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Productivity Statistics: 1978−2009
Embargoed until 10:45am  –  16 March 2010
Technical notes

What is productivity?

Productivity is a measure of how efficiently inputs are being used within the economy to produce outputs. Productivity is commonly defined as a ratio of a volume measure of output to a volume measure of input. Growth in productivity means that a nation can produce more output from the same amount of input. Productivity growth is an important contributing factor to a nation’s long-term material standard of living.

Productivity measures can be either single factor (ie relating a measure of output to a single measure of input), or multifactor (ie relating a measure of output to a bundle of inputs). Labour and capital productivity are single (or partial) factor productivity measures; they show productivity growth in terms of that particular input. Hence, productivity changes shown in these indexes may be due to a change in the mix of total inputs rather than a direct productivity increase from the relevant input. For example, if additional machinery (capital input) is used to assist in production, less labour input may be required to produce the same level of output. This will increase labour productivity, simply because the mix of the inputs has altered. On the other hand, multifactor productivity takes into account substitution between labour and capital inputs, and is therefore not directly affected by a change in the mix of total inputs.

The output measure chosen may be either gross output or value-added. The official productivity series all use constant price value-added as the output measure. Separate series are produced for labour productivity, capital productivity, and multifactor productivity (MFP).

Productivity measurement

The Statistics NZ method of estimating productivity statistics is based on OECD guidelines, as outlined in the OECD (2001) manual Measuring Productivity–OECD Manual Measurement of Aggregate and Industry-level Productivity Growth (available from OECD website, www.oecd.org). The approach adopted is referred to in the manual as “the index number approach in a production theoretic framework".

The calculation of productivity statistics begins by postulating a production function of the form:

V = A(t) x f(L,K)

where V = value-added in constant prices
L = real labour inputs
K = real capital inputs
f(L,K) = a production function of L and K that defines an expected level of output
A(t) = a parameter that captures disembodied technical shifts over time, ie outward shifts of the production function allowing output to increase with a given level of inputs (= MFP)

Given the existence of index values for labour volume and value-added, it is possible to calculate labour productivity for the measured sector as:

LP = V / L

Where LP = an index of labour productivity. This is an index of value-added in constant prices divided by an index of labour inputs.

Similarly, a capital productivity index KP is calculated as:

KP = V / K

Where KP = an index of capital productivity. This is an index of value-added in constant prices divided by an index of capital inputs.

Care is needed in interpreting the partial measures of productivity. For example, labour productivity only partially measures 'true' labour productivity, in the sense of capturing the personal capacities of workers or the intensity of their efforts. Labour productivity reflects the level of capital available per worker and how efficiently labour is combined with the other factors of production. Labour productivity may change due to a substitution of capital for labour (capital deepening) or due to a change in technology, with no change occurring in the labour input itself.

The final productivity index that can be calculated is for multifactor productivity (MFP). The technology parameter that represents disembodied technological change (or MFP) cannot be observed directly. By rearranging the production function equation, it can be shown that the technology parameter can be derived residually as the difference between the growth in an index of outputs and an index of inputs:

A(t) = V / f(L,K)

Certain assumptions must be met for MFP to be a measure of disembodied technology change. The key assumptions are that the production function must exhibit constant returns to scale and all inputs need to be included in scope of the production function.

In practice, these conditions will not be met and the resulting MFP residual needs to be interpreted with some caution. Given the importance of technological progress as an explanatory factor in economic growth, attention often focuses on the MFP measure as though it was a measure of technological change. However, this is not always the case. When interpreting MFP, the following should be noted:

  • Not all technological change translates into MFP growth. Embodied technological change, such as advances in the quality of capital or improved human capital, will be captured in the measured contributions of the inputs, provided they are measured correctly (ie the volume input series includes quality change).
  • MFP growth is not necessarily caused by technological change. Other non-technology factors will be picked up by the residual, including economies of scale, cyclical effects, inefficiencies, and measurement errors.

Calculating labour, capital, and multifactor productivity therefore relies on appropriate output indexes, and labour, capital, and total input indexes to be created. The steps taken to calculate those indexes are described below.

Output series methodology

This is defined as constant-price value added. The annual value added for the measured sector is derived following the same procedures as used to derive constant price GDP, that is, as a chained Laspeyres volume index of the constant-price value added of the industries that comprise the measured sector.

