# Capital and labour income shares

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

19.109    The capital and labour income shares, $$S_K$$ and $$S_L$$ are derived from the current price factor income accounts. For a given industry or aggregate, total income can be decomposed into:

• gross operating surplus (GOS) of corporations and general government;
• gross mixed income (GMI) of unincorporated firms;
• compensation of employees (COE); and
• taxes less subsidies on production and imports (IBT).

19.110    Note that total income includes the GOS of general government but not the GOS of dwellings owned by persons, as ownership of dwellings is excluded from the market sector.

19.111    Both GMI and IBT include capital and labour components. They can be further decomposed into income attributable to labour and capital, as described in the next two sections. Total income can be written as:

$$Total\:Income = GOS + GMI\left( K \right) + GMI\left( L \right) + COE + IBT\left( K \right) + IBT\left( L \right)$$

where K and L are income attributable to capital and labour, respectively.

19.112    The income share of capital is thus:

$$\large {S_K} = \frac{{GOS + GMI\left( K \right) + IBT\left( K \right)}}{{Total\:Income}}$$

and the income share of labour is:

$$\large {S_L} = \frac{{COE + GMI\left( L \right) + IBT\left( L \right)}}{{Total\:Income}}$$

## Capital and labour shares of gross mixed income

19.113    The labour and capital shares of income earned by unincorporated enterprises are subsumed into one national accounts aggregate: gross mixed income. The following procedure is used to impute labour and capital shares of this aggregate for each industry in the market sector.

19.114    An estimate of labour income is imputed by assuming that proprietors and unpaid helpers receive the same average compensation per hour as wage and salary earners. Similarly, an estimate of proprietors' capital income is derived by multiplying the unincorporated productive capital stock of each asset type by the corporate rental prices. These estimates are then scaled so they sum to the observed GMI. The capital and labour shares of GMI are the corresponding scaled estimates.

19.115    That is, the capital share of GMI is:

$$\large {s_i}\sum\limits_j {{r_{c,i,j}}{K_{u,i,j}}}$$

where $$s_i$$ is the scaling factor for industry $$i$$;

$$r_{c,i,j}$$ is the corporate rental price of asset $$j$$ in industry $$i$$; and

$$K_{u,i,j}$$ is the productive capital stock of asset $$j$$ in industry $$i$$ for unincorporated enterprises.

The labour share of GMI is:

$$\large {s_i}{w_i}{H_{u,i}}$$

where $$s_i$$ is (again) the scaling factor for industry $$i$$

$$w_i$$ is the average hourly income for wage and salary earners in industry $$i$$; and

$$H_{u,i}$$is the hours worked by proprietors and unpaid helpers in industry $$i$$.

19.116    The scaling factor $$s_i$$ for industry $$i$$ is given by:

$$\large {s_i} = \frac{{GMI}}{{{{\widehat {GMI}}_{u,i}}}}$$

and $${\widehat {GMI}_{u,i}}$$ for each industry is imputed, based on the labour and capital cost as:

$$\large {\widehat {GMI}_{u,i}} = {w_i}{H_{u,i}} + \sum\limits_j {{r_{c,i,j}}{K_{u,i,j}}}$$

19.117    Some taxes and subsidies on production and imports can be attributed solely to either capital or labour (for example, land tax and payroll tax). Such taxes and subsidies, however, make up only a small proportion of total net taxes. The capital and labour shares of net taxes are thus allocated proportionally, using the other income components attributable to labour and capital

## Gross output income shares

19.118    The gross output income shares are derived similarly except that intermediate inputs need to be included:

\begin{aligned} Total\:Income &= GOS + GMI\left( K \right) + GMI\left( L \right) + COE + IBT\left( K \right) + IBT\left( L \right)\\&\hspace{0.6cm}+ Intermediate\:inputs \end{aligned}

19.119    Thus, the income share of capital is:

$$\large {Z_K} = \frac{{GOS + GMI\left( K \right) + IBT\left( K \right)}}{{Total\:Income}}$$

and the income share of labour is:

$$\large {Z_L} = \frac{{COE + GMI\left( L \right) + IBT\left( L \right)}}{{Total\:Income}}$$

and the income share of intermediate inputs is:

$$\large {Z_M} = \frac{{Intermediate\:inputs}}{{Total\:income}}$$