# Productivity Statistics: 1978−2006

## Technical notes

### What is productivity?

Productivity is a measure of how efficiently inputs are being used in the economy to produce outputs. Productivity is commonly defined as a ratio of a volume measure of output to a volume measure of input.

Productivity measures can be either single factor (that is, relating a measure of output to a single measure of input), or multifactor (that is, relating a measure of output to a bundle of 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 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 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.

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.

### Estimating growth cycles

This release contains productivity data presented as annual averages within growth cycles. A range of univariate filters used to generate cycles within the series were investigated, and ultimately the Hodrick-Prescott filter was determined to be the most appropriate filter. While the productivity model assumes no differences (across industry and time) in asset capacity utilisation rates, in reality capacity utilisation of capital will vary across a cycle. The starting points for the cycles are estimated as years where capacity utilisation is at its highest point, hence the cycles chosen are 'peak-to-peak'. 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, available at 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. This is 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 table below with reference to the Australian New Zealand Standard Industrial Classification 1996 (ANZSIC 96).

 Measured sector industries Omitted industries 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

### 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. The series is compiled using a number of data sources, from which the best characteristics of each are utilised 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 together 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 table 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 was the sole source for employee counts and hours paid for this component until 1989, 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 Dataset (LEED) 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, Population of Census 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 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.

#### Revisions to labour input index

The introduction of LEED as the main data source of counts of employees and working proprietors from 2000 has resulted in revisions to labour input from 2001 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, ie. 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 anunal 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.

#### 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 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 in the Productivity measurement section of these Technical notes.

### 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 by firstly allocating taxes directly to labour and capital where appropriate, then apportioning the remaining net taxes using 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.

The average capital and labour income shares remain relatively stable over the 1978–2006 period, with the capital share at approximately 40 percent of total income and the labour share at approximately 60 percent of total income.

### Published series

The productivity indexes have an expression base: year ended March 1996=1000, consistent with the published national accounts. The first year of the series is the March 1978 year. The measured sector GDP data used to calculate productivity indexes from 1978 to 1988 is currently provisional. Final GDP data will be available for incorporation into the output series, for the next productivity release in 2008.

### 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 1978–2006. Both publications are available from the Statistics New Zealand website (http://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: 1978–2007 is scheduled to be released in March 2008.