Labour series methodology

The labour volume series

The labour volume series is an estimate of paid hours for all employed persons engaged in the production of goods and services in the measured sector in New Zealand. The series is compiled using a number of data sources, from which the best characteristics of each are used for productivity measurement.

Throughout the series, there are three components that are summed to an industry level:

  • employees in industries covered by employment surveys
  • employees in industries out of scope of employment surveys
  • working proprietors.

For each of these components, the labour volume series is constructed by estimating:

  • job/worker counts
  • weekly paid hours per job/worker.

These are multiplied to give total weekly paid hours for the measured sector. An annual (March year) average of the weekly paid hours is calculated at the industry level. It is aggregated to the measured sector level, as published in tables 3, 1.3, and 2.3.

For the first of the three components, data from the Department of Labour (DoL) Employment Information Survey is used up to 1980, when it became the DoL Quarterly Employment Survey (QES). The DoL data is the sole source for employee counts and hours paid for this component until 1987, from which point annual business demography counts are rated forward by quarterly movements in employee counts from the QES. The resulting quarterly series of employee numbers is then multiplied by average weekly paid hours from the QES to achieve a quarterly series for paid hours. In 1989, Statistics NZ assumed responsibility for administering the QES. From 2000 onwards, monthly linked employer-employee data has replaced business demography as the sole data source for employee counts, and is combined with QES data on average weekly paid hours.

The second component includes employees in the following ANZSIC industries that are omitted from the coverage of the surveys above:

  • A01 – Agriculture
  • A02 – Services to agriculture
  • A04 – Commercial fishing
  • I6301 – International sea transport
  • L7711 – Residential property operators
  • M813 – Foreign government representation
  • Q97 – Private households employing staff.

Prior to 2000, Census of Population and Dwellings data provides benchmarks for employee counts and average weekly hours for this component. Prior to 1986, counts are interpolated using data from the Agriculture Census where appropriate. From 1986 to 2000, quarterly estimates of change from the Household Labour Force Survey (HLFS) are used to interpolate weekly hours between census benchmarks. From 2000 onwards, LEED provides monthly data on employee counts, while the average hours methodology remains unchanged.

For working proprietors, the third component, prior to 1986, census benchmarks are used to calculate both counts and average hours for almost all industries, supplemented by data from the DoL employment surveys and the Agriculture Census where appropriate. From 1986 to 2000, both hours and count data are benchmarked using totals from the census and interpolated using data from the HLFS, as in the previous component. From 2000 onwards, LEED provides annual benchmarks for working proprietor counts, supplemented by data from the HLFS and QES. Census data continues to provide average hours benchmarks during this period.

The different data sources are linked together to remove discontinuities in the time series. For example, two main points requiring linking are 1987/88 with the introduction of business demography data, and 2000, with the introduction of LEED. In 1987/88, employee count data are linked at the ANZSIC 3-digit level, with the business demography level being preferred to the pre-1987/88 level originating from the DoL QES. In 2000, data are linked at the ANZSIC 3-digit level, separately for both employees and working proprietors. The LEED level is preferred to the pre-2000 level, based on business demography data. This implies that any revisions in LEED in 2000 (the June 1999 quarter for employees, or the March 2000 year for working proprietors) will result in revisions right back to the start of the series.

Use of LEED

LEED is the main data source of counts of employees and working proprietors from 2000 onwards. The LEED dataset is created by linking a longitudinal dataset from the Statistics NZ Business Frame with longitudinal data from administrative taxation sources. Statistics NZ sees LEED as the best available data source for measuring labour counts for the reasons outlined below.

For measurement of employees, LEED data differs to the previous Business Demography Database (BDD) in the following ways:

  • LEED employee count data is monthly, whereas under the previous approach, quarterly data was used. Therefore LEED captures the seasonality of labour volume better.
  • Unlike the previous approach, LEED counts are not interpolated using survey information, reducing the effect of sample error on the series.
  • LEED data includes information about secondary jobs for industries outside of the scope of the Quarterly Employment Survey (QES). These jobs were previously excluded from the series.

For measurement of working proprietors, LEED data differs to the previous census/HLFS measurement in the following ways:

  • The majority of the working proprietor data is based on LEED annual benchmarks, based on a working proprietor's main income source over the year, that is, it is not a point-in-time estimate. It is modified to incorporate seasonality using the HLFS and QES, however the annual average counts remain the same.
  • LEED data includes information about people with secondary jobs (based on income) as a working proprietor. These jobs were previously excluded from the series.
  • Under the previous methodology, census benchmarks could be extrapolated forward for up to five years before being finalised. However, LEED provides annual benchmarks and at most, it is only the latest year which will be extrapolated forward.
  • Working proprietors who pay themselves a salary can now be identified more accurately using LEED.

