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Data sources and methods

Australian System of National Accounts: Concepts, Sources and Methods
Reference period
2020-21 financial year

The scope of measurement

19.29    The growth accounting framework is initially developed for measuring productivity in the private sector of the economy. As such, MFP statistics relate to selected industries rather than the whole economy. Ideally, MFP measures should cover all market economic activities, but this is only possible if all of the necessary data are available.

19.30    For this reason, official MFP estimates internationally are confined to particular industries in the private sector, with varying degrees of coverage depending on data suitability and availability. Statistics Canada terms their coverage as the business sector, and Statistics New Zealand labels their coverage as the measured sector. In Australia, the ABS labels the relevant group of industries as the market sector. This grouping is used to present economic statistics including MFP estimates in the ASNA.

The market sector

19.31    The market sector comprises sixteen industries under the Australian and New Zealand Standard Industrial Classification, 2006 (ANZSIC06); that is, from ANZSIC06 Divisions A to N, plus Divisions R and S. The detailed industries included in the market sector are as follows:

ANZSIC
DivisionIndustry
AAgriculture, Forestry and Fishing
BMining
CManufacturing
DElectricity, Gas, Water and Waste Services
EConstruction
FWholesale Trade
GRetail Trade
HAccommodation and Food Services
ITransport, Postal and Warehousing
JInformation, Media and Telecommunications
KFinancial and Insurance Services
LRental, Hiring and Real Estate Services
MProfessional, Scientific and Technical Services
NAdministrative and Support Services
RArts and Recreation Services
SOther Services

19.32    Under the Australian and New Zealand Standard Industrial Classification 1993 (ANZSIC93), the market sector consisted of twelve industries (Divisions A to K and P). Coinciding with the implementation of ANZSIC 2006, the ABS expanded the scope of the market sector to include four new services industries (Divisions L, M, N and S – see above). The expanded definition improves relevance in two key respects: it reflects the growing influence of services industries in the economy; and improves economic coverage.⁸⁰

19.33    While the new definition of market sector results in much improved coverage of the total Australian economy, the time span available for constructing meaningful productivity indicators is shortened. Productivity measures for the expanded coverage commence in 1994-95, when suitable output measures for the newly added industries become available. Prior to 1994-95, volume estimates of gross value added in Divisions L, M, N and S were derived (in part) using input indicators (such as hours worked).

19.34    Since the 2009-10 issue of ASNA, the ABS MFP statistics have been presented in line with the new definition of the market sector. As such, these productivity measures are based on significant changes in coverage, and do not represent updated estimates to past releases. The current estimates are not directly comparable to those published in past releases due to significant changes in coverage.

Twelve selected industries

19.35    The time span available for constructing meaningful productivity indicators is shortened while the expanded definition of the market sector results in much improved coverage of the total Australian economy. To accommodate user requirements for longer time series of MFP statistics, ABS continues to compile aggregate MFP statistics for the group of twelve selected ANZSIC06 industries (divisions A to K and R). Commencing 1973-74, this aggregate is the nearest approximation to the earlier definition of the market sector grouping under ANZSIC93, and is useful for analysing productivity performance from the perspective of a longer time series.

19.36    Both the market sector and twelve selected industries include all institutional sectors, as well as general government attributable to those industries. Conceptually, there is a strong justification for netting out the general government component of each industry because general-government activity is mainly not marketed. It has not been removed because of the difficulty of excluding general government components from outputs and inputs. In any case, general-government activity only accounts for a very small portion of most market-sector industries.

The non-market sector

19.37    The industries included in the 'non-market sector' are:

  • Public Administration and Safety;
  • Education and Training;
  • Health Care and Social Assistance; and
  • Ownership of Dwellings.

19.38    The production of these government-dominated industries largely comprises those goods and services which fall within the production boundary of the national accounts but are not for sale, or not sold at full market prices. Examples are the provision of government services which relate to the community as a whole, or for which no charge (or a purely nominal charge) is made. Ownership of dwellings is excluded from the market sector because no employment is associated with it.

19.39    Aggregate measures of labour productivity (gross value added per hour worked) are published for the total of all industries (including the non-market sector); for the market sector; and for twelve selected industries. Indexes of gross value added per hour worked are also published for each individual industry in the ASNA.

Endnotes

  1. As at 2010-11, the market sector represented approximately 80 per cent of total chain volume gross value added at basic prices. By comparison, the twelve selected industries aggregate represented approximately 60 per cent.

The measurement of output

19.40    By the SNA definition, output consists of those goods and services that are produced within an establishment (or plant) that become available for use outside establishment, plus any goods and services produced for own final use. This definition of output is equivalent to the gross output definition in the productivity measurement.

19.41    The gross output definition is preferred because it is a natural output concept and consistent with the traditional production theory which links output to primary as well as intermediate inputs.⁸¹ Hulten argues that gross output 'is the correct concept for measuring the structure of production'.⁸² 

19.42    To facilitate the comparisons of productivity performance across different industries, a value-added concept is developed in the productivity measurement. This definition is based on the assumption that the components of value added are separable from that of intermediate inputs. The assumption of value-added output at the industry level also implies a specific way that productivity growth affects the usages of primary and intermediate inputs.⁸³

19.43    At an aggregate level, the value-added concept is more appropriate as it needs to remove inter-industry transfers in aggregating industry outputs to derive the total output of the component industries. In this context, the aggregate value-added output definition does not contradict the gross output concept at the corresponding disaggregate level.

19.44    The implications of alternative output measures on the interpretation of MFP measures are discussed in paragraphs 19.25-19.26. 

19.45    There are three output measures in the ABS productivity statistics:

  • industry gross output;
  • industry value added; and
  • aggregate value added.

Industry gross output

19.46    Gross output refers to the value of goods and services produced in the accounting period, including production that remains incomplete at the end of that accounting period. While this definition is straightforward for goods-producing industries, some clarification of treatment is useful for service industries such as Transport, Postal and Warehousing, Wholesale Trade and Retail Trade:

  • The gross output of transport services is measured by the amounts receivable for transporting goods or persons. That is, the transporting from one location to another is a process of production and is referred to as a transport margin that adds to the quality from the same good as it changes location;
  • The activity of storage relates to the 're-transporting' of goods from one point in time to another (as opposed to locations in the instance of transport services).  So the increase in price due to storage reflects storage costs incurred as a production process;
  • The main output of the wholesale and retail trade industries is the value of the service provided in selling goods (i.e. goods purchased and resold are not treated as part of intermediate consumption). The value of the service is equal to the trade margins realised on the goods sold.

19.47    The measurement of these services at basic prices is analogous to that for goods producing industries: output at basic prices is the value of the trade margins, including the value of any subsidies received, and excluding taxes on production of the service.

19.48    Much of the gross output of finance and insurance industry needs to be estimated indirectly. In the ASNA, FISIM is an output of banks, other depository corporations, central borrowing authorities and securitisers. For banks and other depository corporations it is the sum of the imputed service charges for both borrowers and depositors while, for central borrowing authorities and securitisers, it is the sum of the imputed service charge for borrowers. Similarly, the value of the insurance service charge, which forms part of the output of insurance and pension funds, is estimated indirectly from the total receivables and payables of insurance enterprises, including the income accruing from the investment of technical reserves.

Intermediate inputs

19.49    Intermediate inputs are the value of goods and services consumed as inputs into the production process. These goods and services may be transformed or completely used up. Capital leased from other industries is also included in intermediate inputs and recorded in services. The boundary between consumption of intermediate inputs and gross fixed capital formation is not always clear. In general, intermediate inputs are goods and services that are immediately transformed or used up in the process of production within one year while gross fixed capital formation involves the acquisition of capital assets which contribute to production for more than a year. Also included in intermediate consumption is the value of all goods and services used as inputs into ancillary activities.

