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Productivity Statistics: 1988−2006 Revised 1 May 2007 – See attached Erratum
Embargoed until 10:45am  –  01 May 2007
Technical notes

What is productivity?

Productivity is a measure of how efficiently inputs (labour and capital, for example) are being used in the economy to produce outputs. It is commonly defined as a ratio of a volume measure of output to a volume measure of input use.

Productivity measures may be either single factor (relating a measure of output to a single measure of input) or multifactor (relating a measure of output to a bundle of inputs), and 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 New Zealand method of estimating productivity statistics is based on OECD guidelines, as outlined in the OECD Manual Measuring Productivity (OECD, 2001). The approach adopted is referred to in the manual as “the index number approach in a production theoretic framework. The growth accounting technique examines how much of an observed rate of change of an industry’s [or economy’s] output can be explained by the rate of change of combined inputs. Thus the growth accounting approach evaluates the MFP growth residually.”

In its simplest form, a production function is postulated as follows:

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)

or, rearranging the equation, we have:

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

As the technology parameter cannot be observed directly, MFP growth is derived residually as the difference between the growth in an index of outputs and an index of inputs. For MFP to be a measure of disembodied technology change, certain assumptions must be met, the key ones being that the production function must exhibit constant returns to scale and the coverage of the inputs needs to be complete.

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 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 include 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.

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 also 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.

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 – mainly government non-market industries whose services, such as administration, health and education, are provided free or at nominal charges – whose real value-added in the national accounts is largely measured using input methods, such as number of employees. The measured sector is defined in the table below with reference to the Australia New Zealand Standard Industrial Classification (ANZSIC) (1996):

 Measured sector industries  Omitted industries
 A Agriculture, forestry and fishing  L Property and business services
 B Mining  M Government administration and defence
 C Manufacturing  N Education
 D Electricity, gas and water supply  O Health and community services
 E Construction  Q Personal and other services
 F Wholesale trade  
 G Retail trade
 H Accommodation, cafes and restaurants
 I Transport and storage
 J Communication services
 K Finance and insurance
 P Cultural and recreational services

Revisions

This release contains regular revisions arising from new and more up-to-date information. These result from:

  • revisions to quarterly constant price gross domestic product
  • incorporation of the 2002 revised and 2003 balanced annual national accounts
  • revision of the Linked Employer-Employee Data (LEED) based benchmarks in the labour input series for 2004 and 2005
  • incorporation of revised land, livestock, standing stock of timber and gross fixed capital formation data from 2002 to 2005.

This release also contains revisions resulting from improved methodology. These are:

  • A more appropriate data source used to calculate gross mixed income
  • An improvement to the allocation of net taxes on production. Specific taxes and subsidies directly attributable to labour and capital are now apportioned to these factors where appropriate.

While there have been minor revisions to some annual movements, the underlying trend of the productivity series has remained unchanged.

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, namely, 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. There are three components which are summed to an industry level:

  • Employees in industries covered by Statistics NZ's Quarterly Employment Survey (QES): For this component, annual Business Demography counts of employees are rated forward by quarterly movements in employee count 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.
  • Employees out of scope of the QES: The following ANZSIC industries are omitted from the QES coverage:
     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.
                      
  • Paid hours for these employees are estimated using the same procedures adopted for working proprietors below.
  • Working proprietors: Both hours and employment data are benchmarked using totals from the population census. The series is interpolated between benchmarks using quarterly estimates of change from the Household Labour Force Survey.

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.

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 stocks 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 stock series are built up using a perpetual inventory model (PIM) that generates productive 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 three other assets, namely livestock, exotic timber grown for felling, and land in use in agriculture and forestry.
  • 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 endogenous 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.

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 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 given above.

Published series

The productivity indexes have an expression base: year ended March 1996=1000, consistent with the published national accounts. At present, the first year of the series is the March 1988 year.

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. Two technical papers are also available. 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. Both publications are available from the Statistics New Zealand website (www.stats.govt.nz/).

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.

Next release...

 Productivity Statistics: 1978–2006 is planned to be released later in 2007.

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