Evaluation of the Australian Wage Subsidy Special Youth ...

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(7) E(Y c | D=1) = E P(X) {E[Y c | P(X)=P(x)] , D=0| D=1}
Where the outer expectation is taken over the distribution of the propensity score in the
treated population (Hujer and Caliendo (2000)). Equation 7 can be used for estimation.
Thus, with an estimate of the propensity {P(X)} gained from data {P(x)}, then the
evaluation of the programme can take place by pairing participants with non-participants
that have the same propensity score. For participants and comparisons with the same
propensity score the distributions of the covariates are the same, and so they are balanced.
The assumption required to identify the effect satisfactorily is generally termed CIA now.
CIA is the term used in Lechner (2000). However the same assumption is also referred to
as selection on observables in Heckman and Robb (1985), and as ignorable treatment
assignment in Rosenbaum and Rubin (1983). Frölich (2001) p2 describes the validity of
CIA as the requirement that all variables that affect simultaneously the potential
employment outcome and the probability to be sampled from the comparison instead of
the target population are observed and included in X.
The estimate of the propensity is used to balance the distributions of the covariates across
the treated and comparison groups. The empirical power of propensity score matching in
reducing the problem of selection bias depends on the quality of the estimate of the
propensity score. Additional to these needs, there has to exist a comparison person with a
propensity score very similar, but preferably equal, to that of each treated person. Thus
although in theory PSM can be powerful in estimating the effect of treatment on the
treated, the practical implementation of PSM is subject to common parametric issues of
how effectively the empirical estimation corresponds to the assumptions of the method.
4.4 The propensity score matching protocol implemented
There are several means of applying propensity score matching (PSM). One to one
matching takes the outcome of the single most similar comparison unit, to provide a
match to each treated unit. The comparison individual whose propensity score is the
closest in value to the score for a treated unit is selected as the ‘nearest neighbour’. This