Evaluation of the Australian Wage Subsidy Special Youth ...

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Each individual has two potential outcomes, Y t treatment in the program and Y c no
treatment, i.e. they are in the comparison group. Actual participation can be denoted with
D, with values D=1 in treatment, or D=0 no treatment. The difference between potential
outcomes defines the treatment effect, ∆:
(14) ∆ = Y t - Y c
The observed outcome for each individual is:
(15) Y= DY t + (1-D) Y c
As noted, Y t and Y c can never be observed simultaneously. In equation (14), the
unobserved component is then termed the counterfactual outcome. In examining
individuals there is an underlying assumption of Stable Unit Treatment Value (SUTVA)
(Rubin (1986): 961). This infers that the treatment effect ∆ on each individual is
independent of the treatment of other individuals. SUTVA assumes that the outcome for
any exposure to the treatment is the same regardless of the mechanism of assignment to
the treatment. Rubin (1986) p961 notes that if there exist unrepresented versions of the
treatment, so that the outcome might depend on which version of treatment received, then
SUTVA is violated. The population has an average gain from treatment, usually termed
average treatment effect on the treated:
(16) E ( ∆ | D = 1 ) = E (Y t | D=1 ) - E (Y c | D=1 )
The second term in equation (16) is the unobservable component for the treated. To allow
the mean outcome of non-participants to proxy for the counterfactual of participants the
following assumption must be invoked:
(17) E (Y c | D=1 ) = E (Y c | D=0 )