# Chapter 19 Productivity measures

### Introduction

19.1    The ABS produces annual indexes of labour and multifactor productivity (MFP) for the market sector as well as for each industry division within the market sector. The ABS also produces quarterly estimates of labour productivity (i.e. GDP per hour worked) for the market sector and for the whole economy, and quarterly and annual GDP per capita. The annual productivity measures for the market sector are published in Australian System of National Accounts (ASNA), and annual industry level MFP indexes in Estimates of Industry Multifactor Productivity. Quarterly indexes of GDP per hour worked are published in Australian National Accounts: National Income, Expenditure and Product (NIEP).

19.2    Estimates of industry level KLEMS (Capital (K), Labour (L), Energy (E), Materials (M) and Services (S)) multifactor productivity (MFP) for the 16 market sector industries are also published from 1995–96, in Estimates of industry level KLEMS Multifactor Productivity (KLEMS). The KLEMS datacube is supported by the companion Information Paper: Experimental Estimates of Industry Level KLEMS Multifactor Productivity, 2015.

19.3    Productivity is typically measured as output divided by input; that is, as output per unit of input. Partial measures of productivity take into consideration a single input like labour or capital. Labour productivity is frequently used as an indicator of productivity growth, which is simply measured as output per hour worked. When multiple inputs such as labour and capital are taken into consideration, it is called multifactor productivity (MFP), which is measured as output per unit of a combined bundle of labour and capital.

19.4    Of specific interest to economists are the underlying causes of economic growth. Typically, single indexes are not sufficient for this purpose. Labour productivity indexes reflect not only the contribution of labour to changes in production per labour unit, but are also influenced by the contribution of capital and other factors affecting production such as technological change. In comparison, MFP measures offer more comprehensive explanations to the sources of output growth. Specifically, MFP statistics are designed to inform how much economic growth originates from productivity growth (increased outputs from the same quantity of inputs) and how much from increased inputs (increased outputs from more capital goods or additional working hours). MFP, therefore, is most commonly used in rigorous productivity analysis.

19.5    The MFP measures are compiled in the standard growth accounting framework, which originates from the neoclassical theory of economic growth formulated by Solow.⁶⁶  In the original Solow growth accounting framework, the stock of capital was used as a measure of capital input, and labour input was measured as hours worked without accounting for compositional changes in the labour force.  Using his traditional growth accounting framework, Solow attributed almost all of the U.S. economic growth to the productivity growth, measured as the well-known Solow residual.

19.6    In comparison, the modern growth accounting framework is characterised by incorporation of quality changes into the measurement of capital and labour input.⁶⁷ The major cornerstone underlying this development was the introduction of constant quality indexes of capital and labour inputs by Griliches and Jorgenson⁶⁸ and Jorgenson, Gollop & Fraumeni.⁶⁹ Within the modern growth accounting framework, a substantial fraction of the Solow residual (technical progress) can be explained by changes in the quality of inputs. The part of technical progress captured in constant quality of input indexes is referred to as embodied technical progress, while disembodied technical progress relates to spill-over effects through diffusion of advances in science and technology, which is beyond the input measurement. In this context, productivity growth (technical progress) within the modern growth accounting framework is interpreted as disembodied technical progress. According to the modern growth accounting analysis, economic growth is largely driven by input growth and (disembodied) technical progress contributes only a small proportion.

19.7    The OECD has produced a number of handbooks and manuals to set out a guide for 'best practice' in productivity measurement by statistical agencies, to assist official statistical agencies to compile MFP statistics employing the growth accounting framework.⁷⁰ The ABS was a major contributor to the development of the OECD Capital Manual, which is an important document for guiding practitioners on how to measure the capital services component of productivity measures.⁷¹

19.8    The methods used by the ABS in compiling productivity statistics align with international best practice as implemented by most OECD countries. The ABS MFP statistics are compiled on the basis of the standard growth accounting framework, which is widely adopted by leading statistical agencies and recommended by the OECD.

19.9    In 1989, ABS first released its experimental MFP estimates in the information paper, Development of Multifactor Productivity Estimates for Australia, 1974-75 to 1987-88.⁷² In 1990, the detailed technical issues in relation to those preliminary MFP estimates were covered in the occasional paper: Estimates of Multifactor Productivity Australia.⁷³ Estimates of MFP were first included in the publication, Australian National Accounts: Multifactor Productivity, released in June 1994. From 1999, the aggregate MFP statistics were incorporated into the ASNA.

19.10    The availability of Supply Use tables since 1995 makes it possible to compile industry level MFP statistics and KLEMS growth accounts. The ABS started to compile and release industry level MFP statistics data cube since 2007, and, since 2015, KLEMS growth accounts. Both data cubes provide MFP estimates for individual industries in the Australian economy. They go beneath the aggregate economy in order to measure the productivity of individual industries.

