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# Links between industry level and the market sector productivity measures

Australian System of National Accounts: Concepts, Sources and Methods
Reference period
2020-21 financial year

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.