The DoL Employment Estimates framework offers employment estimates for detailed 5 digit ANZSIC96 industries as well as 5 digit NZSCO occupations (click here for a link to more detail on how the estimates are derived). The latter is derived using occupational shares of industry employment and allows us also to estimate employment of a detailed occupation in a detailed industry. It is then possible to decompose the change of occupational employment in an industry into various effects that offer further insight into labour market dynamics at a detailed level.  In particular, we are interested to find out whether growth in employment of a selected occupation in a selected industry can be attributed to:

1. Fixed Industry Share Effect: to what degree change in employment of an occupation in an industry can be attributed to industry growth alone. Put differently, is the occupation benefiting from strong industry growth or not, i.e. is the selected occupation employed in the “right” industry.
2. Occupational Shift Effect: to what degree can change in employment of an occupation in an industry be attributed to the occupation becoming more important in the industry relative to other occupations employed in that industry. In other words, is employment in an occupation growing faster than total employment in an industry it is employed in.

In formal terms, the Fixed Industry Share Effect for an occupation can be written as:

`DeltaE`fixindshr`
`= sum_(i=1)^n E_i^(t=2) E_i^(t=1)/{: sum_(i=1)^n E_i^(t=1) :} - E_i^(t=1)`
`= (sum_(i=1)^n E_i^(t=2) - sum_(i=1)^n E_i^(t=1)) E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :}`

In which E is employment, t is time and i is the industry. Thus, the employment share of year 1 (`E_t^(t=1) // {: sum_(i=1)^n E_i^(t=1) :}`) is applied to (multiplied with) total employment in year 2, `sum_(i=1)^n E_i^(t=2)`, so as to arrive at a notional employment that would have been realised if the share of the occupation’s employment in industry i had remained the same as in year 1.

Since we are performing an additive decomposition, the Occupational Shift Effect is simply the difference between the full employment change of an occupation in an industry and the change due to the fixed industry share effect.

`DeltaE`occshft`= DeltaE`full` - DeltaE `fixindshr`
`= ( E_i^(t=2)- E_i^(t=1) ) - ( sum_(i=1)^n E_i^(t=2) - sum_(i=1)^n E_i^(t=1) ) E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :}`
`= ( E_i^(t=2) - E_i^(t=1) ) - ( sum_(i=1)^n E_i^(t=2) E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :} -E_i^(t=1) )`
`= E_i^(t=2) - sum_(i=1)^n E_i^(t=2) E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :}`
`= E_i^(t=2) {: sum_(i=1)^n E_i^(t=2) :} / {: sum_(i=1)^n E_i^(t=2) :} - sum_(i=1)^n E_i^(t=2) E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :}`
`= sum_(i=1)^n E_i^(t=2) ( E_i^(t=2) / {: sum_(i=1)^n E_i^(t=2) :} - E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :} )`

Thus the change in the occupational employment share in industry i, `( E_i^(t=2) / {: sum_(i=1)^n E_i^(t=2) :} - E_i^(t=1) / {: sum_(i=1)^n E_i^(t=1) :})` is applied to (multiplied) with total occupational employment of year 2, across all industries.