Evaluation of the Australian Wage Subsidy Special Youth ...

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6.2 Results of weighting the PSM
Weighting the Heckman bivariate probit is a relatively simple task of ensuring the
weights are used in estimating the model. In contrast, weighting the PSM requires a little
more attention. Frölich et al. (2001) is one of the few applications of PSM found where
weights have been applied to reflect the selective nature of the sample surveyed. As the
application of weights in PSM is not generally treated in the literature, details of the
approach are made clear. 146
6.2.1 Weighting protocol
In order to correctly adjust the PSM for the attrition, two steps need to be taken. The
weighting protocol steps are shown in Table 6.2. The probit model of SYETP used to
estimate the propensity scores, must be weighted with the attrition weight. The common
support for the weighted propensity needs to be checked. Once again, the minimum and
maximum of the weighted SYETP propensity scores are used to define the common
support. Once the matches have been found for these estimated propensity scores, then
the final match needs to be re-weighted. The balance of the treatment group in the
population is the only consideration. The weights that formerly applied to the comparison
cases are then discarded. Instead, the weight that applies to the SYETP case to which
they are matched is donated to the comparison case. In this way, the final match is
weighted using only the weights of the treated. This is done so that only the
characteristics of the treated have influence, as the parameter of interest is the impact of
treatment on the treated. One other important step also applies when weighting. In
assessing the standardized bias for the performance of the match, weighted mean and
variance statistics must be used to construct the standardized bias.
Table 6.2 Weighting protocol steps
• Weight the propensity probit
• Weight the final match, using only the weight of the treated; where comparison
case used with replacement, sum the applicable treated case weights.
146 I am grateful to Michael Lechner who in response to an email query made clear the steps in the protocol.