19.50    The separation of intermediate inputs into the three categories – energy, materials and services can be useful for analysis of the effects of changes in the input mix on output growth. For example, increases in the proportion of services intermediate inputs could reflect growth in out-sourcing. Separate deflators are used to deflate each input to derive a Laspeyres volume index for intermediate inputs. 

19.51    The intermediate inputs indices for energy, materials and services and their respective shares are sourced from the SUT compiled by the ABS. The classification of supply–use products into these three categories is provided in Appendix 2 of the KLEMS Information paper. Data for the three non–market industry divisions (i.e. Public administration and safety, Education and training, Health care and social assistance) are excluded.

19.52    The main advantage of deriving the indices and shares for energy, materials and services using this method is to control for heterogeneity in both the prices and volumes of the components and to recognise more explicitly that the way in which each of these components contributes to production differs. A key development in the SUT has been the wider application of the double deflation method, that is, real output and real intermediate inputs are derived separately for most industries. By sourcing more specific price deflators, the approach enables improved volume estimation, particularly for intermediate inputs.

19.53    The SUT is a powerful tool to compare and contrast data from various sources and improve the coherence of the economic information system.  It reconciles the supply of products within the economy within an accounting period with their use for intermediate consumption, final consumption, capital formation, and exports.  They permit an analysis of markets and industries and allow productivity to be studied at this level of disaggregation.  The SUT tracks the production and consumption of 301 groups of products across 67 groups of industries in a time series stretching back to 1994–95.  These groupings facilitate the aggregation of product groups into energy, materials and services.  Shown in Table 3 is a representation of the intermediate use component of the SUT.  The tables are calculated on both a current price basis (for estimating the KLEMS cost shares) and volume basis (for deriving the KLEMS indices for energy, materials and services).

Industry value added

19.54    Industry value added is equal to the total value of gross outputs at basic prices less the total intermediate consumption at purchasers' prices.

19.55    A key development in the supply and use tables has been the wider practice of using the double deflation method; that is, real gross value added and real intermediate inputs are derived separately for most industries. By sourcing more specific price deflators, the approach enables improved volume estimation, particularly for intermediate inputs.

Aggregate outputs

19.56    The aggregate output for the market sector (or twelve selected industries) is the sum of gross value added produced by the component industries at basic prices. Basic prices are the prices producers receive and exclude taxes less subsidies on products. This valuation is consistent with the recommendations of the 2001 OECD Manual - Measuring Productivity, which states that:

From the perspective of productivity measurement, the choice of valuation should reflect the price that is most relevant for the producer's decision making, regarding both inputs and outputs. Therefore, it is suggested that output measures are best valued at basic prices.⁸⁴

19.57    The basic price valuation aligns the concept of production with that of factor incomes which include other taxes less subsidies on production and imports. Since industry value added is also at basic prices, the industry shares of aggregate output to sum to unity. Moreover, valuation consistency is necessary for additive growth accounting between industry and aggregate productivity measures. 

19.58    The aggregate output measure for calculating the economy wide labour productivity, i.e. GDP per hour worked, is valued at purchasers' prices, inclusive of taxes less subsidies on products.

Productivity growth cycles

19.59    Productivity growth accounts are most useful when presented over productivity growth cycles. MFP growth cycles are defined as periods between selected peak deviations of annual MFP from their corresponding long-term trend estimates. MFP is widely used as an indicator of technological change. In the short to medium term, MFP estimates are subject to data limitations and assumptions, such as variations in capacity utilisation, economies of scale and scope, reallocation effects of capital and labour, and measurement error.

19.60    Variations in the utilisation of inputs would ideally be measured as changes in inputs when MFP is calculated. However, due to current data limitations, reliable information for adjusting capital service flows for variation in utilisation are not available.⁸⁵

19.61    Growth cycle averages, within the growth account not only scale the growth according to its contribution, average growth rates between growth-cycle peaks dampens cyclically related distortions like capacity utilisation rate. To facilitate this, the growth cycle peaks need to be selected. They are chosen with reference to peak deviations which are determined by comparing MFP estimates with their corresponding long-term trend. The peak positive deviation between these two series is the primary indicator of a growth-cycle peak. General economic conditions at the time are also considered. In this way, most of the effects of variations in capacity utilisation and much of the random error is removed. However, average growth rates may still reflect any systematic bias resulting from the methodology and data used.

19.62    The ABS publishes growth cycles in both the ASNA and in Estimates of Industry Multifactor Productivity. They are available for the market sector, 12 selected industries, and each market sector industry.⁸⁶

19.63    In addition, the approach used to identify growth cycle peaks has been strengthened to ensure that growth cycle peaks are resilient to revisions to upstream data sources by adopting a multiple filter approach. In addition to the Henderson 11 filter, the Hodrick and Prescott⁸⁷, and Christiano and Fitzgerald⁸⁸ filters are used. The multiple filter approach copes better with volatility for lower aggregates (like industry) than any single filter.

19.64    For industry growth cycles, a peak is considered robust if deviations equal to, or greater than one percentage point are identified by all three filters. Where identified robust peaks were found less than four years apart (peaks inclusive), additional rules were required to obtain growth cycles of a reasonable length. Additional criteria include:

  • Choosing the peak with the relatively largest deviation;
  • If the difference in deviation is negligible, choose the peak which produces the longer cycle;
  • If the two adjacent peaks have a similar deviation size and suggest a similar cycle length, assess with the prevailing macro-economic conditions;
  • Consider the ‘nearly’ robust peaks (i.e., suggested by the three filters but with a deviation of less than one percentage point) next to neighbouring troughs; and
  • Test for deterministic trend.⁸⁹

19.65    Growth cycles are also available for industries that have long periods of decline in MFP growth. Peaks in this context still represent a deviation from a (declining) trend, and thus indicate where an industry has halted the decline in productivity for a short period. This phenomenon can be seen in Mining and Electricity, gas, water and waste services, and Rental, hiring and real estate services.

Estimates of state productivity

19.66    The method adopted to estimate experimental State Multifactor productivity (MFP) - output produced per unit of combined inputs of labour and capital - aligns with the concepts and definitions used for MFP industry and market sector aggregates.

19.67    State output and experimental capital stock data is sourced from Australian National Accounts: State Accounts while labour inputs are sourced from Labour Force, Australia. State output is defined as Gross Value Added (GVA) in chain volume terms while labour inputs are defined as hours worked.

19.68    A number of simplifying assumptions have been adopted in addition to those adopted at the national level. Where State level data is unavailable, national industry proportions are applied to impute the missing values:

  • National inventories are allocated to States using State current price GVA proportions for the stock of inventories, as a State dimension is not available. The ABS also compared allocations using estimated resident population proportions and found that the State MFP aggregates were not sensitive to either choice.
  • To separate State by industry combined gross operating surplus and mixed income (GOSMI) into its components, gross mixed income (GMI) is estimated using the same industry’s GMI proportion in GOSMI at the national level. GMI was then split into income attributable to capital and labour using the same method to impute labour and capital shares of GMI at industry national level.

19.69    Rental prices by State by industry are imputed using the national industry asset rental prices. This method assumes there is no variation in price between the States for any given asset in a given industry for the same year. For example, the rental price of other transport equipment in wholesale trade is assumed to be the same across all States and territories. This simplifying assumption is not expected to distort rental prices significantly because, in estimating state capital stock, the nationally assumed asset lives (and therefore depreciation rates), and GFCF price indexes were applied to the same assets at State level. Importantly, for any given asset, variations in the rental prices between industries are completely captured under this method.