New to this release, LEED is now being used in a different manner. The data is collected at the geographic unit (GEO) level, which represents a business location engaged in one, or predominantly one, kind of economic activity at a single physical site or base. However, to be consistent with the BDD and the QES, LEED has been aggregated to the kind-of-activity (KAU) level. A KAU is engaged in predominantly one activity for which a single set of accounting records is available. This improved and more consistent use of LEED has resulted in minor revisions to the labour volume series.

Quality assurance of the industry labour volume series

As a quality assurance measure for the upcoming release of industry level productivity measures, several coherency adjustments were made to the employee count and hours series that feed into the measured sector labour volume series (LVS). The main data sources used in the construction of the LVS are sourced independently of the estimates of compensation of employees (CoE) from the National Accounts. CoE estimates are primarily derived from the Annual Enterprise Survey, while LVS estimates are compiled using a number of different sources as discussed above. Current price CoE estimates were deflated using the QES average hourly earnings measure to provide an implicit LVS. This provided a benchmark for comparing against the LVS at an industry level. Adjustments were made to the industry data, based on alternative labour data sources in years where the LVS showed a significantly different movement to the deflated CoE series. The data published in this release is completely consistent with that to be published in the forthcoming industry level productivity release.

Rating forward the Labour Volume Series to calculate 2009 values

LEED employee count data is unavailable for the last quarter of the series and LEED working proprietor count data is unavailable for the last year of the series, apart from some working proprietors who are included in the employee data. Therefore, both are rated forward. Employee counts are rated forward using QES movements, and HLFS movements are used for industries outside the QES scope. Working proprietor counts are rated forward using HLFS movements. Adjustments are made to the HLFS data where necessary. Average hours worked per industry is calculated as in previous years, however the data is adjusted to account for the proportion of secondary jobs for employees in industries out of scope of the QES and working proprietors.

The labour input index

The industry volume series are aggregated to the measured sector level by means of a chained Törnqvist index. The quantity relatives in the index are two-period ratios of industry labour volumes. Industry two-period mean shares of measured sector nominal labour income form the exponential weights.

Composition-adjusted labour input

Composition-adjusted productivity measures account for the impact of changes in the skill-composition of workers. These are theoretically better measures of productivity as they allow output growth to also be explained by changes in labour composition, thereby reducing the contribution of the residual (ie MFP) to growth.

Composition-adjusted labour is calculated by adjusting the Labour Volume Series using movements in a labour composition index, which estimates changes in skill composition using proxies for skill, namely education attainment and work experience. The labour composition index is calculated using the HLFS to estimate the proportions of each skill category of worker, while the New Zealand Income Survey (NZIS), an annual supplement to the HLFS, is used to compile income shares for each of these groups.

Due to the availability of NZIS data, the composition-adjusted series runs from 1998. For further background on composition-adjustment, and details on the methodology, consult the Statistics NZ information paper Accounting for Changes in Labour Composition in the Measurement of Labour Productivity, available on www.stats.govt.nz.

Capital input series methodology

The capital services input index measures the flow of capital services generated by the use of the stock of capital assets for a given March year. No allowance is made for differences (across industry and time) in asset capacity utilisation rates.

As capital service flows cannot be directly measured, industry level flows are modelled, based on the productive capacity of industry capital stock. The industry level flows are aggregated to the measured sector level using industry shares of the measured sector current-price capital income as weights. More specifically, the following steps occur:

  • The starting point is the annual constant-price productive capital stock series. An asset's productive capital stock is its gross capital stock adjusted for the decline in its efficiency. Measured in constant prices, the productive stock represents standardised efficiency units and can be interpreted as a measure of the potential capital services that the asset can contribute to the production process. The productive capital stock series are built up using a perpetual inventory model (PIM) that generates productive capital stock estimates for 26 asset types by industry, of which only 24 are used in the capital services index. The model specifies for each asset type a mean expected useful life, a retirement function based on a distribution about this life and its pattern of (hyperbolic) efficiency decline. These parameters, and gross fixed capital formation in constant prices, are used to estimate an asset type's productive capital stock in constant prices.
  • In addition to the PIM-derived fixed asset stocks, the range of capital included in the productivity measures is supplemented by estimates for eight other assets, namely livestock, exotic timber grown for felling, inventories, and six different types of land: agricultural, forestry, commercial, industrial, mining, and other land.
  • Capital service flows are assumed to be proportional to these productive stock estimates, and are aggregated to the industry level using a Törnqvist index, with weights based on implicit rental prices (or user costs) which are a function of an exogenous rate of return, depreciation, net taxes on production, and asset price changes.

