Evaluation of the Australian Wage Subsidy Special Youth ...

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If employability is assumed to be a latent variable y*, and the probability of being
selected onto the programme is d*, then the bivariate probit of the joint probabilities of
selection and employment then takes the form:
1) y i *=αd i + β′x i + ε i employment equation
where y i =1 for y i *>0
y i =0 otherwise
2) d i *=γz i + v i participation equation
where d i =1 for d i *>0
d i =0 otherwise
d i = dummy variable with value 1 for participation in wage subsidy, 0 otherwise
d i *=probability of being selected for participation in wage subsidy
x i =vector of exogenous individual characteristics
v i = error term, distributed as standard normal
ε i =error term, distributed as standard normal
y i =employment with value 1 for employed in a time period, 0 otherwise
y i *=employability
z i = vector of exogenous individual characteristics
Each subscript i indicating the individual.
Employment y is observed where y=1 if the periods is employed in some period, and y=0
otherwise. If y=1 when y*>0 and y=0 otherwise, then equation 1 can be estimated as a
probit if it is assumed that ε i is distributed as a standard normal. However, it may be there
is a selection problem as programme participants are not randomly selected from the
population. If the probability of being selected onto the programme d* is determined by
equation 2, and v i are distributed as a standard normal, and there are unobserved
characteristics that affect programme entry and subsequent employability, then ε i and v i
are correlated. The bivariate probit assumes that ε i and v i are correlated, and that they
follow a bivariate normal distribution.
E(ε i v i )=ρ
Prob (y i =1, d i =1) = Φ (αd i + β′x i , γz i , ρ)