Data sources

19.70    National accounts data constitute the source of output measures required by a variety of productivity measures. Output data for the annual MFP statistics are sourced from the Supply Use tables which are used as the key framework for balancing national accounts at the ABS. The industry gross output is the basic ingredient of output measures. Industry gross output equals value added based output plus intermediate inputs and is used in the KLEMS growth accounting framework. 

19.71    Chapter 9 describes the definitions of gross output, intermediate inputs and gross value added in detail, and Tables 9.1 to 9.32 outline the data sources and methods used in the estimation of each of these for each industry. For the years from 1994-95 up to the year previous to the latest year, these estimates have been compiled using Supply Use tables and are in balance with the expenditure estimates. The main data source for non-financial corporations and non-profit institutions serving households (NPISH) in the annual benchmarks is the Annual Industry Survey (AIS), the results of which are published in Australian Industry.

Endnotes

  1. Balk, Bert M. (2010) 'An Assumption-free Framework for Measuring Productivity Change', The Review of Income and Wealth, Vol. 56, Issue 1 (June), pp.224-256.
  2. Hulten, Charles R. (1992) 'Accounting for the Wealth of Nations: The Net versus Gross Output Controversy and its Ramifications', Scandinavian Journal of Economics, 94 (Supplement), pp.9-24.
  3. Bosworth, B.P. and J.E. Triplett (2003) Services Productivity in the United States: Griliches' Services Volume Revisited, Washington, DC: Brookings Institute.
  4. OECD (2001) OECD Productivity Manual: A Guide to the Measurement of Industry Level and Aggregate Productivity Growth. Paris:  Organisation for Economic Co-operation and Development (OECD), p.77.

  5. Changes in capital utilisation rates can be modelled using potential output and various employment rate indicators. However, the results are sensitive to the choice and approach taken. For example, see the article Variations in the Utilisation of Productivity Inputs, Nov 2020.

  6. Cyclical fluctuations vary across industries. For example, see Barnes, P. (2011),  Multifactor Productivity Growth Cycles at the Industry Level, Productivity Commission Staff Working Paper and the ABS Feature article: Experimental Estimates of Industry value added growth cycles.

  7. Hodrick, R.J. and Prescott, E.C. (1997) “Postwar U.S. Business Cycles: An Empirical Investigation”, Journal of Money, Credit and Banking, 29, pp. 1–16

  8. Christiano, L. J., and T. J. Fitzgerald. (2003) “The band pass filter”, International Economic Review 44: 435-465

  9. For example, the Augmented Dickey-Fuller test provides evidence whether a series has a deterministic trend or unit root and, thus, the order of integration of the series.

The measurement of capital input

19.72    The measurement of capital input is concerned with estimating the contribution of capital to the production process; that is, the flow of capital services from the capital stock used in the production process. Capital services have both quantity and price dimensions. The quantity of capital services represents hours a machine is used or months a building is occupied. The price dimension, called the rental price, represents an hourly rate for using the machine or a monthly rate for occupying a building.   

Productive capital stock and quantity of capital services

19.73    The quantity of capital services is estimated by assuming that capital services produced by an asset are proportional to the value of productive capital stock of the asset; that is:

    \(\large K_t = u_t PKS_t\)

where \(K_t \)is the quantity of capital services, and \(PKS_t \)is the productive capital stock and \(u_t\) is the capacity utilization rate.

19.74    The capacity utilization rate is assumed to be constant over time. This assumption has two implications. First, as \(u_t\) is constant and invariant to time, a change in the quantity of capital services delivered from any given capital asset is tantamount to a change in its productive capital stock. Second, variations in the utilization of the capital stock are not accounted for in the estimation of its capital services, and as a consequence changes in the capital services over time may reflect the impact of short-term business cycles, other than movements of capital input.

19.75    The productive capital stock estimates are derived from data on gross fixed capital formation (except inventories and land), using the PIM. The essence of this method is to transform all capital assets of different vintages into equivalent efficiency units and then add them up into an estimate of the productive capital stock. Chapter 14 provides a full description of the procedures used to derive the productive capital stock. Chapter 10 provides a full description of the data sources and procedures used to compile estimates of gross fixed capital formation.

Imputing rental prices

19.76    In estimating the value of labour services, statisticians can directly observe labour rental prices as wage rates paid to workers. In the case of capital however, the rental prices for capital have to be imputed. The rental price reflects the price at which an investor is indifferent between two alternatives:

  1. earning a nominal rate of return on a different investment; and
  2. buying a capital asset, renting it out, collecting rent and selling it in the next period. 

19.77    A standard specification for the capital rental price in the absence of taxes is the arbitrage equation⁹⁰:  

     \(\large P_j,_{t-1}(1+i_t) = r_{j,t}+(1-δ_j)P_{j,t}\)         - - - - - - - (19.1)

where \(i_t\) is the nominal interest, \(P_{j,t-1}\) is the acquisition price of capital asset \(j\) at the beginning of the period, \(r_{j,t}\) is the rental price, \(P_{j,t}\) is the price of capital asset j at the end of the period and \(δ_{j,t}\) is the rate of economic depreciation.

19.78    This can be rearranged into the expression:

    \(\large r_{j,t}=i_tPj_{,t-1}+δ_{j,t}P_{j,t}- \pi _{j,t}\)         - - - - - - - (19.2)

where \(\pi_{j,t} = P_{j,t} - P_{j,t-1}\) is the asset-specific capital gains term.

19.79    Equation (19.2) shows that the capital rental price consists of three components: the rate of return to capital, the depreciation rate and the capital gain or loss due to revaluation. The industry dimension is supressed here.

19.80    When tax considerations are given to the measurement of capital rental prices (both capital income taxes and indirect business taxes), the tax-adjusted rental price equation becomes:

    \(\large r_{i,j,t}=T_{i,j,t}(i_{i,t}P_{i,j,t-1}+δ_{j,t}P_{i,j,t}-π_{i,j,t})+x_{i,t}P_{i,j,t-1}\)         - - - - - - - (19.3)

where \(i\) indexes industries, \(T_{i,j,t}\) is the income tax parameter and \(x_{i,t}\) is the effective net indirect tax rate on production. The description of data sources for constructing the tax parameter is provided in Annex C.

19.81    The rate of return to capital \(i_t\) can be estimated by either endogenously or exogenously. Under the endogenous approach, the total value of capital services in each industry is assumed to be equal to the compensation for all assets in that industry. The resulting internal rate of return exhausts capital income and is consistent with constant returns to scale. The nominal rate of return is the same for all assets in an industry but may vary across industries.

19.82    In the case of the exogenous approach, the nominal rate may equal the Treasury bond rate, or the dividend yield on a stock index. This method allows the value of capital income to deviate from property compensation, assuming imperfect competition and non-constant returns to scale. For a detailed discussion of these two alternative methods and associated sensitivity analysis, see Appendix 2 Sensitivity Analysis of Capital Inputs, in the Information paper, Experimental Estimates of Industry Multifactor Productivity.

19.83    The ABS follows the endogenous method in producing its official productivity estimates. For the corporate sector, iit, is solved for all assets in each industry by assuming that gross operating surplus, \(GOS_{it}\) equals the rental price multiplied by the real productive capital stock in each industry:

    \(\large GO{S_{i,t}} = \sum\limits_j {{r_{i,j,t}}{K_{i,j,t}}}\)         - - - - - - - (19.4)

and substituting for the rental price in equation (19.4) giving:

    \(\large GO{S_{i,t}} = \sum\limits_j {{K_{i,j,t}}\left( {{T_{i,j,t}}\left( {{i_{i,t}}{P_{i,j,t - 1}} + {\delta _j}{P_{i,j,t}} - {\pi _{i,j,t}}} \right) + {x_{i,t}}{P_{i,j,t - 1}}} \right)}\)         - - - - - - - (19.5)

so

    \(\large {i_{i,t}} = \frac{{GO{S_{i,t}} - \sum\nolimits_j {{K_{i,j,t}}\left( {{T_{i,j,t}}\left( {{\delta _j}{P_{i,j,t}} - {\pi _{i,j,t}}} \right) + {x_{i,t}}{P_{i,j,t - 1}}} \right)} }}{{\sum\nolimits_j {{K_{i,j,t}}{T_{i,j,t}}{P_{i,j,t - 1}}} }}\)         - - - - - - - (19.6)

19.84    To prevent negative rental prices, the ABS imposes a floor limit on the internal rate of return of CPI plus 4 per cent; otherwise, the endogenous rate is used.