### Endnotes

1. Solow, R. M. (1957). Technical change and the aggregate production function. The review of Economics and Statistics, 39(3), 312-320.
2. Another radical departure from the traditional growth accounting framework includes output measurement and aggregating methodology, as discussed in Jorgenson, D.W. et al. (2005) Information Technology and the American Growth Resurgence. Cambridge, MA: MIT Press.
3. Griliches, Zvi and D.W. Jorgenson (1966) 'Sources of Measured Productivity Change: Capital Input', American Economic Review, 56 (May), pp.50-61.
4. Jorgenson, D.W., Gollop, F.M. and B.M. Fraumeni (1987) Productivity and U.S. Economic Growth. Cambridge, MA: Harvard University Press.
5. 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).
6. OECD (2009) Measuring Capital OECD Manual (Second Edition). Paris:  Organisation for Economic Co-operation and Development (OECD).
7. ABS (1989) Development of Multifactor Productivity Estimates for Australia 1974-75 to 1987-88, Canberra: Australian Bureau of Statistics (ABS).
8. Aspden, Charles. & Australian Bureau of Statistics. (1990). Estimates of multifactor productivity, Australia. Canberra:  Australian Bureau of Statistics

# Concepts

## Labour productivity

19.11    Labour productivity is defined as a ratio of some measure of output to labour input; that is, output per unit of labour. Labour productivity is usually expressed in terms of growth rate.

19.12    Labour productivity is widely used for making historical, inter-industry and inter-country growth comparisons. Furthermore, labour productivity is often regarded as an indicator of improvements in living standards as growth in labour productivity has a close long-term relationship with growth in labour earnings.

19.13    Labour productivity has a close relationship to multifactor productivity. In the growth accounting framework, growth in labour productivity can be decomposed into growth in capital deepening (the ratio of capital to labour), growth in labour quality and growth in MFP. More detail is provided in Annex 19B.

## Capital productivity and capital deepening

19.14    Capital productivity is defined as a ratio of some measure of output to capital input; that is, output per unit of capital. Obviously, changes in this ratio can also reflect technological changes, and changes in other factor inputs (such as labour).

19.15    The measure of capital input used by the ABS in its estimates of capital productivity is the flow of capital services coming from the stock of capital and most assets are estimated using the Perpetual Inventory Method (PIM). They are calculated by weighting chain volume measures of the productive capital stock of different asset types together using their rental prices in the weights. Rental prices can be regarded as the 'wages' of capital.

19.16    Capital deepening (or capital intensity) refers to changes in the capital to labour ratio. Increased capital deepening means that, on average, each unit of labour has more capital to work with to produce output, so is an indicator of ability to augment labour. Labour saving practices, such as automation of production, will result in increased capital deepening, which is often associated with a decline in capital productivity. Thus, growth in capital deepening is an important driver (alongside MFP) of labour productivity growth. It may not be very useful to interpret declines in capital productivity in isolation since declines in capital productivity can be more than offset by labour productivity (resulting in MFP growth).

## Multifactor productivity

19.17    MFP is defined as a ratio of some measure of output to a combined input of multiple factors, such as labour and capital. In empirical analyses, it is expressed in terms of growth rate; that is, growth rate of output minus the growth rate of inputs.

19.18    At the aggregate and industry level, MFP is defined as the ratio of real value added to the combined inputs of capital and labour. At an industry level, MFP is also measured as the ratio of gross output to the combined inputs of capital, labour, and intermediate inputs.

19.19    In the productivity measurement literature, gross output based MFP is a preferred measure at a disaggregated level, as it requires less restrictive assumptions (see Jorgenson et al., 2005 and Diewert, 2008).⁷⁴ Ideally, MFP measures disembodied technical change attributable to improved use of factor inputs. In the case of gross output, this efficiency can be attributed to improvements in not only the use of primary inputs, capital and labour, but also in the use of intermediate inputs.

## The KLEMS growth accounting framework

19.20    The KLEMS growth accounting framework is a useful tool in addressing the challenge of developing more detailed industry performance indicators for the formulation and evaluation of policies involving long–term growth, efficiency and competitiveness. It provides, through a more detailed statistical decomposition, more information on the inputs contributing to output growth, and production efficiency. This helps policy makers and economists to identify factors associated with economic growth, such as structural changes in industry’s input mix, particularly with regards to the relative contribution from the intermediate inputs. This also facilitates a more disaggregated analysis of the industry origins of aggregate productivity growth, such as changes in the relative importance of input components over time.

19.21    Within intermediate inputs, the classification into energy (E), materials (M) and services (S) is beneficial in that they have distinctively different roles in the production process. This helps in evaluating trends in the way industries interact. One key interaction is that the intermediate input components reflect renting, hiring and out-sourcing between industries. An industry’s reliance on primary inputs relative to intermediate inputs may change due to changes in leasing and hiring arrangements rather than the productive process itself. When capital is rented under an operational lease arrangement from a firm in another industry, the use of the capital is classified as an intermediate input of the lessee. 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 by the lessor in the rental and hiring industry.

19.22    The intermediate inputs indices for energy, materials and services and their respective shares are sourced from the Supply Use tables (SUT) compiled by the ABS. 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.

## Measured productivity and technical progress

19.23    It is useful to distinguish between measured productivity and technical progress in productivity analysis. Productivity statistics aim to measure technical progress or the efficiency of production. In practice, productivity changes are measured by the difference between the growth in the volume of output and the growth in the volume of inputs, reflecting more than just technical progress. Year-to-year changes also contain 'noise' that is distinct from the notion of technical progress; it is therefore advisable to examine productivity changes over an extended period to look through some of the short-term volatility.

