Evaluation of the Australian Wage Subsidy Special Youth ...

132
4.8 Results of Matching: one-to-one nearest-neighbour
Matching is now performed. On a case-by-case basis, amongst the remaining comparison
group members, members are identified that are similar to each individual of the
treatment group, i.e. their ‘match’. The basis for the match is the propensity score. The
matching should produce a counterfactual for those in the treatment group. In this case,
one-to-one nearest-neighbour within-caliper 86 matching with replacement is first
applied. 87 For a pre-specified distance, the caliper width δ, the treated unit is matched to
the comparison unit so that the nearest single neighbour criterion is satisfied within the
caliper,
1) δ > | p i - p j | = min k ∈ { D=0} { | p i – p k | }
Where
δ = caliper width
i = treated unit
j = comparison unit
p = propensity score p(x) = Probability { D=1 | X = x }
x = set of pre-treatment characteristics
D = indicator of treatment, 1= treatment, 0 = no treatment
4.8.1 Discussion of the results
The results of the matching are shown in Table 4.6. There is no general rule as to what
caliper width is suitable. However the theory underlying PSM indicates the caliper needs
to provide a comparison person with a propensity score very similar but preferably equal
to that of the treated persons. Thus a small caliper width is preferable, or so small the
propensity scores can be deemed roughly equal. Pagan and Ullah (1999) in discussing
bandwidth selection for kernel density, suggest inspecting the data in order to choose a
‘suitable’ width. It can observed from the summary of the propensity scores shown in
86 Gu and Rosenbaum (1993) introduced this pair matching technique.
87 The STATA ado file by Barbara Sianesi is used to implement this method (psmatch.ado).