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Evaluation of the Australian Wage Subsidy Special Youth ...

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133<br />

Table 4.5, that <strong>the</strong> variance <strong>of</strong> <strong>the</strong> propensity score <strong>of</strong> <strong>the</strong> SYETP group is about 0.012<br />

while for <strong>the</strong> comparison it is 0.006.<br />

It could be inferred that <strong>the</strong> smaller caliper allows for <strong>the</strong> best match, with <strong>the</strong> minimum<br />

limit being <strong>the</strong> need to find at least one case to match within <strong>the</strong> caliper. As <strong>the</strong><br />

comparison group is so much larger is size than <strong>the</strong> treated, <strong>the</strong>re is <strong>the</strong> possibility <strong>of</strong><br />

several matches being available within each caliper. With single-nearest neighbour<br />

matching, increasing <strong>the</strong> width <strong>of</strong> caliper simply widens <strong>the</strong> pool <strong>of</strong> comparisons that are<br />

available. The quality <strong>of</strong> <strong>the</strong> match might decrease as <strong>the</strong> pool is increased to <strong>the</strong> extent<br />

that more SYETP cases are <strong>the</strong>n matched to dissimilar comparison cases. This would be<br />

<strong>the</strong> case if it were difficult to match because <strong>the</strong> support space was ‘sparse’, or had<br />

‘sparse’ regions. However, once a single match has been accomplished within <strong>the</strong> caliper,<br />

that nearest-neighbour match does not alter by widening <strong>the</strong> caliper. On <strong>the</strong> o<strong>the</strong>r hand,<br />

narrowing <strong>the</strong> caliper could improve <strong>the</strong> match when <strong>the</strong> support space has sparse regions<br />

by making <strong>the</strong> nearest-neighbours matched nearer to each o<strong>the</strong>r, because it forces <strong>the</strong><br />

difference in <strong>the</strong>ir propensity to be smaller. This means that <strong>the</strong> caliper width can affect<br />

match quality, however <strong>the</strong>re is a cost. The key trade<strong>of</strong>f in choosing a caliper width is<br />

between match quality and <strong>the</strong> number <strong>of</strong> treated observations dropped because <strong>the</strong>y do<br />

not have a match inside <strong>the</strong> caliper.<br />

In order to better answer <strong>the</strong> question <strong>of</strong> what caliper width is suitable to apply, a variety<br />

<strong>of</strong> caliper widths was applied. The first column shows <strong>the</strong> smallest caliper width applied<br />

to <strong>the</strong> difference in <strong>the</strong> propensity used to find <strong>the</strong> matched treated and comparison cases,<br />

<strong>the</strong> caliper width 0.001. Each column to <strong>the</strong> right <strong>of</strong> column 1 uses a wider caliper:<br />

Column 2 shows <strong>the</strong> caliper width 0.005, column 3 shows 0.01 caliper width, column 4<br />

shows 0.02 caliper width and finally column 5 shows 0.05 caliper width. To assess <strong>the</strong><br />

matching, for each set <strong>of</strong> matching results is shown <strong>the</strong> matched mean difference, and <strong>the</strong><br />

t statistic <strong>of</strong> <strong>the</strong> statistical significance <strong>of</strong> <strong>the</strong> difference, <strong>the</strong> number <strong>of</strong> treated and<br />

comparison cases matched, <strong>the</strong> number <strong>of</strong> times comparison cases were used because we<br />

used matching with replacement, <strong>the</strong> mean and standard deviation <strong>of</strong> <strong>the</strong> difference in <strong>the</strong><br />

propensity scores and mean total bias statistic.

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