19.24    Although, from a conceptual standpoint, MFP can be interpreted in various ways, a key interpretation of MFP is as disembodied technological change attributable to improved use of factor inputs. Embodied technological change represents advances in the design and quality of new capital and intermediate inputs. Disembodied technological change is generally interpreted as representing costless improvements or knowledge, for example, network effects or spillovers from diffusion of publicly available R&D, and benefits to factor inputs from organisational change or better management. These spillovers and other benefits to factor inputs are generally not quantifiable within the KLEMS growth accounting framework.

19.25    At the industry level, ABS publishes both gross output-based MFP and value added-based MFP – they are complementary. One advantage of the gross output-based MFP approach is that it is a natural output concept⁷⁵ and consistent with the traditional production theory linking output to primary as well as intermediate inputs. By comparison, the value added-based MFP approach assumes that the components of value added are separable from that of intermediate inputs.⁷⁶ ⁷⁷

19.26    For a given industry, the relationship between changes in gross output-based MFP and value added-based MFP can be approximated by:

$$\large \Delta \ln GO\;MFP_i^{} \approx \frac{{V{A_i}}}{{G{O_i}}}\Delta \ln VA\;MFP_i^{}$$

where $$\small{\frac{{V{A_i}}}{{G{O_i}}} , \Delta \ln GO\;MFP , \Delta \ln VA\;MFP}$$ are the two period average of the ratio of nominal industry value added to nominal industry gross output, rate of change in gross output-based MFP, and rate of change in value added-based MFP, respectively.⁷⁸ Since this ratio is always less than unity, gross output-based MFP will always have less amplitude than value added-based MFP, i.e. rise less and fall less. However, the degree to which they differ varies from industry to industry, due to both the variation in each industry’s relative value-added proportion, as well as the degree to which the ratio changes over time.  At an aggregate level, the value-added concept is more appropriate as it removes inter–industry transfers.

19.27    In interpreting MFP, it should be noted that measured productivity growth could include factors other than technological change, for example adjustment costs, cyclical effects and measurement errors.⁷⁹ A limitation of MFP theory is that the assumptions of the neoclassical models do not necessarily hold in practice, which can affect the interpretation of the resulting estimates. For example, imperfect competition can result in gains from increasing market dominance being reflected as productivity gains. Additionally, in static models of production, such as the one used in estimating KLEMS MFP, capital is an exogenous input, which ignores dynamic feedback between MFP and capital. For example, if technological change increases output per person, the additional output per person may lead to further savings and investment and thus a rise in the capital–labour ratio. While traditional growth accounting identifies this induced effect as the contribution of capital growth, the effect can be attributed to an initial shift in technology. Therefore, MFP measures may understate the importance of productivity growth in contributing to output growth.

19.28    The methodology used in compiling the estimates implicitly assumes that the proportion of capital stock used in production (capital utilisation) does not change; therefore any real world change in the extent to which capital is utilised in production will be recorded as a change in productivity. Another assumption of the methodology is each hour of labour input is fully utilised in production. Further, improvements in output due to a firm’s ability to produce more output because of their size, that is, economies of scale, will also appear as a measured productivity improvement.

### Endnotes

1. Jorgenson, D.W., Mun S. Ho, and K.J. Stiroh (2005) Information Technology and the American Growth Resurgence. Cambridge, MA: MIT Press; and Diewert, Erwin (2008) 'OECD Workshops on Productivity Measurement and Analysis: Conclusions and Future Directions', in Productivity Measurement and Analysis: Proceedings from OECD Workshops. Paris:  Organisation for Economic Co-operation and Development (OECD).
2. 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.
3. Bosworth, B.P. and J.E. Triplett (2003) Services Productivity in the United States: Griliches' Services Volume Revisited, Washington, DC: Brookings Institute.
4. Changes in value added-based MFP can also be driven by changes in the efficiencies of intermediate inputs, for example, due to the use of more refined oil or more refined metal ore.
5. The ratio was first described in Bruno (1978). For a more precise reconciliation, see Diewert (2014).
6. 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)

# Data sources and methods

## 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
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
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:

• 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 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).

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

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.

# Accuracy, quality and reliability of productivity measures

19.141    Economic statistics may be fit for one purpose but may not be fit for others. MFP measures are developed for conducting analysis of long-term productivity growth. It is not ideal for users to employ them for assessing short term productivity fluctuations. Caution needs to be exercised in interpreting productivity measures, which are derived as a 'residual', and are therefore subject to any errors in the output and input measures. Such errors carry a relatively greater importance with respect to productivity estimates, which are calculated as a ratio of outputs to inputs. In the short to medium term, MFP estimates are subject to variations in capacity utilisation or other factors such as the weather. Taking into account these factors, MFP estimates are probably most useful when viewed as average growth rates between growth-cycle peaks, which tends to also remove much of the random error.

19.142    The approach taken for estimating MFP is based on neoclassical economic theory using a translog production function in conjunction with two assumptions: constant returns to scale; and that the marginal products of capital and labour are equal to their respective real market prices. This forms the basis of the growth accounting approach to estimating MFP.

19.143    However, these assumptions are unlikely to hold in practice. If there are scale efficiencies, then this will also be captured as an increase in MFP. This possibility is likely as there would be many firms operating in an environment of increasing returns to scale, especially over short periods. The assumption that the marginal products of capital and labour are equal to their market price is based on the existence of perfect competition in factor markets.

19.144    In practice, growth in MFP may contain the impact of many phenomena in addition to disembodied technological change, such as:

• economies of scale and scope;
• reallocation effects of capital and labour;
• changes in the work force and management practices;
• climate and water availability;
• variations in capacity utilisation; and
• measurement error.

