early data should be considered in the light of its small contribution to more recent year capital stock levels. Furthermore, unlike GFCF, most price indexes tend to be reasonably highly correlated over time. 16.61 The underlying price indexes from which the GFCF price indexes are compiled relate to a number of different base periods because of the length of the time series required. For example, ABS price indexes with base years of 1953-54, 1959-60, 1966-67, 1974-75, 1979-80, 1984-85 and 1989-90 are used, as well as non-ABS price indexes prior to 1948-49 which have earlier base years. Therefore, it is necessary to splice the price indexes with different base periods on the basis of relationships in overlapping periods. 16.62 Although only one price index series results for each item, it is a hybrid of several series. When the current price values of machinery and equipment purchased in 1949-50 are calculated for example, price indexes for the early 1950s are used which reflect the composition of GFCF in 1953-54. In the mid to late 1950s, price indexes which reflect the composition of GFCF in 1959-60 are used, etc. Machinery and equipment 16.63 Price deflators for machinery and equipment are compiled for the six equipment categories described above:
16.64 The six equipment deflators are used for all institutional sectors, industries and general government purpose classifications. They are constructed from a supply and use model which allows for the identification and treatment of imported components separate from the treatment of those components which are domestically produced. Price indexes from Import Price Index (Cat. no. 6414.0) are used to revalue the imported components, and price indexes from Price Indexes of Articles Produced by Manufacturing Industry (Cat. no. 6412.0) are used to revalue manufacturers' sales data. Current price and chain volume estimates of the supply of each of the six equipment categories are formed and used to derive implicit price deflators (IPDs) for the six equipment categories. The IPDs for four out of the six asset categories have been extended back to 1948-49 by linking on the total equipment deflator in 1984. The two asset types which have not been linked onto this deflator in 1984 are: computers, because the U.S. Bureau of Economic Analysis computer equipment price index is available back to the early 1960s; and motor vehicles, for which producer price indexes are available back to 1968 (and therefore the total equipment deflator has been linked onto this series in 1968). Livestock 16.65 Acquisition and disposal prices are collected separately for beef cattle (breeding stock), dairy cattle, and wool producing sheep. The GFCF price is then calculated as the unit acquisitions price less the disposals price using the chained based approach at this level of detail. Annual acquisition prices are obtained from ABARE. Disposal prices are estimated using quarterly ABS livestock slaughterings information, as the ratio of the total value of slaughterings to the total number of slaughters, and then annualised. Intangible fixed assets Computer software 16.66 There is no Australian software price index currently available, although several countries have initiated development work to construct such indexes, and several experimental indexes over a limited time span have been published. Statistics Canada has developed an intuitive software price index in the Canadian SNA Input-Output Tables, which declines by 6% a year. This estimate is constructed by observing the trend of software prices over time for popular PC software. The ABS has chosen to use this index for the time being. 16.67 Music - music originals are revalued using the wage cost index for Cultural and Recreational Services in Wage Cost Index (Cat. no. 6345.0). 16.70 From 1969-70 the price index used to revalue both mineral and petroleum exploration expenditure is that used to revalue exploration expenditure in the derivation of chain volume estimates of the gross value added of services to mining - see Chapter 24. This price index is composed of price indexes of inputs to mineral and petroleum exploration. For the years between 1948-49 and 1969-70 the IPD for GDP is used. These series are linked to form the mineral exploration index. Mean asset lives 16.71 The mean asset lives are the most important of the parameters used in the PIM. Together with asset life distributions (see paragraphs 16.95 to 16.103 below), and the age-efficiency functions, they determine when assets are retired from the gross capital stock, the net capital stock, and the rate of depreciation charged. Six main data sources are used to derive estimates of mean asset lives:
Changes in asset lives over time 16.72 Asset lives are influenced by a large number of variables, which may either increase or decrease asset lives over time. These variables include changes in rates of use, technological advances and quality changes. In the case of motor vehicles there is strong evidence that mean lives have increased over the past fifty years, and these increases have been incorporated in the perpetual inventory method (PIM) for estimating the capital stock. It is possible that the lives of other classes of assets have also changed, but there is no conclusive evidence to demonstrate that this has occurred. While the lives of particular classes of assets may change over time, the average life span of all capital equipment also changes as a result of the changes in the composition of capital formation. This effect has been captured to some extent by breaking expenditure on machinery and equipment down into six major classes. Since the 1960s there has been a steady increase in the use of computers, which in 1997-98 comprised about 12 per cent of capital formation on machinery and equipment. Computers are a relatively short lived item of equipment, and the increase in their use has had the effect of reducing average equipment lives. The increased use of computers and the increased lives of motor vehicles have offsetting effects, with the net impact on equipment lives differing between industries according to the relative weights of computers and motor vehicles in their machinery and equipment expenditure. In industries where motor vehicles form a high proportion of machinery and equipment expenditure, such as agriculture, average lives have increased, while for industries such as finance and insurance, where computers form a relatively high proportion of capital formation, average equipment lives have fallen. Machinery and equipment 16.73 Asset lives are estimated for the six classes of machinery and equipment. In calculating average asset lives, implicit tax lives (based on the inverse of the depreciation rates published in the 1997 Master Tax Guide) are used as a basic source of information. While implicit tax lives may change over time, they are regarded as being of insufficient accuracy to calculate changes in economic lives over time. They are, however, industry based and comprehensive in coverage. In principle they are based on industry information about the actual service lives of machinery and equipment. Nevertheless, information from other sources suggests that tax lives are, in general, shorter than economic lives, and additional sources have been used to estimate the actual economic lives of the various types of machinery and equipment.