19.85    The depreciation of a capital asset measures the change in its real economic value during the accounting period. The depreciation rates are derived using asset age-price profiles. The age-price profiles are constructed by using corresponding age-efficiency profiles, multiplied by a suitable discount rate (the ABS chooses a real discount rate at 4 per cent). See Chapter 14 for the detailed description of age-efficiency and age-price profiles and their roles in constructing various capital components.  

19.86    The capital gain or loss due to revaluation can be calculated as an asset-specific deflator or a general deflator. As defined in equation (19.3), the asset-specific capital term is used and calculated as the percentage change in the value of the asset in time t-1 relative to its value in time t. Alternatively, \(π_t\) can be replaced by a general price deflator such as the consumer price index. The former is preferred because it is able to account for the large changes in relative prices across heterogeneous asset classes and therefore reduces measurement errors. However, the disadvantage of using asset-specific deflators is that it often introduces volatility into the rental price equation. 

19.87    The elemental capital inputs are compiled at a detailed level. There are capital input measures for up to 16 asset types for the corporate and unincorporated entities for each of the 16 ANZSIC industry divisions that comprise the market sector. For each capital input there is a volume indicator of the flow of capital services, and a rental price that is used to weight the service flow with the service flows of other capital inputs. 

Capital service flows for fixed assets

19.88    The estimates of fixed assets from the PIM that are used to derive MFP are:

  • machinery and equipment: computers and computer peripherals; electronic and electrical machinery and communications equipment; industrial machinery and equipment; road vehicles; other transport equipment; and other equipment;
  • non-dwelling construction;
  • ownership transfer costs of non-dwelling construction;
  • intellectual property products: computer software; research and development; mineral and petroleum exploration; and artistic originals (Film and TV; music; and literary);
  • orchards, plantations and vineyards; and
  • livestock.

19.89    Ownership transfer costs relating to non-dwelling construction are allocated to industry using industry proportions of chain volume non-dwelling construction by industry. This approach assumes that the proportion of ownership transfer costs to non-dwelling construction at a point in time does not vary between industries.

Inventories

19.90    Volume estimates for the stock of inventory items are obtained for Divisions A to I (see Chapter 10 for more details). They are non-capitalised assets that are used up in the productive process and collected according to three categories:

  • inventories of raw materials, including materials and fuels, spare parts designated for use in fixed assets, containers and packaging materials. Inventories of fuels for sale are included in inventories of finished goods;
  • inventories of work-in-progress, including partially processed or fabricated goods which will be further processed prior to sale, and general work-in-progress less payments billed. Prepayments are excluded;
  • inventories of finished goods, including goods manufactured or processed which are ready for sale, goods purchased from other businesses which are ready for resale without further processing, and fuels for sale. Hired goods, inventories of land, and rented or leased buildings are excluded.

Land

19.91    Land can be further classified as either agricultural (for ANZSIC Division A) or non-agricultural (for the other ANZSIC divisions). Volume estimates of agricultural and non-agricultural land and the corresponding rental prices are constructed separately.

19.92    The volume estimate for agricultural land is derived starting with a nominal estimate obtained from the National Balance Sheet in the ASNA. In particular, the value of 'Rural' land in the reference year is used. As there is no suitable price index for agricultural land, its volume is assumed to be constant over time. The estimates of land values are discussed further in Chapter 17.

19.93    Similarly, a volume estimate of non-agricultural land is derived starting with a nominal estimate of the market sector's non-agricultural land in the reference year. A benchmark estimate is obtained from the National Balance Sheet by multiplying total 'Commercial' and 'Other' land by the proportion of the stock of non-dwelling construction in the market sector. This estimate is then split by industry proportionally using the productive capital stock of non-dwelling construction in the reference year. Then for a given industry, the volume estimate is constructed by assuming that its growth rate is half the growth rate of the industry's real productive capital stock of non-dwelling construction.

19.94    To calculate the rental prices for land, proxy price indicators are used as suitable land price indexes are not available. For agricultural land, the total investment deflator for Agriculture, forestry and fishing is used for the years prior to 1995-96, and the All groups CPI thereafter. For non-agricultural land, the index is based on the weighted aggregation of commercial and industrial rent indexes for Australia's main capital cities, provided by a private sector contractor.

Operating leases and finance leases

19.95    The ABS classifies the use of capital as an intermediate input of the lessee when the capital is rented under an operational lease arrangement from a firm primarily operating in another industry. For example, a construction company may lease a crane from the rental and hiring industry, which is recorded as a service component in the intermediate inputs of the lessee and as capital services held by the lessor. If the proportion of the capital that is leased is changing it can affect value added productivity growth estimates. A reduction in the percentage of capital held within an industry over time, such as when a firm leases rather than purchases capital, would understate growth in the capital service index, which would have the effect of overstating value added MFP growth. For capital held under a long-term finance lease, the capital is treated as capital owned by the lessee and included in the productive capital stock estimates of the lessee industry.

Endnotes

  1. Jorgenson, Dale W., Mun S. Ho, and Kevin J. Stiroh (2005) Information Technology and the American Growth Resurgence. Cambridge, MA: MIT Press.

Measurement of labour input

19.96    There are three common methods of measuring labour input:

  • number of employed persons;
  • hours worked; and
  • quality-adjusted hours worked.

19.97    Indexes of hours worked are preferred to employment numbers because hours worked captures changes in overtime, standard weekly hours, leave, and part-time work. Quality adjusted hours worked further captures changes in the education and experience of the workforce. The ABS publishes productivity statistics on both an hours worked basis and quality adjusted hours worked basis.

Hours worked indexes

19.98    The ABS publishes indexes of hours worked for each ANZSIC06 industry, the market sector, and the whole economy in the ASNA.⁹¹ These indexes capture trends in hours worked and are derived from estimates of hours actually worked obtained from the Labour Force Survey (LFS). They measure the hours worked by all workers engaged in the production of goods and services by civilian wage and salary earners, employers, self-employed persons, unpaid family workers, and members of the Australian Defence Force.

19.99    For productivity measurement, the aggregate indexes of hours worked are considered to be of good quality, though they are published as indexes as levels may be subject to reporting bias. That is, there may be a tendency for respondents in the LFS to either overestimate or underestimate their hours worked. Industry levels of hours worked may also be subject to a reporting bias due both to the number of hours reported, as well as self-selecting the industry they work in.⁹² Industry-based hours worked levels are thus considered less reliable than the aggregate levels. The indices are expected to be of good quality since it is reasonable to assume that the bias does not change over time and so does not affect the growth rate.

19.100    The ABS surveys hours worked for one week in each month, so hours worked for the unobserved weeks are imputed. Adjustments are made for non-random events such as public and school holidays. The labour force survey collects hours worked by industry for the four mid-quarter weeks, so industry proportions for the representative week are assumed to hold for the quarter. Similarly, the arithmetic average of the four representative weeks of each quarter is used to estimate the annual industry proportions. Both of these methods assume that the effects of holidays and other seasonal factors are constant across all industries.⁹³ For a more technical description of the estimation method, see Research Paper: Estimating Average Annual Hours Worked.

