Productivity Measures Statistics

Productivity is a measure of how efficiently inputs (capital and labour) are 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 for example can produce more output from the same amount of input, or the same level of output from fewer inputs. Productivity growth is an important contributing factor to a nation’s long-term material standard of living.

Productivity analysis aims to explain the drivers of output growth. Output growth can be attributed to either an increase in labour or capital input, more efficient utilisation of inputs, or a combination of both. 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 total inputs). Labour and capital productivity are single (or partial) factor productivity measures; they show productivity growth in terms of that particular input. Multifactor productivity (MFP) takes into account substitution between labour and capital inputs, and is therefore not directly affected by a change in the mix of inputs. Productivity measures cover a subset of the economy referred to as the ‘measured sector’. Further detail can be found in the section 'Industry coverage – the measured sector'. Series for output, labour inputs, and capital inputs are used for deriving partial productivity estimates. The two primary inputs (labour and capital) are combined to form a composite input index, which then allows for the residual calculation of MFP. A change in MFP reflects the change in output that cannot be accounted for by changes in the measures of labour and capital inputs.

Productivity measurement

Our method of estimating productivity statistics is based on OECD guidelines, as outlined in Measuring Productivity–OECD Manual Measurement of Aggregate and Industry-level Productivity Growth (OECD, 2001). The approach adopted is "the index number approach in a production theoretic framework".

See OECD for a PDF of the manual.

Calculating productivity

Calculating productivity statistics begins by assuming 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.

Caution needed with interpreting productivity measures

Care is needed in interpreting the partial measures of productivity. For example, labour productivity only partly measures 'true' labour productivity (ie 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 substituting capital for labour (capital deepening) or due to a change in MFP, with no change occurring in the labour input itself.

Capital productivity measures have similar constraints. We assume capital services in production analysis to be proportional to the capital stock. If the relationship does not change over time, the growth rate of capital services is identical to the rate of growth of the capital stock. This is clearly an unrealistic assumption, given the variations in the rates of capacity utilisation of capital stocks. Consequently, swings in the rates of capacity utilisation are picked up by the residual productivity measure, ie MFP.

MFP is the final productivity index we can calculate. The technology parameter that represents disembodied technological change (or MFP) cannot be observed directly. By rearranging the production function equation, we can show 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. We assume the production function exhibits constant returns to scale, and all inputs are assumed to be included in scope of the production function.

In practice, these conditions will not be met and our customers need to interpret the resulting MFP residual with 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, note the following. -Not all technological change translates into MFP growth. Embodied technological change, such as advances in the quality of capital or improved human capital, are 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-technological factors are picked up by the residual, including economies of scale, cyclical effects, inefficiencies, and measurement errors.

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

Output series methodology

Output is defined as constant-price value added. The annual value added for the measured sector is derived by following the same procedures used to derive constant-price GDP (as a chain-volume Laspeyres volume index of the constant-price value added of the industries making up the measured sector).

Labour series methodology

The labour volume series

The labour volume series (LVS) is an estimate of paid hours (ordinary time plus paid overtime) for all employed people engaged in producing goods and services in the measured sector in New Zealand. We compile the series using a number of data sources, from which the best characteristics of each are used for productivity measurement.

The primary data sources are the Quarterly Employment Survey (QES), Business Demography data, and Linked Employer-Employee Data (LEED, from 2000 onwards). The first two sources are establishment-based, and are supplemented with census and Household Labour Force Survey (HLFS) data for working proprietors and for industries excluded from the QES. LEED is an administrative data source that uses data from our Business Register and administrative taxation sources.

Throughout the LVS, three components 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 LVS 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. We calculate an annual (March year) average of the weekly paid hours at the industry level. It is aggregated to the measured-sector level, as published in tables 1.03, 2.03, and 3.03 of this release.

Quality assurance of the industry labour volume series

As quality assurance for the industry productivity measures, the employee job/worker counts and weekly paid hours series that feed into the measured sector LVS, are subject to several coherency adjustments.

The main data sources we use in constructing 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 we compile LVS estimates using a number of different sources. Current-price CoE estimates are deflated using the QES average hourly earnings measure to provide an implicit LVS. This provides a benchmark for comparing against the LVS at an industry level.

For years in which the LVS showed a significantly different movement to the deflated CoE series, we compared both movements to alternative labour volume data sources. Adjustments were then made to the industry LVS where we deemed it appropriate.

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 effect of changes in the skill composition of workers. These are theoretically better measures of productivity as they allow us to also explain output growth by changes in labour composition, thereby reducing the contribution of the residual (ie MFP) to growth.

Composition-adjusted labour is calculated by adjusting the LVS using movements in a labour composition index, which estimates changes in skill composition using proxies for skill (education attainment and work experience). We calculate this index by using the HLFS to estimate the proportions of each skill category of worker, while we use the New Zealand Income Survey (NZIS), an annual supplement to the HLFS, to compile income shares for each group. Due to the availability of NZIS data, the composition-adjusted series runs from 1998.

See Accounting for changes in labour composition in the measurement of labour productivity for further background on composition-adjustment, and details on the methodology.

Capital input series methodology

The capital services input index measures the flow of capital services generated by using the stock of capital assets for a given March year. The capital services measure starts with the chain-volume productive capital stock series from the national accounts, supplemented by estimates of eight other assets: inventories (which include estimates of livestock and timber before 1980), and seven different types of land (commercial, industrial, mining, agricultural, forestry, residential, and other).

We assume capital service flows to be proportional to the productive capital stock of each asset. These flows are aggregated to industry-level using a Törnqvist index, with weights based on asset-specific implicit rental prices (user costs). The industry-level flows are then aggregated to the measured-sector level using industry shares of the measured-sector current-price capital income as weights.

Productivity statistics do not account for changes in capacity utilisation of capital, as we assume capital assets to be used at a constant rate throughout the growth cycle and over their life. Growth in capital input may be understated when capacity utilisation is increasing and capital productivity may be overstated.

Furthermore, capacity utilisation adjustment has minimal impact on long-term growth, leading to marginally lower capital input growth and higher MFP growth at the measured sector level. In the short term, the effects of adjusting productivity statistics for variable capacity utilisation are more significant, leading to less volatile MFP estimates.

See Adjusting productivity statistics for variable capacity utilisation: Working harder or hardly working? for detailed explanation on this subject.

Capital and labour income shares

We calculate the measured-sector capital and labour nominal-income shares 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 CoE, 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. In calculating the labour income of working proprietors, we assume that the average hourly wage rate of a working proprietor in a given industry is equivalent to that of an employee.

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

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

Weights within productivity

Capital and labour income shares are used as weights within the productivity series. We use mean two-period industry income shares 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 calculating 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.

We also use the capital income share to weight the contribution of capital deepening within the growth accounting for labour productivity equation.

Total input series methodology

We construct a composite total input index 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 us to calculate the labour productivity, capital productivity, and MFP measures, using the formula under Productivity measurement.

Growth accounting decomposition

The growth accounting technique examines how much of an industry’s output growth can be explained by the growth rate in different inputs (labour and capital). We determine the additional output growth – known as MFP – residually. 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, we decompose output growth into an additional variable – 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 also examines how much of an industry’s labour productivity growth can be determined by growth in the amount of capital available per worker. Again, we determine the additional labour productivity growth residually – it is MFP.

Expression base

The productivity indexes for the measured sector now have an expression base of the year ended March 1996=1000, while the former measured sector used March 1978=1000, consistent with the first year of the series. The composition-adjusted productivity indexes have an expression base of the year ended March 1998=1000, also the first year of the series.