19.145    Also, MFP estimates are subject to the vagaries of the growth in the business cycle (as capacity utilisation varies so does MFP growth). Taking into account all of these factors, MFP estimates are probably most useful when computed as average growth rates between growth-cycle peaks, which are determined as peak deviations of the market sector MFP index from its long-term trend. In this way, most of the effects of variations in capacity utilisation and much of the random error are removed. However, average growth rates still reflect any systematic bias resulting from the methodology and data used.

# Annex A Growth accounting framework

19A.1    The growth accounting framework is derived from a model based on a production function. A production function gives the maximum obtainable output for given inputs at a specific point in time.

19A.2    When output is measured as value added and the inputs considered are labour and capital, output is modelled:

$$\large {V_t} = {A_t}F\left( {{K_t},{L_t}} \right)$$         - - - - - - - (19A.1)

where

$$V_t$$ is real value added at time $$t$$:

$$A_t$$ is multifactor productivity at time $$t$$;

$$F$$ is the production function at time $$0$$;

$$K_t$$ is the real capital input at time $$t$$;

$$L_t$$ is the real labour input at time $$t$$; and

$$t$$ is a continuous measure of time.

19A.3    Note that the production function $$F$$ s not observable for the actual economy. Thus to measure productivity an expression for $$A_t$$ not involving $$F$$ must be derived. To do so, two assumptions are made about the production function $$F$$. First, that it exhibits constant returns to scale. That is, for any positive $$λ∂$$ the production function satisfies

$$\large F\left( {\lambda K,\lambda L} \right) = \lambda F\left( {K,L} \right)$$

19A.4    In words, this means that (say) doubling both inputs will double the output. Second, we assume that the marginal returns to capital and labour equal their respective real market prices. That is, we assume that

$$\large \frac{{\partial V}}{{\partial K}}\left( {{K_t},{L_t}} \right) = {r_t}$$

and

$$\large \frac{{\partial V}}{{\partial L}}\left( {{K_t},{L_t}} \right) = {w_t}$$

where $$r_t$$ is the real rental price of a unit of capital (at time $$t$$); and

$$w_t$$ is the real wage rate for a unit of labour (at time $$t$$)

19A.5     Now, differentiating $$V_t$$ with respect to time gives:

\large \begin{aligned} {\mathop V\limits^.} _t &= {{\mathop A\limits^. }_t}F\left( {{K_t},{L_t}} \right) + {A_t}\left( {\frac{{\partial F}}{{\partial K}}{{\mathop K\limits^. }_t} + \frac{{\partial F}}{{\partial L}}{{\mathop L\limits^. }_t}} \right) \\ &= \mathop {{{\mathop A\limits^. }_t}F\left( {{K_t},{L_t}} \right) + }\limits^. \frac{{\partial V_t}}{{\partial K}}{\mathop K\limits^.} _t + \frac{{\partial {V_t}}}{{\partial L}}{\mathop L\limits^.} _t \end{aligned}         - - - - - - - (19A.2)

where for any variable $$X$$, $$\mathop{X}\limits^.$$ denotes the derivative of a function $$X$$ with respect to time.

19A.6    Now dividing equation (19A.2) by $$V_t$$ gives:

\large \begin{aligned} \frac{{\mathop{V}\limits^.}_t}{V_t}&=\frac{{\mathop{A}\limits^.}_t}{A_t}+\frac{\partial V_t}{\partial K}\frac{{\mathop{K}\limits^.}_t}{V_t}+\frac{\partial V_t}{\partial L}\frac{{\mathop{L}\limits^.}_t}{V_t} \\&=\frac{{\mathop{A}\limits^.}_t}{A_t}+\frac{\partial V_t}{\partial K}\frac{{\mathop{K}}_t}{V_t}\frac{{\mathop{K}\limits^.}_t}{K_t}+\frac{\partial V_t}{\partial L}\frac{L_t}{V_t}\frac{{\mathop{L}\limits^.}_t}{L_t} \end{aligned}         - - - - - - - (19A.3)

19A.7    Since we have assumed that the marginal products of capital and labour are equal to their respective real market prices, equation (19A.3) becomes

$$\large \frac{{{{\mathop V\limits^. }_t}}}{{{V_t}}} = \frac{{{{\mathop A\limits^. }_t}}}{{{A_t}}} + {S_{K,t}}\frac{{{{\mathop K\limits^. }_t}}}{{{K_t}}} + {S_{L,t}}\frac{{{{\mathop L\limits^. }_t}}}{{{L_t}}}$$         - - - - - - - (19A.4)

where

$${S_{K,t}} = {r_t}\frac{{{K_t}}}{{{V_t}}}$$

$${S_{L,t}} = {w_t}\frac{{{L_t}}}{{{V_t}}}$$

19A.8    Note that $$S_{K,t}$$ and $$S_{L,t}$$ are the (value added) income shares of capital and labour, respectively. As the production function exhibits constant returns to scale, income can be attributed to either capital or labour; that is:

$${S_{K,t}} + {S_{L,t}} = 1$$

19A.9    To translate equation (19.4) into a discrete time equivalent, a Törnqvist index formula is chosen. Using a Törnqvist index follows international best practice. It is preferred to other index formulas due having desirable properties (from a microeconomic perspective) as shown by Diewert.¹⁰¹ In particular, an index of multifactor productivity is calculated using the equation:

$$\large \ln \left( {\frac{{{A_t}}}{{{A_{t - 1}}}}} \right) = \ln \left( {\frac{{{V_t}}}{{{V_{t - 1}}}}} \right) - {\overline S _{K,t}}\ln \left( {\frac{{{K_t}}}{{{K_{t - 1}}}}} \right) - {\overline S _{L,t}}\ln \left( {\frac{{{L_t}}}{{{L_{t - 1}}}}} \right)$$         - - - - - - - (19A.5)

where

$${\overline S _{K,t}} = \frac{1}{2}\left( {{S_{K,t}} + {S_{K,t - 1}}} \right)$$

and

$${\overline S _{L,t}} = \frac{1}{2}\left( {{S_{L,t}} + {S_{L,t - 1}}} \right)$$

19A.10    Note that $$\ln(\frac{X_t}{X_{t-1}})$$ is an approximation to the growth of $$X_t$$ when this growth is small; that is:

$$\large \ln \left( {\frac{{{X_t}}}{{{X_{ - 1}}}}} \right) \approx \frac{{{X_t} - {X_{t - 1}}}}{{{X_{t - 1}}}}$$

19A.11    Equation (19A.5) provides the standard growth accounting framework for growth in real value added. From this equation the contributions of MFP, capital, and labour to growth in value added are quantified:

• the contribution of capital is defined to be the growth rate of capital input times the capital share of value added $${\overline S _{K,t}}\Delta \ln {K_t}$$,
• the contribution of labour is defined to be the growth rate of labour input times the labour share of the value added $${\overline S _{L,t}}\Delta \ln {L_t}$$, and
• the contribution of multifactor productivity is defined as the residual

$$\hspace{1.6cm} \large \ln \left( {\frac{{{V_t}}}{{{V_{t - 1}}}}} \right) - {\overline S _{K,t}}\ln \left( {\frac{{{K_t}}}{{{K_{t - 1}}}}} \right) - {\overline S _{L,t}}\ln \left( {\frac{{{L_t}}}{{{L_{t - 1}}}}} \right)$$

that is, as the growth of value added not attributed to capital or labour.

19A.12    Note that when labour is measured as quality adjusted hours worked the contribution of labour can be further decomposed into the contributions of labour quality and hours worked.

## Gross output production function

19A.13    The gross output-based measure of MFP is an approach that includes the use of intermediate inputs as a source of output growth. For each industry, a production function postulated is as follows:

$$\large {G_t} = {A^G}H\left( {{K_t}{L_t}{X_t}} \right)$$         - - - - - - - (19A.6)

where

$$G_t$$= real output;

$$K_t$$ = real capital input;

$$L_t$$ = real labour input;

$$X_t$$ = real intermediate input;

$$A_t^G$$ = the gross output index of MFP, reflecting technological change, etc.;

$$H(K_tL_tX_t)$$ = a function of factor inputs [$$K_t$$$$L_t$$ and $$X_t$$] defining the expected level of output at time $$t$$, given the conditions of technology in the base period; and

$$t$$ = a continuous measure of time.

19A.14    For equation (19A.6), we make the assumptions of constant returns to scale and competitive equilibrium. Then differentiating with respect to time and dividing both sides by $$G_t$$ it can be shown that

$$\large \frac{{{{\mathop G\limits^. }_t}}}{{{G_t}}} = \frac{{\mathop {{A^G}}\limits^. }}{{{A^G}}} + {S_K}\frac{{{{\mathop K\limits^. }_t}}}{{{K_t}}} + {S_L}\frac{{{{\mathop L\limits^. }_t}}}{{{L_t}}} + {S_X}\frac{{{{\mathop X\limits^. }_t}}}{{{X_t}}}$$         - - - - - - - (19A.7)

where $$\mathop{G}\limits^.$$$$\mathop{K}\limits^.$$$$\mathop{L}\limits^.$$ and $$\mathop{X}\limits^.$$ are derivatives with respect to time:

$$\large \mathop G\limits^. = \frac{{\partial G}}{{\partial t}},etc.$$

the weights $$S_K$$$$S_L$$ and $$S_X$$ are the output elasticities of the three inputs:

$$\large {Z_K} = \frac{{\partial G}}{{\partial K}}\frac{K}{G},$$

$$\large {Z_L} = \frac{{\partial G}}{{\partial L}}\frac{L}{G},and$$

$$\large {Z_X} = \frac{{\partial G}}{{\partial X}}\frac{X}{G}$$

and weights $$Z_K$$$$Z_L$$ and $$Z_X$$ are the relative cost shares of capital, labour and intermediate inputs in the total cost:

$$\large {Z_K} = \frac{{K{r_K}}}{{G{p_G}}},$$

$$\large {Z_L} = \frac{{L{w_L}}}{{G{p_G}}},and$$

$$\large {Z_X} = \frac{{X{p_X}}}{{G{p_G}}}$$

where

$$r_K$$ = the rental price of capital services;

$$w_L$$ = the price of labour;

$$p_X$$ = the price of intermediate inputs; and

$$p_G$$ = the price of gross output

19A.15    Equation (19A.7) can be rearranged to show that the growth rate of multifactor productivity is equal to the growth rate of the ratio of output to inputs as follows:

$$\large \frac{{\mathop {{A^G}}\limits^. }}{{{A^G}}} = \frac{{\left( {\frac{{\mathop G\limits^. }}{I}} \right)}}{{\frac{G}{I}}}$$

where

$$\large \frac{{\mathop I\limits^. }}{I} = {Z_K}\frac{{\mathop K\limits^. }}{K} + {Z_L}\frac{{\mathop L\limits^. }}{L} + {Z_X}\frac{{\mathop X\limits^. }}{X}$$