Other buildings and structures 16.80 The estimated average lifespan of other buildings and structures (including alterations and additions) are given in table 16.5. These estimates are based on the findings of Walters and Dippelsmann, and a detailed dissection of the mean life of other buildings and structures into new buildings, construction (other than building), alterations and additions, and a weighted average were reported in table 22.1 in the previous edition of Australian National Accounts: Concepts, Sources and Methods. These estimates have been checked against data on the age of buildings demolished in the Sydney and Melbourne central business districts over a ten year period. The Sydney and Melbourne data broadly support the age estimates used by Walters and Dippelsman, giving an average age at demolition of 62 years. The short time span for which data are available and the relatively small number of buildings demolished over that period do not permit any significant conclusions to be drawn as to whether building lives have been increasing or decreasing over time. It can be argued, a priori, that as a result of economic and population growth the use of core infrastructure becomes more intensive (i.e. the flow of services from that infrastructure increases) and that, all things being equal, the life span of those facilities would be reduced. However, in the absence of clear empirical evidence to support that proposition, the asset lives used by Walters and Dippelsman have been retained. 16.81 Taxation lives are considered too short, and lacking in discrimination between different industries and types of buildings. Unpublished data used in compiling Building Activity, Australia (Cat. no. 8752.0) were obtained showing separately new work and alterations and additions for different types of buildings. Alterations and additions are assumed to have an average asset life about half that of new work, in that they can occur at most stages in the life of the primary building. Information on types of other construction for the private sector is obtained from Engineering Construction Activity, Australia (Cat. no. 8762.0). Estimates are finalised on a subjective basis, taking into account lives used in other OECD countries, accounting estimates, and estimated proportions of new buildings, alterations and additions and non-building construction. 16.82 For public corporations, separate investigations are undertaken for electricity, gas and water; transport and storage; communication; accommodation, cafes and restaurants, cultural and recreational services; and personal and other services. Mean lives for public corporations are also reported separately in table 16.5. Together, these industries account for around 90 per cent of public corporations GFCF. For other industries, the estimates of private sector asset lives are used. 16.83 Other buildings and structures consists mostly of offices, schools, hospitals and roads. The average life of total other buildings and structures is estimated to be 54 years, with new government buildings assumed to have the same average life as private commercial buildings of 65 years. As with private commercial buildings, the evidence as to whether the average lives of buildings are changing over time is inconclusive, and lives are assumed to remain constant over time. For non-dwelling construction on roads the mean asset lives used by Walters and Dippelsman, in their capital stock estimates published in 1985, have been retained. Dwellings 16.84 The estimates used by Walters and Dippelsman in 1985 have been retained, as no more recent information is available. For each type of dwelling, it is assumed that there has been no change in mean asset life over time. However, the composition of dwellings by type of structure has been changing over time. Ownership transfer costs 16.85 The treatment for ownership transfer costs in the PIM is unique: these costs are depreciated instantaneously. Effectively the GFCF is fully recorded as consumption of fixed capital in the same period. This treatment means that the effective life of ownership transfer costs is zero.
Livestock 16.86 Information about mean asset lives of breeding and dairy cattle, and wool producing sheep, are obtained from several industry bodies (Bureau of Rural Sciences, Woolmark Company, Dairy Farmers Corporation, and Meat and Livestock Association). Asset lives used are: breeding cattle stock - mean 7 years; dairy cattle - mean 10 years; and sheep for wool - mean 6 years (see table 16.6 below). Intangible fixed assets Computer software 16.87 It is important to distinguish between the different types of software because they are known to have different asset lives, partly due to the different lives of mainframe and personal computers. The software 'mix' has also been changing over time, in favour of PC-based software. 16.90 Music - general information about the life cycle of typical Australian music titles is obtained from the Australian Record Industry Association (ARIA). Indications point to an average life of two years and a maximum life of five years. However, detailed information is not obtained from ARIA's membership to verify the accuracy of these indications. 16.93 Asset lives for mineral exploration are assumed to coincide with mine and oilfield lives. These are derived indirectly using economic demonstrated resources (EDR) from the balance sheets. First, average annual production for each commodity is divided into its EDR to derive the asset life for each commodity. Using exploration expenditure proportions for each commodity as weights, the average lives for the commodities are aggregated to an average mine life for all commodities. The average mine life used for mineral exploration is 34 years (see table 16.6).
Asset life distributions 16.95 The PIM is applied at a relatively high level of aggregation, with each component of GFCF consisting of a large variety of individual assets, each with its own life span. Even within particular types of assets, variations in lives will occur because of differences in the rate of use, maintenance etc. Because of the lack of recent empirical evidence, asset life distribution curves developed by Winfrey (4) in 1938 are used. The Winfrey S3 is a bell-shaped symmetric curve, with approximately three quarters of assets retiring within 30 per cent of the mean asset life. It is empirically based, related to variations in lives of particular types of assets, and is consistent with the general presumption that the expected life for a particular asset will follow an approximately normal distribution.
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