Evaluation of the Australian Wage Subsidy Special Youth ...

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For CIA to be plausible, a ‘rich’ dataset is needed as it is assumed that all the variables
affecting participation and employment are observed. Under CIA, the distribution of the
counterfactual outcome for participants is the same as that of non-participants, and the
matching is then analogous to creating a fictional experiment where conditional upon the
observed characteristics, the selection process is random. If CIA is satisfied, then
selection bias ceases to be an issue. Violation of the conditional independence
assumption cannot usually be accurately tested in non-experimentally designed
observational data. Rosenbaum (1984) points out that theory about the causal mechanism
being investigated can be the chief source, and that theory together with random
assignment or experimental data can produce useful tests. Some tests are also outlined in
Heckman and Hotz (1989), but these are most commonly carried out with experimental
data.
The plausibility of matching depends then on a rich set of conditioning variables
(Heckman, Lalonde and Smith (1999): 1995). Specifically, the variables should allow
control for all characteristics that will affect both the participation and outcomes jointly.
In this case, the data used here provides what may be considered a suitable set of
explanatory variables which are defined prior to treatment, covering labour market
history, family background, education and skills, and attitudes amongst others. In order to
enhance the comparability with the former analyses, the same variables are initially used
to estimate the propensity score as were previously used in the SYETP participation
equation. 79 In the later chapter 7, sensitivity analysis of this probit for the propensity
score is performed, with some variables removed. This exploration is done in light of
Lechner (2000) and Lechner (2001). Once again, the probit model is used to fit the
probability of SYETP participation. Using the parametric model of the probability of
treatment moves the matching technique from non-parametric into a semi-parametric
approach.
79 Including the same variables in the propensity score as are included in the participation model from the
bivariate probit could be problematic, since the two models of probability of participation are designed with
different intentions. In the bivariate probit, there are exclusion restrictions to capture variation in the
probability of participation unrelated to outcomes, but a propensity score model does not usually include
instruments – only variables that influence both employment and participation. However, in the broad
context of this work, the exclusion restrictions, which appear to be weak, are of interest, and this issue is
treated further later.