Capital and labour income shares
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:
\(\large {Z_M} = \frac{{Intermediate\:inputs}}{{Total\:income}}\)