The measured sector capital services index is calculated, in turn, as a Törnqvist index of the industry indexes, with mean two-period industry shares of the measured sector current-price capital income providing the weights.

Enhancements to the capital input series methodology for this release

The methodology underlying the capital input series has been altered for this release. Two enhancements have been incorporated into the series, namely:

  1. Inclusion of inventories
    Inventories are now included within the scope of capital assets. They have been included from 1978 for the agriculture and forestry industries, and from 1987 onwards for the manufacturing; wholesale trade; retail trade; and accommodation, cafes, and restaurants industries, reflecting the availability of source data. The price and volume data for estimating the productive capital stock of inventories are sourced from Statistics NZ's national accounts.
  2. Treatment of livestock and timber assets
    With the inclusion of inventories in the capital asset scope, the treatment of livestock and timber assets has changed. Timber and livestock assets are now sourced from the National Accounts as a part of the inventories series from 1980 onwards. Prior to 1980, movements are calculated using the previous methodology, and are linked on to the National Accounts-sourced series at this point.

Capital and labour income shares

The measured sector capital and labour nominal income shares are calculated as the ratio of capital and labour income, respectively, to total income. Capital and labour nominal income totals are calculated at the industry level, and are derived from the income measure of GDP within the national accounts.

The income measure of GDP is calculated as compensation of employees plus gross operating surplus plus taxes on production and imports less subsidies (taxes less subsidies are known as net taxes). Included within gross operating surplus is the income of working proprietors, which is termed mixed income.

Mixed income is split into labour and capital components by calculating the labour income of working proprietors directly, and deriving the capital income of working proprietors residually.

Net taxes on production and imports are split into labour and capital components according to existing industry income shares.

Labour income is calculated as compensation of employees plus labour mixed income plus net taxes on production and imports attributable to labour. Capital income is calculated as gross operating surplus plus capital mixed income plus net taxes on production and imports attributable to capital.

Capital and labour income shares are used as weights within the productivity series. Mean two-period industry income shares are used to weight the capital and labour input indexes from the industry level to the measured sector level. Mean two-period measured sector income shares are then used to weight capital and labour when deriving the total inputs index, which is used in the calculation of MFP. Capital and labour income shares are also used to weight the contribution of capital input and labour input, respectively, within the growth accounting framework.

Graph, Measured Sector Labour and Capital Income Shares

The average capital and labour income shares remain relatively stable over the 1978–2009 period, with the capital share at approximately 40 percent of total income and the labour share at approximately 60 percent of total income. The increase in the capital income share in 1984 is due to the significant capital and infrastructural investment following the 'Think Big' projects. The small level shift in the series in 1996 is due to the introduction of business services, and personal and other community services into the measured sector.

Total input series methodology

A composite total input index is constructed by combining the labour and capital input indexes at the measured sector level. The total inputs index is a Törnqvist index, with the industry factor income shares providing the weights.

Calculating the productivity indexes

The construction of output, labour input, capital input, and composite total input indexes then allows for the calculation of the labour productivity, capital productivity and multifactor productivity measures, using the formulae in the 'Productivity measurement' section of these 'Technical notes'.

Growth accounting decomposition

Growth accounting is the decomposition of output growth into its contributing factors. For a given production function, changes in output are due to changes in the volumes of labour and capital, and/or changes in the multifactor productivity term. Under the composition-adjusted approach, changes in output can also come from a change in the skill composition of labour.

The growth accounting decomposition for output (ie value added, or real GDP) is presented as follows:

V = (L ^ W L) x (K ^ W K) x MFP

V = the change in value added (over one period)
L = the change in labour input (over one period)
K = the change in capital input (over one period)
MFP = the change in MFP (over one period)
W L = labour's share of total income
W K = capital's share of total income

As can be seen, the changes in labour input and capital input are exponentially weighted by their respective shares of total income. This gives the contribution of labour input and capital input, respectively, to output growth.

