Appendix 3 – Deriving age-specific employment rates for Alternative Specification 5
We set
(7) 
where 
is the actual labour force participation rate for Swedes in age-sex group 
in the year 2001, 
is the hypothetical rate for New Zealanders in age-sex group , and 
is an unknown constant. Let 
be the hypothetical rate for the whole New Zealand population aged 15 and over, which we set at 71.1%. Then
(8) 
where 
is the number of New Zealanders in age-sex group . Substituting Equation 7 into Equation 8 and rearranging yields an expression for ,
(9) 
which can be fed back into Equation 7 to give values for .