19A.16    This implies that productivity can be expressed as the ratio of output to a composite index of inputs:

$$\large A_t^G = \frac{{{G_t}}}{{{I_t}}}$$         - - - - - - - (19A.8)

where the index $$I_t$$ is computed as a Törnqvist index as follows:

$$\large \frac{{{I_t}}}{{{I_{t - 1}}}} = {\left( {\frac{{{K_t}}}{{{K_{t - 1}}}}} \right)^{\left( {{Z_{Kt}} + {Z_{K\left( {t - 1} \right)}}} \right)/2}}{\left( {\frac{{{L_t}}}{{{L_{t - 1}}}}} \right)^{\left( {{Z_{Lt}} + {Z_{L\left( {t - 1} \right)}}} \right)/2}}{\left( {\frac{{{X_t}}}{{{X_{t - 1}}}}} \right)^{\left( {{Z_{Xt}} + {Z_{X\left( {t - 1} \right)}}} \right)/2}}$$

and $$Z_{Kt}$$$$Z_{Lt}$$ and $$Z_{Xt}$$ are the respective relative cost shares of capital, labour and intermediate inputs respectively. In the KLEMS growth accounting framework, the growth in intermediate inputs $$(X_t/X_{t-1})$$ is further partitioned into energy, materials and services. For a more detailed description of the KLEMS growth accounting framework, see Information Paper: Experimental Estimates of Industry Level KLEMS Multifactor Productivity, 2015.

### Endnotes

1. Diewert, Erwin (1976) 'Exact and Superlative Index Numbers', Journal of Econometrics, 2(May), pp.115-145.

# Annex B Compiling quality-adjusted labour input indexes

19B.1    This annex provides a detailed description of how quality adjusted labour inputs (QALI) indexes are compiled for each market sector industry, and the market sector and twelve selected industries aggregates. Recall that QALI indexes can be written as a combination of labour composition and unadjusted hours worked. Census data are used to estimate labour composition for each industry. Then these estimates are combined with hours worked data for each industry, the market sector and twelve selected industries aggregates to obtain the corresponding QALI indexes.

19B.2    The general formula for calculating QALI indices is as follows. The workforce is partitioned into groups $$g_1,....., g_K$$ for each year $$t$$. This assumes that for each group $$g$$ we have an hours worked index $$H_{g,t}$$. Note that the sum of hours worked over each group:

$$\large {H_t} = \sum\limits_{g = 1}^K {{H_{{g_j},t}}}$$

is the unadjusted hours worked index. It is further assumed that for each group $$g$$ we have the average hourly income $$w_{g,t}$$ . Then the QALI index $$\frac{L_t}{L_{t-1}}$$ is given by:

$$\large \frac{{{L_t}}}{{{L_{t - 1}}}} = \prod\limits_{g = 1}^K {{{\left( {\frac{{{H_{g,t}}}}{{{H_{g,t - 1}}}}} \right)}^{\left( {{S_{g,t}} + {S_{g,t - 1}}} \right)/2}}}$$         - - - - - - - (19B.1)

where

$$\large {S_{g,t}} = \frac{{{w_{g,t}}{H_{g,t}}}}{{\sum\nolimits_{g = 1}^K {{w_{g,t}}{H_{g,t}}} }}$$

is income share of group $$g$$ in year $$t$$.

19B.3    Now labour composition is defined to be the ratio $$\frac{L_t}{H_t}$$. For the equation above, we see that an index for labour composition is given by

$$\large Q_t=\frac{L_t/H_t}{L_{t-1}/H_{t-1}}=\frac{L_t/L_{t-1}}{H_t/H_{t-1}}$$         - - - - - - - (19B.2)

The term $$Q_t$$ is the compositional change (in year $$t$$).

19B.4    Let $${p_{g,t}} = \frac{{{H_{g,t}}}}{{{H_t}}}$$ be the proportion of hours worked by group $$g$$ in year $$t$$. Then we can write $$Q_t$$as

$$\large {Q_t} = \prod\limits_{g = 1}^K {{{\left( {\frac{{{P_{g,t}}}}{{{P_{g,t - 1}}}}} \right)}^{\left( {{{\widehat S}_{g,t}} + {{\widehat S}_{g,t - 1}}} \right)/2}}}$$         - - - - - - - (19B.3)

where

$$\large {\widehat S_{g,t}} = \frac{{{w_{g,t}}{P_{g,t}}}}{{\sum\nolimits_{g - 1}^K {{w_{g,t}}{P_{g,t}}} }}$$

19B.5     To calculate the compositional changes from the census data the workforce is grouped by education, age, and sex (see Table 19.1). For education, there are four categories: Unqualified, Skilled Labour, Bachelor Degree, and Higher Degree; for age there are five categories: 15 to 24 years, 25 to 34 years, 35 to 44 years, 45 to 54 years, and 55 to 64 years; for sex there are two categories: Male and Female. Definitions of the education categories are given in Table 19.2. From the census data, we derive the proportion of hours worked and average hourly wage of workers with a given education level, age group, and sex (for all choices of education level, age group, and sex). Note that to take into account time spent in education, we restrict the age range of workers considered depending on the education category (see Table 19.2).