Quality adjusted hours worked index

19.101    Measuring labour input as hours worked implicitly assumes that the workforce is homogeneous. That is, it does not recognise improvements to human capital due to the varying educational achievements and experience within the workforce. An alternative approach is to use quality adjusted labour inputs (QALI). QALI indexes are published for the market sector; each market-sector industry; and the twelve selected industries aggregates in Estimates of Industry Multifactor Productivity.⁹⁴

19.102    The quality changes in labour input are captured through accounting for heterogeneity across different types of workers. The traditional method of measuring labour input is to simply sum hours of all types of worker with identical weights. The modern growth accounting framework measures labour input as weighted aggregates of different types of workers with weights reflecting differences in productive capacity across different types of workers. In this way, increases in labour input can be divided between total hours worked and compositional changes in the labour force. As the workforce evolves with more educated workers replacing less educated workers, this compositional change can directly affect how much output can be produced from a given quantity of hours worked. The labour compositional change combined with labour share has become a standard method for quantifying the contribution of human capital to economic growth within the modern growth accounting framework.⁹⁵

19.103    The underlying conceptual framework for QALI is discussed in more detail in the Research paper, Quality-adjusted Labour Inputs, Nov 2005. Estimation methods have changed and are described below; in particular, of wage rates for each type of workers.

19.104    The workforce is cross-classified by sex, education and age groups. The details of this classification are provided in Tables 19.1 and 19.2.

Table 19.1 Classification of workers for each industry
CharacteristicCategories
SexMale
 Female
EducationUnqualified
 Skilled labour
 Bachelor degree
 Higher degree
Age15 to 24 years
 25 to 34 years
 35 to 44 years
 45 to 54 years
 55 to 64 years
Table 19.2 Descriptions of education categories
Education categoryDescription
UnqualifiedWorkers with at most a high school qualification
Skilled labourWorkers with a non-university post-secondary qualification (e.g. a TAFE qualification of an apprenticeship)
Bachelor degreeWorkers with a university degree other than a Masters or a Doctorate
Higher degreeWorkers with a Masters or a Doctorate

19.105    Hours worked indexes for each group are combined as a Törnqvist index using income shares as the weights. So, a QALI index measures both changes in hours worked and changes in quality (that is, changes in educational achievement and experience). In the productivity growth accounts, the changes in quality are also referred to as labour composition.

19.106    The aggregate QALI indexes have grown faster than the corresponding unadjusted hours worked indexes, implying that labour quality has been increasing. Assuming that higher wages reflect a higher marginal product of labour, labour quality will increase when the high wage rate groups of workers increase their hours worked faster than the low wage rate groups.

19.107    MFP on an hours-worked basis has generally exceeded MFP on a quality adjusted hours worked basis. The difference in the MFP growth rates represents the change in labour composition, which is explicitly identified when the growth accounts are expressed on a quality adjusted hours worked basis.

19.108    Aggregate QALI indexes for the market sector and twelve selected industries are compiled using full Australian Census data. Note that since the census data are used, the inter-census periods are interpolated so care should be taken interpreting year on year changes in labour composition.

Endnotes

  1. Hours worked indexes for the market sector and the whole economy are also published in the quarterly national accounts (NIEP). Estimates of industry multifactor productivity also include hours worked for each industry, the market sector and the twelve selected industries.
  2. Caution is recommended making level comparisons, particularly for industries as differences in collection methods between the LFS and variables sourced from other economic collections (using the ABS business register) may distort comparisons.

  3. The hours worked indexes published in the ASNA and the industry productivity data cubes contain the holiday correction; however, this correction has not been applied to the ABS’ detailed labour force estimates.

  4. Wei and Zhao present some preliminary QALI results for each of the twelve selected industries in 'The Industry Sources of Australia’s Productivity Slowdown', paper presented at the Second World KLEMS Conference at Harvard University, 2012.

  5. For example, see Chapter 1 The Human Capital Century in Goldin, C. and L.F. Katz (2008) The Race between Education and Technology. Cambridge, MA:  Harvard University Press.

Capital and labour income shares

19.109    The capital and labour income shares, \( S_K\) and \(S_L\) are derived from the current price factor income accounts. For a given industry or aggregate, total income can be decomposed into:

  • gross operating surplus (GOS) of corporations and general government;
  • gross mixed income (GMI) of unincorporated firms;
  • compensation of employees (COE); and
  • taxes less subsidies on production and imports (IBT).

19.110    Note that total income includes the GOS of general government but not the GOS of dwellings owned by persons, as ownership of dwellings is excluded from the market sector.

19.111    Both GMI and IBT include capital and labour components. They can be further decomposed into income attributable to labour and capital, as described in the next two sections. Total income can be written as:

    \(Total\:Income = GOS + GMI\left( K \right) + GMI\left( L \right) + COE + IBT\left( K \right) + IBT\left( L \right)\)

where K and L are income attributable to capital and labour, respectively.

19.112    The income share of capital is thus:

    \(\large {S_K} = \frac{{GOS + GMI\left( K \right) + IBT\left( K \right)}}{{Total\:Income}}\)

and the income share of labour is:

    \(\large {S_L} = \frac{{COE + GMI\left( L \right) + IBT\left( L \right)}}{{Total\:Income}}\)

Capital and labour shares of gross mixed income

19.113    The labour and capital shares of income earned by unincorporated enterprises are subsumed into one national accounts aggregate: gross mixed income. The following procedure is used to impute labour and capital shares of this aggregate for each industry in the market sector.

19.114    An estimate of labour income is imputed by assuming that proprietors and unpaid helpers receive the same average compensation per hour as wage and salary earners. Similarly, an estimate of proprietors' capital income is derived by multiplying the unincorporated productive capital stock of each asset type by the corporate rental prices. These estimates are then scaled so they sum to the observed GMI. The capital and labour shares of GMI are the corresponding scaled estimates.

19.115    That is, the capital share of GMI is:

    \(\large {s_i}\sum\limits_j {{r_{c,i,j}}{K_{u,i,j}}}\)

where \(s_i\) is the scaling factor for industry \(i\);

 \(r_{c,i,j}\) is the corporate rental price of asset \(j\) in industry \(i\); and

\(K_{u,i,j}\) is the productive capital stock of asset \(j\) in industry \(i\) for unincorporated enterprises.

The labour share of GMI is:

    \(\large {s_i}{w_i}{H_{u,i}}\)

where \(s_i\) is (again) the scaling factor for industry \(i\)

\(w_i\) is the average hourly income for wage and salary earners in industry \(i\); and

\(H_{u,i} \)is the hours worked by proprietors and unpaid helpers in industry \(i\).

