Evaluation of the Australian Wage Subsidy Special Youth ...

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method is also known as the single nearest neighbour method, and can additionally be
limited using the caliper or radius method. 76 The radius provides a bound on how far the
propensity of the nearest neighbour can be from the treated case. Selection of the
comparison can be performed with or without replacement. Allowing the pool of
comparison group members to be selected for a match to a treated unit more than once
has been shown to improve the performance of the match (Dehija and Wahba (1998)).
Also, not allowing replacement in nearest-neighbour-matching produces results which are
not invariant to the order in which the data were sorted for matching (Friedlander et al.
(1997): 1818). The choice of matching with or without replacement involves a tradeoff
between bias and variance. Matching with replacement tends to lowers bias, because on
average the matches are closer, but increases the variance, because fewer separate
observations are used to construct the counterfactual mean.
In this study, two types of PSM are implemented. Firstly nearest-neighbour, within
caliper with replacement PSM is applied, then as a sensitivity analysis of the choice of
PSM protocol, all-in-radius 77 PSM. While kernel PSM 78 is an alternative, this is not used
here as the choice of kernel and bandwidth is not straightforward, and little literature
exists on how best to critically implement these choices in the context of matching.
The match is based upon observable characteristics. This is the key identifying
assumption of matching known as the conditional independence assumption (CIA).
Under CIA, when controlling for observable differences in the characteristics of the
programme participants and non-participants, the outcome in the absence of treatment is
the same for each of these groups. More generally, the conditional independence
assumption assumes that the selection on unobservables does not affect outcomes.
76 Caliper matching usually means single nearest neighbour matching with a maximum limit placed on the
distance between the treated observation and the corresponding nearest neighbour from the comparison
group. Radius matching may also be used to indicate this, or using all the comparison group observations
within a given radius to construct the estimated counterfactual, which we term all-in-radius. The literature
is not clear in applying these terms.
77 Also termed all-in-caliper.
78 Frölich suggests in monte carlo analysis that a variant of kernel matching is preferred to nearest
neighbour, caliper and radius matching when using minimization of mean squared error as a criterion.