Table 19B.1 Age range of workers considered by education category
Education categoryAge range of workers
Unqualified15 to 64
Skilled labour20 to 64
Bachelor degree21 to 64
Higher degree23 to 64

19B.6    Compositional changes for the whole economy are calculated from 1981 until the current year using census data. Census data are only available every five years (in 1981, 1986, etc.), so much data has to be interpolated. The years falling between census years are linearly interpolated for both $$p_{g,t}$$ and $$w_{g,t}$$. For example, the years 1982 to 1985 are defined as:

$$\large {P_{g,1981 + t}} = {P_{g,1981}} + \frac{t}{5}\left( {{P_{g,1986}} - {P_{g,1981}}} \right)$$

and

$$\large {w_{g,1981 + t}} = {w_{g,1981}} + \frac{t}{5}\left( {{w_{g,1986}} - {w_{g,1981}}} \right)$$

For $$t=1,2,3,4,...,Q_t$$ is then calculated or years 1981 to the latest census year for which data is available. Finally, the compositional changes for years past the last census year are extrapolated using the following formula:

$$\large {Q_{2006 + t}} = {Q_{2006}}{\left( {\frac{{{Q_{2006}}}}{{{Q_{2001}}}}} \right)^{t/5}}$$

19B.7    The extrapolation assumes that the yearly changes in compositional change past the last census year are equal to the (average) yearly change during the latest inter-census period.

# Annex C Measurement of the income tax parameter

19C.1    The income tax parameter,$$T_{ijt}$$ allows for the variation of income tax allowances according to different industries, asset types, and variations in allowances over time. Changes in corporate profit taxes over time are also allowed for. Corporate taxes aside, these provisions increase the after-tax returns on investment and lower the rental price of capital. For each industry $$i$$, and asset type $$j$$, $$T_{ijt}$$ is expressed as:

$$\large {T_{ijt}} = \frac{{1 - {u_t}{z_{ijt}} - {u_t}{a_{ijt}}}}{{1 - {u_t}}}$$

where

$$u_t$$ = the corporate profit tax rate;

$$Z_{ijt}$$ = the present discounted value of one dollar of depreciation allowances; and

$$a_{ijt}$$ = the additional allowance rate.

19C.2    The tax parameter reflects the differing tax circumstances that owners of capital face. The method adopted by ABS follows Jorgenson$$¹⁰²$$ and Hall and Jorgenson¹⁰³ ¹⁰⁴ and reflects changes to:

• tax concessions;
• write off periods (i.e. tax lives);
• deductions allowable;
• allowable capital expenditure;
• special allowances; and
• amortisation of capital.

19C.3    For example, allowance is made for the differing depreciation and additional allowances available to specific industries and asset types over time.  These allowances tended to be more generous in the Agriculture, forestry and fishing, Mining, and Manufacturing industries, especially for certain types of equipment.  In addition, the Australian Taxation Office (ATO) allowed for faster depreciation rates over time through shorter effective tax lives. Since 1985, various research and development (R&D) tax concessions have been introduced to encourage increased investment in R&D by Australian companies. These concessions have had the effect of reducing rental prices on R&D considerably.

19C.4    The Corporate Profit Tax Rates ($$u$$) are obtained from the ATO website.

## Depreciation allowances

19C.5    The depreciation allowance ($$z$$) is the present discounted value (PDV) of the stream of deductions multiplied by the marginal tax rate applicable in that year. Asset lives and a nominal discount rate are used to determine the present discounted value of depreciation allowances. Prior to 1980, the average asset lives used to calculate capital stock for each asset type are used. After 1980, the asset life consistent with the shortest life within broad asset life bands specified by the ATO is used. Broad banding reduces the effective life of the asset. The nominal discount rate is based on the business overdraft rate published in the Reserve Bank Bulletin.  It assumes that the business overdraft rate applies to all borrowers for investment in equipment or structures and contains a risk premium (over and above government bonds).

19C.6    Specific rulings on eligible depreciation allowances are obtained from the Master Tax Guides (MTG), ATO rulings published online, and Commonwealth Budget Papers. Of the two depreciation schedules permitted, the diminishing value method has been chosen. Prior to 10 May 2006, it allowed software and machinery and equipment assets to be geometrically depreciated at 150 per cent of the straight-line rate (the other schedule permitted). From 10 May 2006, the government introduced a 200 per cent diminishing balance rate for eligible new plant and equipment assets.

19C.7    From 1980, broad banded depreciation rates were introduced, allowing assets with effective lives over a particular band of years to depreciate at a certain rate. In 1996, for example, assets with a life of 0-3 years could be depreciated immediately, and assets with a life of 3 to 5 years could be depreciated at a prime cost rate of 40 per cent of its purchase price.

19C.8    In addition to broad banding, the Commonwealth Government allowed a loading factor of between 18 per cent and 20 per cent from 1990, depreciating some assets more quickly. Most equipment except motor vehicles was permitted to use loading factors.