19.116    The scaling factor \(s_i\) for industry \(i\) is given by:

    \(\large {s_i} = \frac{{GMI}}{{{{\widehat {GMI}}_{u,i}}}}\)

and \({\widehat {GMI}_{u,i}}\) for each industry is imputed, based on the labour and capital cost as:

    \(\large {\widehat {GMI}_{u,i}} = {w_i}{H_{u,i}} + \sum\limits_j {{r_{c,i,j}}{K_{u,i,j}}}\)

19.117    Some taxes and subsidies on production and imports can be attributed solely to either capital or labour (for example, land tax and payroll tax). Such taxes and subsidies, however, make up only a small proportion of total net taxes. The capital and labour shares of net taxes are thus allocated proportionally, using the other income components attributable to labour and capital

Gross output income shares

19.118    The gross output income shares are derived similarly except that intermediate inputs need to be included:

    \(\begin{aligned} Total\:Income &= GOS + GMI\left( K \right) + GMI\left( L \right) + COE + IBT\left( K \right) + IBT\left( L \right)\\&\hspace{0.6cm}+ Intermediate\:inputs \end{aligned}\)

19.119    Thus, the income share of capital is:

    \(\large {Z_K} = \frac{{GOS + GMI\left( K \right) + IBT\left( K \right)}}{{Total\:Income}}\)

and the income share of labour is:

    \(\large {Z_L} = \frac{{COE + GMI\left( L \right) + IBT\left( L \right)}}{{Total\:Income}}\)

and the income share of intermediate inputs is:

    \(\large {Z_M} = \frac{{Intermediate\:inputs}}{{Total\:income}}\)

Estimation formulae

Capital services index

19.120    Capital services index for each industry is estimated (for both corporate and unincorporated entities) by weighting together the real growth in the productive capital stock of different assets, weighted together using the two-period average value share of each type of capital services. The indexes are compiled in the form of a Törnqvist index (i.e. the weighted geometric mean of the component growth rates). The quantity index of capital services in industry i is calculated as: 

    \(\large \ln \left( {\frac{{{K_{i,t}}}}{{{K_{i,t - 1}}}}} \right) = \sum\limits_j {{s_{K,i,j,t}}\ln \left( {\frac{{{K_{i,j,t}}}}{{{K_{i,j,t - 1}}}}} \right)}\)         - - - - - - - (19.7)

and the two-period average value share of each type of capital services is given by:

    \(\large {s_{K,i,j,t}} = \frac{{\left( {\frac{{{r_{i,j,t}}{K_{i,j,t}}}}{{\sum\nolimits_j {{r_{i,j,t}}{K_{i,j,t}}} }} + \frac{{{r_{i,j,t - 1}}{K_{i,j,t - 1}}}}{{\sum\nolimits_j {{r_{i,j,t - 1}}{K_{i,j,t - 1}}} }}} \right)}}{2}\)

where

    \(\ln \left( {\frac{{{K_{i,t}}}}{{{K_{i,t - 1}}}}} \right)\) is the capital input growth rate for industry \(i\) from period \(t-1\) to period \(t\), and

    \(\ln \left( {\frac{{{K_{i,j,t}}}}{{{K_{i,j,t - 1}}}}} \right)\) is the productive capital stock growth rate for capital asset \(j\) in industry \(i\), from period \(t-1\) to period \(t\).

19.121    The capital input growth rate for the market sector \(\ln \left( {\frac{{{K_{m,t}}}}{{{K_{m,t - 1}}}}} \right)\), is given by:

    \(\large \ln \left( {\frac{{{K_{m,t}}}}{{{K_{m,t - 1}}}}} \right) = \sum\limits_i {{s_{K,i,t}}\ln \left( {\frac{{{K_{i,t}}}}{{{K_{i,t - 1}}}}} \right)}\)         - - - - - - - (19.8)

and the two-period average value share of each type of capital services is given by:

    \(\large {s_{K,mjt}} = \frac{{\left( {\frac{{GO{S_{i,t}} + GMI{{\left( K \right)}_{i,t}} + IBT{{\left( K \right)}_{i,t}}}}{{\sum\nolimits_i {GO{S_{i,t}} + GMI{{\left( K \right)}_{i,t}} + IBT{{\left( K \right)}_{i,t}}} }} + \frac{{GO{S_{i,t - 1}} + GMI{{\left( K \right)}_{i,t - 1}} + IBT{{\left( K \right)}_{i,t - 1}}}}{{\sum\nolimits_i {GO{S_{i,t - 1}} + GMI{{\left( K \right)}_{i,t - 1}} + IBT{{\left( K \right)}_{i,t - 1}}} }}} \right)}}{2}\)

19.122    That is, the industry capital income shares are derived as the proportion of \(GOS + GMI\left( K \right) + IBT\left( K \right)\) in each industry to \(GOS + GMI\left( K \right) + IBT\left( K \right)\)for the market sector.⁹⁶

Labour input index

19.123    Labour input index for each industry is calculated as a Törnqvist volume index of hours worked of different types of workers: 

    \(\large \ln \left( {\frac{{{L_{i,t}}}}{{{L_{i,t - 1}}}}} \right) = \sum\limits_j {{s_{L,ijt}}\ln \left( {\frac{{{H_{i,j,t}}}}{{{H_{i,j,t - 1}}}}} \right)}\)         - - - - - - - (19.9)

and the two-period average value share of each type of workers in the industry labour compensation is given by:

    \(\large {s_{L,ijt}} = \frac{{\left( {\frac{{{W_{i,j,t}}{H_{i,j,t}}}}{{\sum\nolimits_j {{W_{i,j,t}}{H_{i,j,t}}} }} + \frac{{{W_{i,j,t - 1}}{H_{i,j,t - 1}}}}{{\sum\nolimits_j {{W_{i,j,t - 1}}{H_{i,j,t - 1}}} }}} \right)}}{2}\)

where

    \(\ln \left( {\frac{{{L_{i,t}}}}{{{L_{i,t - 1}}}}} \right)\) is the labour input growth rate for industry \(i\), from period \(t-1\) to period \(t\);

    \(\ln \left( {\frac{{{H_{i,j,t}}}}{{{H_{i,j,t - 1}}}}} \right)\) is the growth rate of hours worked for \(j\) the type of workers in industry \(i\), from period \(t-1\) to period \(t\); and

    \({W_{i,j,t}}\) is the wage rate for \(j\) the type of workers in industry \(i\) at time \(t\).

19.124    Labour input index for the market sector is calculated as a Törnqvist volume index of hours worked of different types of workers: 

    \(\large \ln \left( {\frac{{{L_{m,t}}}}{{{L_{m,t - 1}}}}} \right) = \sum\limits_j {{s_{L,mjt}}\ln \left( {\frac{{{H_{m,j,t}}}}{{{H_{m,j,t - 1}}}}} \right)}\)         - - - - - - - (19.10)

and the two-period average value share of each type of workers in the industry labour compensation is given by:

    \(\large {s_{L,mjt}} = \frac{{\left( {\frac{{{W_{m,j,t}}{H_{m,j,t}}}}{{\sum\nolimits_j {{W_{m,j,t}}{H_{m,j,t}}} }} + \frac{{{W_{m,j,t - 1}}{H_{m,j,t - 1}}}}{{\sum\nolimits_j {{W_{m,j,t - 1}}{H_{m,j,t - 1}}} }}} \right)}}{2}\)

where

    \(\ln \left( {\frac{{{L_{m,t}}}}{{{L_{m,t - 1}}}}} \right)\) is the labour input growth rate for the market sector, from period \(t-1\) to period \(t\);

    \(\ln \left( {\frac{{{H_{m,j,t}}}}{{{H_{m,j,t - 1}}}}} \right)\) is the growth rate of hours worked for \(j\) the type of workers in the market sector, from period \(t-1\) to period \(t\); and

    \({W_{m,j,t}}\) is the wage rate for \(j\) the type of workers in the market sector at time \(t\).

Industry combined primary inputs index

19.125    Industry combined primary inputs index is calculated as a Törnqvist index of primary inputs - capital and labour:

    \( \ln \left( {\frac{{I_{i,t}^{\left( V \right)}}}{{I_{i,t - 1}^{\left( V \right)}}}} \right) = \frac{1}{2}\left( {{v_{K,i,t}} + {v_{K,i,t - 1}}} \right)\ln \left( {\frac{{{K_{i,t}}}}{{{K_{i,t - 1}}}}} \right) + \frac{1}{2}\left( {{v_{L,i,t}} + {v_{L,i,t - 1}}} \right)\ln \left( {\frac{{{L_{i,t}}}}{{{L_{i,t - 1}}}}} \right)\)         - - - - - - - (19.11)

where

    \(\ln \left( {\frac{{I_{i,t}^{\left( V \right)}}}{{I_{i,t - 1}^{\left( V \right)}}}} \right)\) is primary input growth rate for industry \(i\) from period \(t-1\) to period \(t\);

    \(\ln \left( {\frac{{{K_{i,t}}}}{{{K_{i,t - 1}}}}} \right)\) is the capital input growth rate for industry \(i\);

    \(\ln \left( {\frac{{{L_{i,t}}}}{{{L_{i,t - 1}}}}} \right)\) is the labour input growth rate for industry \(i\);

    \(v_{K,i}\) is the capital share in value-added based total industry income; and

    \({v_{L,i}}\) is the labour share in value-added based total industry income.