Under the composition-adjusted approach, output growth is decomposed into an additional variable, namely the skill composition of labour. This is presented in the equation below:

V = (L ^ W L) x (S ^ W L) x (K ^ W K) x MFP

S = the change in skill composition (over one period)

To obtain the contribution of skill composition towards output, it also needs to be exponentially weighted by labour's share of total income.

The growth accounting technique can also be used to decompose the changes to labour productivity. The change in labour productivity can be accounted for by the weighted amount of capital per worker and the change to MFP.

Estimating growth cycles

This release contains productivity data presented as annual averages within growth cycles. These estimates acknowledge the variations in asset capacity utilisation rates across cycles, that are not accounted for in the productivity model described above. A range of univariate filters were used to generate cycles within the series, and the Hodrick-Prescott filter was determined to be the most appropriate filter. The cycles are chosen as 'peak to peak' and their starting points are determined by a number of factors, such as where output growth and multifactor productivity growth are at their highest deviation from trend, and where capacity utilisation is at its highest point. The final growth cycles selected also take into account economic events throughout the time period. For further detail on the methodology and associated economic commentary used for determining the growth cycles, refer to the Statistics NZ information paper Extracting Growth Cycles from Productivity Indexes, on Productivity statistics – Information releases webpage, available on the Statistics NZ website www.stats.govt.nz.

Industry coverage – the measured sector

The productivity measures do not cover the entire economy. The industry coverage of the statistics is defined as the 'measured sector', consisting of industries for which estimates of inputs and outputs are independently derived in constant prices. Excluded are those industries for which real value-added in the national accounts is largely measured using input methods, such as number of employees. These are mainly government non-market industries that provide services, such as administration, health, and education, free or at nominal charges. The measured sector is defined in the following table.

Productivity Industry Coverage(1) 
 Measured sector industries  Omitted industries
 A Agriculture, forestry, and fishing  LA Property services
 B Mining  LB Ownership of owner occupied dwellings
 C Manufacturing  M Government administration and defence
 D Electricity, gas and water supply  N Education
 E Construction  O Health and community services
 F Wholesale trade  
 G Retail trade
 H Accommodation, cafes, and restaurants
 I Transport and storage
 J Communication services
 K Finance and insurance
 LC Business services (2)
 P Cultural and recreational services
 Q Personal and other community services (2)
(1) Based on the Australian and New Zealand Standard Industrial Classification 1996 (ANZSIC96).
(2) Included from March 1996 onwards in the measured sector

Since the Productivity Statistics: 1978–2007 release, the measured sector has been expanded to include business services, and personal and other community services from March 1996 onwards.

The former measured sector tables, now published as supplementary to this release, cover industries A to K and P. They maintain continuity with the previously released series. They are the best series for comparing with the official Australian productivity statistics, which are now based on ANZSIC 2006.

Published series

The productivity indexes now have an expression base year ended March 1978=1000, consistent with the first year of the series. The composition-adjusted productivity indexes have an expression base year ended March 1998=1000, consistent with the first year of the series. The measured sector GDP data used to calculate productivity indexes from 1978 to 1988 is currently provisional.

Copyright

Information obtained from Statistics NZ may be freely used, reproduced, or quoted unless otherwise specified. In all cases Statistics NZ must be acknowledged as the source.

Liability

While care has been used in processing, analysing and extracting information, Statistics NZ gives no warranty that the information supplied is free from error. Statistics NZ shall not be liable for any loss suffered through the use, directly or indirectly, of any information, product or service.

Further information

The information paper Productivity Statistics: 1988–2005 was released in March 2006 and provides additional material on the nature of the productivity measures, their construction, and comparisons with similar productivity statistics published by the Australian Bureau of Statistics and the OECD.

The information paper Accounting for changes in labour composition in the measurement of labour productivity was released in December 2008. It provides background to, and application of, adjusting for compositional change in the labour productivity series. The primary output of the paper is the experimental composition-adjusted productivity series, which have now been updated to include 2009, and incorporated into this release.

Two technical papers are also available on Productivity statistics – Information releases web page, on the Statistics NZ website (www.stats.govt.nz). Productivity Statistics: Sources and Methods details the sources and methods used to compile the series and Estimating Growth Cycles from Productivity Indexes details the methodology used to derive growth cycles for the published series from 1978–2007.

Timing

Timed statistical releases are delivered using postal and electronic services provided by third parties. Delivery of these releases may be delayed by circumstances outside the control of Statistics NZ. Statistics NZ accepts no responsibility for any such delays.

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