19C.9    Double depreciation allowances were permitted for most assets for the period in 1974-76. Between 1 July 1974 and 30 June 1976, companies were allowed to depreciate new investment excluding motor vehicles at twice the stated rates. Once purchased, the asset continued to be depreciated at these accelerated rates until completely depreciated.  We treat this by doubling the loading factor which has the effect of doubling the depreciation rate.

19C.10    In 1980, the Commonwealth Government permitted a separate allowance for buildings. Depending on the year, a straight-line allowance of 2.5 per cent or 4 per cent was permitted. This allowance is treated in the same way as depreciation allowance in the tax parameter.

19C.11    On 1 July 2001, the government introduced the 'uniform capital allowances regime'. This regime replaced the special capital allowance provisions for the Mining industry. The regime applied to all depreciable assets except where specific provisions apply to R&D activities, investments in Australian films, or cars.

19C.12    In 2002, statutory effective life caps were introduced, allowing an accelerated depreciation for certain types of equipment. Specifically, statutory life caps halved the effective tax lives of aircraft (to 10 years) and buses and trucks (larger than 3.5 tonnes) to 7.5 years.

## Computer software

19C.13    Depreciation rates are applied to purchased (packaged) software, customised, and in-house software combined. MTG defines in-house software as: computer software, or a right to use such software, that is acquired, developed or commissioned, and that is mainly for the taxpayer to use in performing the functions for which the software was developed (i.e. not for resale).  From May 1998, acquiring, developing or commissioning software is depreciable at 40 per cent per annum, so that the asset life is 2.5 years.

## Non-dwelling construction

19C.14    The effective lives of 'industrial' buildings and 'non-industrial' buildings are 25 years and 40 years respectively.

## Non-depreciable assets

19C.15    For land and inventories, the effective life does not apply to these capital assets as they are not subjected to depreciation resulting from production.

19C.16    The additional allowance rate ($$a$$) is an immediate write-off which results in tax savings (i.e. discounting is not required). The value of an allowance is the tax savings which is the product of the tax rate and the rate of the allowance. For example, if the allowance rate is 50 per cent and the profit tax rate is 30 per cent, then the company effectively saves 15 per cent of the purchase price of the asset in tax savings ($$30\%×50\% =u×a$$). Most equipment types have attracted an allowance of some kind.

19C.17    There are general allowances across all industries and special allowances. Special allowances vary widely according to asset type and time period. In 1996, for example, purchasers of machinery and equipment (other than motor vehicles) were permitted to deduct an additional ten per cent in the purchase year.

19C.18    Pro rata adjustments are made to align the dates of the tax law with the financial year, assuming that investment occurred evenly over the tax year. This leads to determining pro rata depreciation rates based on the portion of the year covered.

19C.19    Some allowances may have not been taken into consideration because of the assets eligible may be at a finer detail than assets classes to which tax parameters can be assigned (i.e. the asset classification in the Perpetual Inventory Model), or because further research was needed. The ABS welcomes comments which may assist in improving the accuracy and fitness-for-purpose of tax parameters.

## Film tax concessions

19C.20    According to the MTG 2011, three types of film concession were available in 2010-11. Since a film's eligibility for tax concessions is limited to one of the concession types, the 'additional allowance rate' for film has been set at 15 per cent, which is the lowest available concession rate.

## Research and development

19C.21    Since 1985, tax incentives have been available to encourage increased investment in research and development (R&D) by Australian companies. Up until 2010-11, the 'R&D Tax Concession' program was in place. The most recent elements of the R&D Tax Concession included:

• An enhanced rate of tax deduction at 125 per cent of eligible expenditure incurred on Australian R&D activities of at least $20,000. Eligible R&D expenditures included salaries and wages to company employees associated with the R&D activities, along with expenditure on materials used and an allowance for the decline in value of capital equipment used in R&D. • A premium 175 per cent rate of tax deduction applied to the amount of R&D expenditure that exceeds a given company's average expenditure over the previous 3 years. 19C.22 This tax concession scheme had been treated as a general allowance for all industries. Between 1985 and 2011, the allowance in (a) ranged from 125 to 150 per cent. 19C.23 From July 1, 2011, the 'R&D Tax Concession' was replaced by the 'R&D Tax Incentive'. The R&D Tax Incentive aims to encourage companies to engage in R&D activities where the knowledge gained is likely to benefit the wider Australian economy. The two key components of the R&D tax incentive are: • A 45 per cent refundable tax offset (equivalent to a 150 per cent deduction at a 30 per cent company income tax rate) on Australian R&D activities of at least$20,000 for companies with an aggregated turnover of less than \$20 million per annum. Companies can receive a cash refund for income years where a tax loss is recorded.
• A non-refundable 40 per cent tax offset (equivalent to a 133 per cent deduction at a 30 per cent company income tax rate) to all other companies, allowing for unused offset amounts to be carried forward for use in future income years.

19C.24    Effectively, the treatment of the tax parameter is the same for both schemes. The ABS estimates that most R&D spending will fall into (d), attracting the 40 per cent tax offset.

### Endnotes

1. Jorgenson, D. W. (1963). Capital theory and investment behavior. The American Economic Review, 53(2), 247-259.

2. Hall, R. E., & Jorgenson, D. W. (1967). Tax policy and investment behavior. The American Economic Review, 57(3), 391-414.

3. Jorgenson, D., Hall, R. E. (1971). Application of the theory of optimum capital accumulation. In G. Fromm (Ed.), Tax incentives and capital spending (pp. 9-60). Washington: The Brookings Institution