Gross output based combined input index

19.126    The gross output based combined input index is constructed as:

    \(\begin{aligned}\ln \left( {\frac{{I_{i,t}^{\left( G \right)}}}{{I_{i,t - 1}^{\left( G \right)}}}} \right) &= \frac{1}{2}\left( {{z_{K,i,t}} + {z_{K,i,t - 1}}} \right)\ln \left( {\frac{{{K_{i,t}}}}{{{K_{i,t - 1}}}}} \right) + \frac{1}{2}\left( {{z_{L,i,t}} + {z_{L,i,t - 1}}} \right)\ln \left( {\frac{{{L_{i,t}}}}{{{L_{i,t - 1}}}}} \right) \\&\hspace{0.6cm}+ \frac{1}{2}\left( {{z_{X,i,t}} + {z_{X,i,t - 1}}} \right)\ln \left( {\frac{{{X_{i,t}}}}{{{X_{i,t - 1}}}}} \right)\end{aligned}\)         - - - - - - - (19.12)

where

    \(\ln \left( {\frac{{I_{i,t}^{\left( G \right)}}}{{I_{i,t - 1}^{\left( G \right)}}}} \right)\) is the gross output based input growth rate for industry \(i\) from period \(t-1\) to period \(t\);

    \(\ln \left( {\frac{{{X_{i,t}}}}{{{X_{i,t - 1}}}}} \right)\) is the intermediate input growth rate for industry \(i\), and \(z_{K,i,t}\)\(z_{L,i,t}\); and 

    \(z_{X,i,t}\) are the capital, labour and intermediate input share of total industry income respectively.

Market sector primary input index

19.127    The combined primary input index for the market sector is calculated as:

    \(\ln \left( {\frac{{I_{M,t}^{\left( V \right)}}}{{I_{M,t - 1}^{\left( V \right)}}}} \right) = \frac{1}{2}\left( {{v_{K,t}} + {v_{K,t - 1}}} \right)\ln \left( {\frac{{{K_{M,t}}}}{{{K_{M,t - 1}}}}} \right) + \frac{1}{2}\left( {{v_{L,t}} + {v_{L,t - 1}}} \right)\ln \left( {\frac{{{L_{M,t}}}}{{{L_{M,t - 1}}}}} \right)\)         - - - - - - - (19.13)

where

    \(\ln \left( {\frac{{{K_{M,t}}}}{{{K_{M,t - 1}}}}} \right)\) is the capital input growth rate for the market sector;

    \(\ln \left( {\frac{{{L_{M,t}}}}{{{L_{M,t - 1}}}}} \right)\) is the labour input growth rate for the market sector, and

    \({v_{K,t}}\) and \({v_{L,t}}\) is the capital and labour share respectively in total income in the market sector

19.128    The capital and labour income shares, \(v_K\) and \(v_L\) respectively, are defined below:

    \(\large {v_{K,t}} = \frac{{\sum\nolimits_{i \in M} {\left( {GO{S_{i,t}} + GMI{{\left( K \right)}_{i,t}} + IBT{{\left( K \right)}_{i,t}}} \right)} }}{{\sum\nolimits_{i \in M} {\left( {CO{E_{i,t}} + GMI{{\left( L \right)}_{i,t}} + IBT{{\left( L \right)}_{i,t}}} \right)} + \sum\nolimits_{i \in M} {\left( {GO{S_{i,t}} + GMI{{\left( K \right)}_{i,t}} + IBT{{\left( K \right)}_{i,t}}} \right)} }}\)

    \(\large v_{L,t} = \frac{{\sum\nolimits_{i \in M} {\left( {CO{E_{i,t}} + GMI{{\left( L \right)}_{i,t}} + IBT{{\left( L \right)}_{i,t}}} \right)} }}{{\sum\nolimits_{i \in M} {\left( {CO{E_{i,t}} + GMI{{\left( L \right)}_{i,t}} + IBT{{\left( L \right)}_{i,t}}} \right)} + \sum\nolimits_{i \in M} {\left( {GO{S_{i,t}} + GMI{{\left( K \right)}_{i,t}} + IBT{{\left( K \right)}_{i,t}}} \right)} }}\)

Industry value added based MFP calculations

19.129    The industry value-added based MFP growth is calculated as the industry value added growth rate minus the industry combined primary input growth rate:

    \(\large \ln \left( {\frac{{A_{i,t}^{\left( V \right)}}}{{A_{i,t - 1}^{\left( V \right)}}}} \right) = \ln \left( {\frac{{{V_{i,t}}}}{{{V_{i,t - 1}}}}} \right) - \ln \left( {\frac{{I_{i,t}^{\left( V \right)}}}{{I_{i,t - 1}^{\left( V \right)}}}} \right)\)         - - - - - - - (19.14)

where

    \(\ln \left( {\frac{{A_{i,t}^{\left( V \right)}}}{{A_{i,t - 1}^{\left( V \right)}}}} \right)\) is the industry value added MFP growth rate; and

    \(\ln\left( {\frac{{{V_{i,t}}}}{{{V_{i,t - 1}}}}} \right)\) is the industry value-added growth rate.

Industry gross output based MFP calculations

19.130    Gross output-based MFP index is calculated as the industry gross output growth rate minus the industry gross output based combined input growth rate:

    \(\large \ln \left( {\frac{{A_{i,t}^{\left( G \right)}}}{{A_{i,t - 1}^{\left( G \right)}}}} \right) = \ln \left( {\frac{{{G_{i,t}}}}{{{G_{i,t - 1}}}}} \right) - \ln \left( {\frac{{I_{i,t}^{\left( G \right)}}}{{I_{i,t - 1}^{\left( G \right)}}}} \right)\)         - - - - - - - (19.15)

where

    \(\ln \left( {\frac{{A_{i,t}^{\left( G \right)}}}{{A_{i,t - 1}^{\left( G \right)}}}} \right)\) is the industry gross output-based MFP growth rate; and 

    \(\ln \left( {\frac{{{G_{i,t}}}}{{{G_{i,t - 1}}}}} \right)\) is the industry gross output growth rate.

Multifactor productivity for the market sector

19.131    The market sector MFP is calculated as the market sector output growth rate minus the market sector combined input growth rate:

    \(\large \ln \left( {\frac{{A_{M,t}^{\left( V \right)}}}{{A_{M,t - 1}^{\left( V \right)}}}} \right) = \ln \left( {\frac{{{V_{M,t}}}}{{{V_{M,t - 1}}}}} \right) - \ln \left( {\frac{{I_{M,t}^{\left( V \right)}}}{{I_{M,t - 1}^{\left( V \right)}}}} \right)\)         - - - - - - - (19.16)

where

    \(\ln \left( {\frac{{A_{M,t}^{\left( V \right)}}}{{A_{M,t - 1}^{\left( V \right)}}}} \right)\) is the market sector MFP growth rate; and

    \(\ln \left( {\frac{{{V_{M,t}}}}{{{V_{M,t - 1}}}}} \right)\) is the market sector output growth rate.

Endnotes

  1. A special case is that industry aggregation shares to the market sector are identical using either industry distribution of income or capital when the internal rate of return (IRR) is solved endogenously. In practice, a lower bound exogenous IRR of CPI+4% is frequently imposed and thus market sector capital services may differ using a pure capital aggregator.

Links between industry level and the market sector productivity measures

19.132    Aggregate productivity measures, such as the market sector labour productivity and MFP statistics, represent the average set of efficiencies and productivity levels across the individual industries making up the market sector. Aggregate productivity can improve because some industries further raise their productivity, or the more productive industries increase their relative shares in the market sector. In this context, such measures are inherently linked to industry productivity measures. 

19.133    The links between the ABS aggregate productivity measures and the industry productivity are implicit. An aggregate production function approach is applied in compiling market sector productivity measures, whereby aggregate outputs, aggregate labour input, aggregate capital and aggregate productivity, are separately defined and measured. This approach treats the market sector as a single big 'industry'. In this case, the ABS aggregate productivity statistics are independent of corresponding industry productivity measures. Some standard methods have been developed to conduct this analysis in order to quantify the industry contributions to the market sector productivity performance.

Decomposition of aggregate labour productivity

19.134    Stiroh⁹⁷ developed a decomposition framework to identify the industry sources of aggregate labour productivity growth, which becomes a standard method for analysing industry contributions to aggregate labour productivity growth⁹⁸ ⁹⁹. An ABS productivity research paper¹⁰⁰ has applied this method to link the market sector labour productivity growth to the industry sources. The decomposition formula is given as:

    \(\small {\begin{aligned}\ln \left( {\frac{{AL{P_t}}}{{AL{P_{t - 1}}}}} \right) &= \sum\limits_i {{w_{i,t}}\ln \left( {\frac{{LP_{i,t}^y}}{{LP_{i,t - 1}^y}}} \right)} + \left[ {\sum\limits_i {{w_{i,t}}\ln \left( {\frac{{{H_{i,t}}}}{{{H_{i,t - 1}}}}} \right) - \sum\limits_i {{h_{i,t}}\ln \left( {\frac{{{H_{i,t}}}}{{{H_{i,t - 1}}}}} \right)} } } \right] \\&\hspace{0.6cm}- \left[ {\sum\limits_i {{m_{i,t}}\left( {\ln \left( {\frac{{{X_{i,t}}}}{{{X_{i,t - 1}}}}} \right) - \ln \left( {\frac{{{Y_{i,t}}}}{{{Y_{i,t - 1}}}}} \right)} \right)} } \right] \end{aligned}}\)         - - - - - - - (19.17)

19.135    Using the value added concept of labour productivity, equation (19.17) can be simplified to

    \(\ln \left( {\frac{{AL{P_t}}}{{AL{P_{t - 1}}}}} \right) = \sum\limits_i {{w_{i,t}}\ln \left( {\frac{{LP_{i,t}^V}}{{LP_{i,t - 1}^V}}} \right)} + \left[ {\sum\limits_i {{w_{i,t}}\ln \left( {\frac{{{H_{i,t}}}}{{{H_{i,t - 1}}}}} \right) - \sum\limits_i {{h_{i,t}}\ln \left( {\frac{{{H_{i,t}}}}{{{H_{i,t - 1}}}}} \right)} } } \right]\)         - - - - - - - (19.17a)

where

    \(ALPt\) is the aggregate labour productivity (aggregate value added per hour);

    \(LP_{i,t}^{y}\) is the gross output labour productivity for industry \(i\);

    \(LP_{i,t}^v\) is the value added labour productivity for industry \(i\);

    \(w_{i,t}\) is the two-period average of industry \(i\)'s share in aggregate value added;

    \(m_{i,t}\) is the two-period average of the ratio of industry \(i\)’s intermediate input in aggregate value added;

    \(h_{i,t}\) is the industry \(i\)’s share in aggregate hours in period \(t-1\); and

    \(M\), \(Y\) and \(H\) stand for intermediate input, gross output and hours worked respectively. 

19.136    The first term in equation 19.17 is a 'direct productivity effect', which is equal to the weighted sum of industry gross output productivity growth rates, with the industry shares in total value added as weights. This term captures the impact of productivity growth in each industry. As industry labour productivity rises, the aggregate labour productivity also improves in proportion to industries’ shares in aggregate output.

19.137    The second term in equation 19.17 is a 'labour reallocation effect' that captures the impact on aggregate output of the shift of labour between low-productivity-level industries and high-productivity-level industries. Aggregate productivity growth depends not only on the rates of productivity within industries but also on changes in the composition of industries. Faster employment growth in high-productivity-level industries contributes to improvements in the aggregate labour productivity growth by increasing the size of aggregate output given the same quantity of hours worked.

19.138    The third term in equation 19.17 is the intermediate input intensity factor. As value added is defined as gross output minus intermediate input, the relative growth of intermediate inputs over gross output must be accounted for in aggregating industry gross output to reach aggregate output, which is a value added concept. For example, if growth of intermediate input usage is faster than that of gross output, the growth of value added is reduced and hence the growth rate of aggregate labour productivity declines. If less intermediate inputs are used for a given level of gross output, then more value added is created and hence aggregate labour productivity improves.

19.139    The 'direct productivity effect' in equation 19.17 can also be expressed in terms of capital services per hour (capital deepening), labour composition, and MFP. Moreover, to facilitate analysis of the productive contribution of information technologies, capital services per hour can be partitioned into IT and non-IT capital services per hour. That is

    \(\begin{aligned}\sum\limits_i {{w_{i,t}}} \ln \left( {\frac{{LP_{i,t}^V}}{{LP_{i,t - 1}^V}}} \right) &= \sum\limits_i {{w_{i,t}}} \left[ {\widetilde s_{i,t}^K\widetilde \alpha _{i,t}^{IT}\Delta \ln \left( {\frac{{K_{i,t}^{IT}}}{{{H_{i,t}}}}} \right) + \widetilde s_{i,t}^K\widetilde \alpha _{i,t}^N\Delta \ln \left( {\frac{{K_{i,t}^N}}{{{H_{i,t}}}}} \right) \\+ \widetilde s_{i,t}^L\Delta \ln {Q_{i,t}} + \Delta \ln A_{i,t}^v} \right]\end{aligned}\)         - - - - - - - (19.18)

Where \(\widetilde s_{i,t}^K\) is industry’s two period capital income share, \(\widetilde \alpha _{i,t}^{IT}\) is the IT share of industry capital (computers and software), \(\widetilde \alpha _{i,t}^{N}\) is the non-IT share of industry capital \(\widetilde s_{i,t}^L\) is industry’s two period labour income share, and \({Q_{i,t}}\) is labour composition. On the RHS of equation (19.18), capital services per hour are partitioned into the change in IT capital services per hour (that is, IT capital deepening from computers and software, \(\frac{{K_t^{IT}}}{{{H_t}}}\), change in non-IT capital deepening \(\frac{{K_t^N}}{{{H_t}}}\), the change in labour composition \(Q_t\), and the change in GVA based MFP, \(A_t^v\).

Endnotes

  1. Stiroh, Kevin J. (2002) 'Information Technology and the US Productivity Revival: What Do the Industry Data Say?', American Economic Review, 92(5), pp.1559-1576.
  2. Bosworth, B.P. and J.E. Triplett (2003) Services Productivity in the United States: Griliches' Services Volume Revisited. Washington, DC:  Brookings Institute.
  3. Timmer, M.P., Inklaar, R., O'Mahony, M. and B. van Ark (2010) Economic Growth in Europe: A Comparative Industry Perspective. Cambridge, MA:  Cambridge University Press.
  4. Wei, Hui and Pengfei Zhao (2012) 'Industry Sources of Australia's Productivity Slowdown', paper presented at the Second World KLEMS Conference at Harvard University, Cambridge, MA.